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					                                          Routes to a better life              Volume 2

                                          Education • Life skills • Careers    Edition 3
                              Your cut-out-and-                                                                                                       Win a Kinetic
                              keep matric                                                                                                              scooter PaGE 6
                              curriculum pull-out

                                        Cash in on

                                 What is this wild ‘n                R
                                                                         omeo and Juliet died for it;   emotions are caused by             the sex hormones testosterone
                                                                         the Black Eyed Peas don’t      chemical reactions in the          and oestrogen urge us to find
                                                                         know where it is; and for      body. They identify three          a lover. While it can lead to
                                 crazy thing we call                 thousands of years poets have
                                                                     said it’s the thing that keeps
                                                                                                        phases all people in love go
                                                                                                        through, and the different
                                                                                                                                           passion, pleasure and true
                                                                                                                                           love, it can also blind you into

                                 romantic love?                      the Earth spinning. “It” is the
                                                                     emotion called love and few
                                                                     people will deny it’s very
                                                                                                        hormones involved in each
                                                                                                         Scientists say that, no matter
                                                                                                                                           choosing lovers from hell.
                                                                                                                                             Following lust without
                                                                                                                                           stopping to think can have
                                 UfRiEda Ho tries to                 powerful. It can turn the
                                                                     smartest of us into fools, and
                                                                                                        the religion, culture or gender,
                                                                                                        humans everywhere
                                                                                                                                           life-changing consequences:
                                                                                                                                           you can pick up sexually

                                 find some answers                   the foolish into noble heroes.     experience the same biological     transmitted diseases like HIV/
Cover design: Keith Tamkei

                                                                                                        reactions to falling in love.      Aids; fall pregnant long before
                                                                     Love chemistry                                                        you’d planned to be a parent;
                                                                     Scientists who’ve researched       Lively lusty love                  or give your heart to someone
                                                                     love say it’s no mystery – its     The first stage is lust, when      who will only break it.
                                                                                                                                                       (Continued on page 2)
      Volume 2 Edition 3                                                              RoMaNCE

    (Continued from page 1)                       from your clan is forbidden. But in          dating” are popular ways to meet            are what really count, so it saves
                                                  Basotho cultural traditions, it is           potential partners. The first speed         valuable time.
    Then you just go crazy                        encouraged.                                  dating event was in the late 1990s and is     Then there’s always online – or
    Scientists call the second phase                Here’s another: in many ancient            credited to American Jews. Jews are         virtual – dating. Helping those who are
    “attraction”. The symptoms of a person        societies, from Rome to Japan,               encouraged to marry                         looking for love through the internet is
    in this phase of love are the same as         homosexuality – especially between a         Jews, so those from                                    increasingly good business.
    someone who is insane. You can’t eat,         boy and a man – was socially accepted.       both sexes gathered at                                       Lonely hearts across
    can’t sleep and can concentrate on            In today’s world, you could face death       a venue and were                                              the planet pay to
    nothing but the object of love when           in some countries for this.                  given about 5 minutes                                           access a dating site;
    awake.                                          Many local marriages these days also       to talk to each                                                  and many virtual
     Scientists say these feelings are            mix together old African traditions –        candidate. Speed                                                  daters have fallen
    caused by neurotransmitters in the            like lobola and ancestral ceremonies –       dating supporters                                                for someone they’ve
    brain called dopamine, norepinephrine         with traditions that began in ancient        argue that first                                                yet to meet.
    and serotonin.                                Rome (like the white dress and placing       impressions
                                                  a ring on the third finger of the left
    Long lasting love                             hand).
    The third stage is known as
    “attachment”, and lasts the longest of        Love’s got nothing to do with it
    the three love phases. Here, two              In Indian and many other
    hormones play a role – oxytocin and           countries, youngsters don’t
    vasopressin. These encourage couples          choose who they marry.
    to stay together and take the next step       Marriages are arranged,
    of making a home together and/or              usually by the parents, who
    having children.                              will consider factors like the
                                                  person’s class, his or her
    Ever-changing rules of love                   astrological chart and
    Humans may have the same chemical             religion, and benefits to the family
    responses, but that’s about where a           from such a union.
    shared experience of love ends.                 Love isn’t seen as important at this
     Cultural views of “right” and “wrong”        stage; it’s expected to grow through
    in matters of love and marriage are so        years of marriage.
    different that sometimes one culture’s
    “never” is another culture’s “must”.          New ways of dating
     Here’s a local example. In Nguni             In countries with a “Westernized”
    marriage traditions, marrying a person        culture, “speed dating” and “virtual

                               Good lovin’ starts
                               with yourself
                                                  best person you can be.
    february is the “month of                      Learning to love yourself is a lifelong
    romance”, and shops are aglow                 process and not everyone gets it right.
                                                   But if you haven’t quite reached this
    with pink, flowers and diamonds.              state of self-love, how do you know you
                                                  are ready for a relationship? Can you be

       f you’re in a good love relationship,      sure you’ll choose someone who’ll be
       you’re expected to treat that special      good for you?                                        To love oneself is the                  Try this for yourself
       someone. If you’re not, the question                                                           beginning of a lifelong                  Think about these questions
                                                                                                                                               carefully, and then write down your
    is: who will be your Valentine?               Think about it                                            romance.                           responses. Be very honest with
                                                  • Relationships take a lot of time and a
                                                                                                             Oscar Wilde                       yourself!
    You’re not a kid anymore                        lot of energy. Am I still going to have
                                                                                                                                               • What kind of person are you?
    Teen years are the time of life we              enough time and energy for my other
    become sexually aware of ourselves and                                                                                                     • During your life, what have you
                                                    dreams and commitments? If not, is it        reasons for relationships being seen
    others. Most people find it very                                                                                                             learned about relationships?
                                                    worth dropping them for this person?         as “wrong” are that the person is from
    challenging to make this adjustment.                                                                                                       • What kind of relationship are you
                                                  • Am I ready for a physical                    a different culture, class, race or
    But it’s one of the biggest steps towards                                                                                                    seeking? List the 5 “must haves”
                                                    relationship? How intimate am I ready        religion; or that it’s is a same-sex
    adulthood and the possibility of                                                                                                             you are looking for in a person.
                                                    to be? Do I draw the line at kissing and     relationship.
    romantic relationships.                                                                                                                    • What do you think you have to
                                                    hugging, or am I comfortable to go           The issue here is not who’s right or
                                                                                                                                                 offer to another person in a
                                                    further?                                   wrong, but whether you’re ready to
    Loving should start with yourself             • Do I know how to use a condom if I         take the consequences of pursuing a
                                                                                                                                               • What kinds of things will you
    Like charity, learning to love should           decide to have sex?                        “wrong” relationship. Ask yourself:
                                                                                                                                                 tolerate in a relationship?
    start with yourself. It’s about               • Almost all cultures and all families       • Will I have my family and friends
                                                                                                                                               • What kinds of things will you not
    understanding who you are, caring for           have fixed ideas about a “right” and a       support for this relationship?
    yourself and believing that you are the         “wrong” kind of relationship. Common       • If not, how will it impact on my life?

                                                                                           Congratulations to the 10 winners of PYf’s Smacked giveaway:
                                                                                           • Phyllis Matsemela, Halfway House         • Godfrey Machete
                                                                                           • Nicolene Campher, Lyttelton              • Allan Madilonga, Chiawelo
                                                                                           • Moabi Mmula, Greenside                   • Maredi Maile, Chuenespoort
                                                                                           • Julian Matthews, Eden Park               • Estelle Myburgh
                                                                                           • G P Kubeka, Katlehong                    • Ervin Alberts, Boksburg
                   Sci Bono Career Centre
            preparing learners for the world of work
        Career website (         Discovery starts here…
                                                                                            in next week’s edition of PYf: Skills you can’t do without
        Career workshops and psychometric         Sci-Bono Discovery Centre
        Career guidance on Saturdays
                                                  Corner Miriam Makeba &
                                                  President Streets                                 SPEaK To US!                                     Write to: PYf, Po Box 1654,
                                                                                                                                                               Saxonwold, 2132
        Study skills workshops: call us to book   Newtown                                     Have questions, problems, or need advice?              fax:      (011) 214-7110
        your place (R5 per learner)               Tel: (011) 639-8400                       Contact PYf and we will do our best to help you.         Email:
    Tune in to LC4U, Learning Channel’s new youth life skills programme, on
    SABC1 at 10.35am on Wednesday, February 14th for more career advice                         To advertise in PYF, please contact Granvil Alexander on
                   from Sci-Bono! Today’s topic: Astronomy.                                         (011) 214 7110 or at
                                                                               RoMaNCE                                                                POWER YOUR FUTURE
                                                                                                                                                        Volume 2 Edition 3       3
Show me the money: jobs in romance
In our money-mad world, people’s never
ending desire for romance is seen as an
opportunity to make a buck. Sometimes
                                           The laws                                    bring to the union, and can secure his
                                                                                       or her legal rights over these things.
                                                                                         There are two kinds of antenuptial
                                                                                                                                      be registered with the Department of
                                                                                                                                      Home Affairs within three months to
                                                                                                                                      be legally recognised.

                                           of getting
it can be a bit ugly and seem like an                                                  contracts to choose                                                • Religious
insult to “love”, like when those pushy                                                between. In the                                                    marriage – are
salespeople try to sell you a very                                                     “accrual system”, any                                              marriages governed

expensive Valentine’s rose.                                                            assets or liabilities                                              by religious laws
  But there’s a huge range of jobs out                                                 gained during the                                                  and customs. A
there that are all linked one way or                                                   course of the                                                      religious marriage
another to human’s pursuit of love and                                                 marriage are shared                                                must also be
romance. Below are some ideas – but if                                                 between the partners.                                              registered with the
you’re a creative thinker, you could       SUzaN CHaLa                                 The other option is to                                             Department of
come up with a new idea to get into the                                                keep all assets and                                                Home Affairs

romance business.
                                               ll countries have “matrimonial”         liabilities entirely                                               within three
• Writing romance: there are many                                                                                LEGALLY BOUND: know the laws on marriage
                                               laws, or laws that govern               separate.                                                          months to be legally
opportunities for gifted writers of
romance. For example, you could write          marriages. These laws define              In the event of                                                  recognised.
romance novels; scripts on romance for     things like who can marry; how they         divorce, having an antenuptial               • Civil union – is the law recently
film or TV; articles on love and           can marry; the responsibilities and         contract usually makes the legal               enacted that recognises same-sex
weddings for magazines; or even the        duties of a married person; as well as      process smoother.                              unions. The union is automically
words of love printed on greeting cards.   the property rights of each person in                                                      registered with the Department of
• Weddings are big business: people        the union.                                  option two: community of property              Home Affairs.
go to incredible lengths (and often into                                               Unless an antenuptial contract is            • Civil marriage – this automatically
incredible debt) to make their Big Day     Make sure you protect yourself              entered into, all marriages are                registers the marriage with the
perfect. They usually need the services    Many newly weds make the mistake of         automatically understood to be in              Department of Home Affairs.
of a florist (to provide the flowers);     ignoring their legal options, often         community of property. This means
caterer (who provide the food, drinks      because they beleive their marriage         that all assets – and liabilities – are      Breaking up is never easy
and wedding cakes); marquee or tent        will last for life.                         legally regarded as belonging to both        A divorce is when a couple dissolve
hire; wedding car hire (usually very         But nothing in life is guaranteed, so     partners.                                    their legal bond. A court grants a
fancy cars to transport the wedding        it’s worthwhile for both to think             Keep in mind that this marriage            divorce and decides what each partner
party); a photographer/video producer;     carefully about the assets and              contract will make you legally liable        gets out of the marriage. The court
a bridal dress designer; a suite hire      liabilities that each bring to the union,   for any debts your partner might run         takes into account any legal contracts,
service; a minister or officiate (to       and whether they want to combine            up during your marriage.                     as well as whether the marriage took
marry the couple); and even a              what they have or not.                                                                   place according to religious,
honeymoon planner (see page 4 for
more on being a wedding planner).
                                                                                       Recognised types of marriages                customary or civil laws.
• For relationships in trouble: couples    option one: antenuptial contracts           South African law recognises four
often need the help of counselors or       This is a contract a couple draws up        kinds of marriages:                          You can also ‘vat en sit’
therapists to work through their           before the wedding.                         • Customary marriage – takes place           Living together without marrying is an
problems (turn the page for more about       This type of marriage contract allows       according to traditional laws. An          increasingly popular option. Legally,
work as a clinical sexologist).            couples to keep their assets (and             example would be the African custom each partner keeps full control over his
  Then, of course, if the marriage goes    liabilities) separate or to combine           of men marrying more than one              or her own assets and is solely
sour, couples wil need a divorce lawyer.   them. Each partner specifies what they        woman. A customary marriage must           responsible for their own liabilities.
       Volume 2 Edition 3                                                                   RoMaNCE

    Queen of                                                                                                                                            It’s not ‘dirty’ to
                                                                                                                                                        it may be taboo for many of us, but sex t

    the perfect                                                                                                                                         is all about. UfRiEda Ho spoke to her ab
                                                                                                                                                        What sort of reaction do you get when
                                                                                                                                                        you tell people that you’re a

                                                                                                                                                        I get everything from those who hang on
                                                                                                                                                        to every word I say, to those – men
                                                                                                                                                        especially – who think they know better
                                                                                                                                                        and can tell me a thing or two about sex.

    Sophie Ndaba is as organised and                                                                                                                    So what do you do?
                                                                                                                                                        Well, in the first place, I don’t go into
                                                                                                                                                        people’s bedrooms and watch them or
    ambitious as the character she plays                                                                                                                tape them as they’re having sex or
                                                                                                                                                        anything like that. As a clinician, I look at
    on TV. She tells SUzaN CHaLa about                                                                                                                  the physiological [physical] and
                                                                                                                                                        psychological [emotional and mental]
    her life off-screen                                                                                                                                 aspects of helping people to have better
                                                                                                                                                        sex lives. I work at a women’s health
                                                                                                                                                        clinic, so many of the issues I deal with
    What kind of teenager were you?                    What does it involve?                                                                            are specific to women’s sexual health
    I was shy - very shy. I knew what I                You basically ensure                                                                             issues.
    wanted but I would not go after it. I              that everything is
    always thought twice. I was afraid of              perfectly planned from                                                                           How did you become a clinical
    failure and disappointment.                        start to finish for the                                                                          sexologist?
      Even when I started acting in                    wedding day. You                                                                                 I was involved with working with HIV/Aids
    Generations, the producer had to keep              identify suppliers – for                                                                         for years and I realised that I was talking
    reminding me of the confident kind of              everything from                                                                                  about sex all the time. So, at the age of
    character I was supposed to be playing.            caterers and plates to        WEDDING WIZARD: Sopie Ndaba makes dreams come true                 38, I decided to study in that direction.
                                                       the bride’s dress and         Pic: Raymond Mokoena                                               Because you can’t study sexology in this
    How similar are you to the character               photographs – that                                                                               country, I went to the United States and
    of Queen Moroka?                                   complement the overall design and              running late and the food wasn’t ready on         did my PhD in human sexuality.
    Like Queen, I’m a go-getter. Queen                 theme of that particular wedding. All of       time. And then, nobody knew where the
    takes everything she does seriously,               this must be done within a set budget.         plates had gone. We eventually had to             What opportunities opened up to you
    whether it’s helping someone or planning                                                          buy paper plates – but then there was no          with this qualification?
    a party, and I guess you could say we              How long does it take to plan a                ice for the drinks! You see, it’s all these       If you prove yourself to be credible and
    are similar in that way.                           wedding?                                       small details that can turn a beautiful           passionate about what you do, then you
      But I think everything about Queen is            A minimum of six months. It’s always           wedding into a nightmare.                         can become involved with a range of
    more exaggerated. I admire Queen,                  better to plan in advance. You have the          So there needs to be someone who’ll             public awareness programmes. I do work
    though – she oozes confidence. I think             advantage of comparing available               make sure all these technicalities are            on radio, TV and I have columns in
    most women can relate to her character;            venues and other suppliers, whereas if         taken care of. The bride shouldn’t have           various magazines and newspapers. I
    she just wants what most women want.               you’re in a rush, you have to settle for       to worry about anything except being              love the educational aspect of my job.
                                                       what is available.                             there for her big day.
    Has your TV career helped your                                                                      I’ve been doing it now for eight years now.     What makes your job particularly
    wedding-planning business?                         Why did you become a wedding                                                                     rewarding?
    Generations has made me a                          planner?                                       How much money can one earn from                  When I’ve helped a couple who have
    household name. People love me                     The idea came to me after struggling to        such an event?                                    been unable to consummate a marriage
    because of Generations – in fact,                  organise Themba Ndaba’s and my                 The standard practice is to charge a              for years and years and they can finally
    sometimes I’m overwhelmed by the                   wedding in 1996. I just wanted a typical       certain percentage of the total cost of the       have a child, for example – that is
    love I get from strangers. And yes, that           township celebration - that’s all!             wedding.                                          something really special.
    has helped advance my wedding-                     Obviously with my Generations’ work as
    planning business.                                 well, there wasn’t enough time to plan         What do you need to be a successful               Why do people find it so difficult to
                                                       everything. I thought it would be easy,        wedding planner?                                  speak openly about sex?
    What is the difference between a                   but I didn’t even know where to go for the First and foremost, you have to be a                  There is so much guilt, shame, fear and
    wedding planner and an events co-                  dress or even plates.                          people’s person. Sometimes as a wedding           negativity associated with sex. We grow
    ordinator?                                           I did my best, of course. I hired a hall     planner you have to be a counsellor too.          up surrounded by sexual images in the
    A wedding is a very personal event,                and found someone to do the                      Then you need to learn business skills.         media, mixed with constant warnings that
    about two people and their nearest and             decorations, which were fabulous. I            Like in any other business, you have to           sex is inappropriate, immoral and quite
    dearest. As a wedding planner, you are             arranged caterers, hired plates, bought        know how to run and grow your business.           possibly deadly. We are lectured by the
    there to make their day as special as              meat, vegetables, lots of drinks, you          Besides this, it’s most important to know         church, schools, and so on, about the
    possible. Your job is to make their                name it!                                       – and love – everything about what                evils of sex from a very young age.
    dreams come true.                                  On the day, first the caterers were            you’re doing.                                      Most parents only give a basic biology

                                                                                               Calling all Grade 10, 11 and 12
        “My Best Lesson”                                                                     Maths, Science and English teachers

                                                                                            Share the secrets of your teaching success and WIN!

                                                                                                                      R90 000
                                                                                                                            worth of prizes
       HOW TO ENTER                             CLOSING DATE
                                                                                                       In 2006 Jenny Young presented a winning Grade
       Post the written description to:         Thursday 10th May
                                                                                                       11 Science lesson that demonstrated how AIDS
       Engen’s “My Best Lesson” Awards,
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                                                                                           RoMaNCE                                                                 POWER YOUR FUTURE
                                                                                                                                                                    Volume 2 Edition 3      5

o talk about sex                                     to their bodies as adolescents. It helps
                                                     them understand these changes better
                                                     and they can also identify what’s normal
                                                                                                   and risks they need to be aware of before
                                                                                                   engaging in a sexual relationship too.
                                                                                                     Two books I can recommend are, for
                                                                                                                                                 For more information, contact:
                                                                                                                                                 The South African Association of
                                                                                                                                                 Sex Researchers, Educators,
                                                     and what’s abnormal.                          boys, What is Happening Down there?           Counsellors and Therapists
talk is what Elna Mcintosh’s work                      They need to concentrate more on their      Answers to Questions Boys Find Hard to        (011) 787-1222 or
bout life as a clinical sexologist                   self-esteem and on feeling good about         Ask, and for girls, The Period Book:          e-mail
                                                     themselves so that they can be                Everything You Don’t Want to Ask but
                                                     comfortable with their bodies.                Need to Know. Both books are by Karen         Visit, for more on
                         and reproduction
                                                       They also need to know that sex is good     Gravelle et al and can be found on            South Africa’s only SAQA-registered
                         sex talk.
                                                     and natural, but there are responsibilities                                sexology course.
                           We send lots of
                         scary and
                         messages to
                         youngsters about
                         sex – like it’s dirty
                         to touch yourself;
                         you’ll go blind from
                         too much
                         masturbation; or
 HOT TOPIC: Sexpert      that masturbation
 Elna McIntosh           causes hair to
                         grow on your
   Well honestly! How many people have
 you seen with hair on their palms?

 What’s the best way to get into this
 Most people enter the field of sexology as
 medical doctors, social workers,
 psychologists or registered psychiatric
 nurses. I think it’s important to have one
 of these qualifications behind you before
 you even think of studying in the direction
 of sexology.
   I also believe that you should be older
 and more mature before you become a
 sexologist. Frankly, if a long-time
 married couple walks into your rooms
 and you’re only 25 years old, no number
 of degrees or qualifications is going to
 make you seem credible.

 What is your message to young people
 around issues of their sexuality?
 Young people should arm themselves with
 education, so they know what’s happening

   Photographer Zanele Muholi uses images such
   as this one (right) to challenge how people see
   blackness, female forms, skins, bodies and

  African, and happy to be gay
                                                                                                                                                step in society’s acceptance that same-
                                                                                                                                                sex unions are here to stay. There are
                                                                                                                                                also numerous NGOs and gay-friendly
                                                                                                                                                churches that support homosexuals.
                                                                                                                                                  But homophobia is still very much
                                                                                                                                                alive, and many suffer because of it.
                                     Stop pretending homosexuals are                                                                            The experience of a guy I know,
                                                                                                                                                Sibusiso Mathebula, is shared by others
                                     ‘unafrican’ and accept the truth, writes                                                                   who fear the rejection of family and
                                                                                                                                                friends that can result from coming out.
                                     STaNLEY MoNGEzi MaBENa                                                                                     Sibusiso, who is now almost 40,
                                                                                                                                                remembers: “I had to force myself to

          offie, isitabane, ugnqingili …              preferences may be.                          Lindiwe Ndlovu from Soweto, will tell        have a girlfriend so no-one would notice
          These are just some of the                   One myth that needs to be challenged        you of ancestors who communicate             that I’m gay. But things did not go right
          insulting words used to label              is that homosexuality is “unAfrican”,         through her who were also homosexual         because there’s no way you can lie to
  homosexuals in South Africa. They are              imported from Western culture. This is        when they were alive.                        yourself and be something that you are
  ugly words that some ignorant “straight”           just not true: historians and other             But during some of our ancestors’          not.”
  people use to keep homosexuals in a                researchers have found definite               lives, there were no rights to protect         He even went as far as getting
  negative box, like we don’t belong in              evidence that homosexuality was – and         homosexuals like we enjoy today . The        married, but was divorced a year later
  “normal” society.                                  in some places, still is – an accepted        apparent absence of homosexuals in           “because I couldn’t stand it anymore”,
    I am a black African man who loves               part of many African cultures. In fact,       those days is therefore not because          he says.
  other men. The word I prefer to use to             it was mainly because of the influence        there were no gay people – it was              I agree with Sibusiso when he says:
  describe my sexual preference is “gay”.            of the Christian missionaries that these      because they were oppressed. So the          “My advice to gay people who are still
  Believe me when I tell you I’m an expert           traditional practices were gradually          fact that more and more African men          in the closet is: ‘Spare yourself the
  on homophobia. I’ve often been on the              condemned by African communities.             and women are coming out and                 trauma and pain by coming out as a gay
  receiving end of this irrational fear of             These researchers haven’t used              expressing their sexual preferences          person. It’s okay to be gay today – the
  gays, expressed as hatred or disgust,              guesswork or their imagination to             freely is not because they are falling for   Constitution protects and recognises our
  sometimes violently. This behaviour                reach the conclusion that homosexuality       a new Western fashion. It is because         relationships. Come out now before it’s
  often erupts because of peer pressure,             has a long history in Africa. They have       our great society protects their right to    too late!’”
  and people who are usually very nice               used hard facts. Those who preach that        do so.
  suddenly turn on you.                              being gay is unAfrican are, therefore,          I don’t believe being homosexual is         Gay and lesbian organisations:
    I believe that people who treat homo-            not basing their view on the facts, but       really a choice. Quite simply, I was born     Behind the Mask
  sexuals as if they have a disease are              on their prejudice.                           a homosexual. To me, being gay is just or (011) 403-5566
  ignorant and need to learn about gays                Gays existed during our ancestors’          being who I am. I believe I add beauty        OUT
  and lesbians, so they can understand               decades and this spirit lives on today. I     and love to the world by being who I or (01) 344-5108
  them better. This is one reason I am               strongly believe that one of my               am, and do no harm to anyone. Changes         Forum for the
  writing this column: to reach out to my            ancestors was a gay man, but he lived         in our society are taking place and I am      Empowerment of Women
  community so we can have harmony                   at a time when it was too dangerous to        very encouraged. One was the passing or (011) 339-1867
  among us, no matter what our sexual                come out. Lesbian sangomas, like              of the Civil Union Act last year, a major
      Volume 2 Edition 3

                                   Broken links in                                                                                                                                Get some answers

                                   the education chain
                                                                                                                                                                                 Diane Crosby asks:
                                                                                                                                                                                 My nephew attends a school in Ennerdale
                                                                                                                                                                                 and failed Grade 10 last year. When he
                                                                                                                                                                                 went to repeat this grade, he was not
                                                                                                                                                                                 allowed to choose his own subjects and
JULia GREY pinpoints some reasons why so many fail at school                                                                                                                     was forced to take new subjects. The
                                                                                                                                                                                 school principal told him that he didn’t

                                                                                                                                                                                 have a choice because he had failed.
        ucceeding at school is, for many,                                                                                                       from its limited curriculum       Is the principal allowed to do this?
        a hit-and-miss struggle. Many                                                                                                           to low-quality (poorly paid)     And if not, what steps can we take to
        learners give up early and leave                                                                                                        Abet teachers.                   make sure these subject choices aren’t
    school; many who stay on repeat the                                                                                                           Several DoE “mass literacy     imposed on the child?
    same grade; and of the few who go as                                                                                                        campaigns” since 1999 have
    far as matric, fewer still pass the                                                                                                         not only failed to “break the    The Gauteng Department of
    exams. Only a tiny fraction of those                                                                                                        back of illiteracy”: eight       Education responds:
    who start out together in Grade 1                                                                                                           years on, there are more –       The principal is not allowed to do that.
    achieve good enough matric results to                                                                                                       not fewer – illiterate adults.   The learner’s parents can get assistance
    go on to higher education.                                                                                                                    Today South Africa has         by contacting Sipho Mkhulisi, the
                                                                                                                                                about 4,7-million                district director of Johannesburg South,
    But wait – it gets worse                                                                                                                    “unschooled” adults (never       on (011) 983-2308.
    If this low success rate is cause for                                                                                                       been to school); and about

                                                                                                                                                                                              t an d
    concern, results of studies comparing                                                                                                       another 5-million who are

                                                                                                                                                                                     Take a s
    achievement levels of learners from                                                                                                         “underschooled” (have less
    different countries set off all the                                                                                                         than five years of
    alarms. One major international study
    in 1998, for example, compared the
                                                                                                                                                  Like ECD, Abet is also a                 yes oR no
    Maths and Science performance of                                                                                                            DoE #1: it receives less than
    Grade 8s from 38 countries. How did                  A GOOD START: Growing up with books makes all the difference                           1 percent of education             The results of readers responses to the
                                                         to success at school                                                                                                       question in PYF 1: “Most township
    our learners compare? Badly. South                                                                                                          budgets.
    Africa came last of the lot, in 38th place.                                                                                                                                        schools do not offer quality
                                                          Weakest link #1                                                           Perhaps there’s a plan                          education and must be improved.”
    So what’s the problem?                                The DoE is fully aware of the value of                                    Although the DoE is yet to announce its               yes 100%       no 0%
    Resources can’t be blamed: many                       ECD and expresses it as a priority in                                     plans, there are signs that another
    countries with much better results in                 policies. But almost nothing is being                                     attempt to address illiteracy and Abet                 DO YOU AGREE?
    this study have far less than we do to                done to provide ECD for the youngest.                                     is coming soon. A DoE committee was            “Homosexuality must be part of
    invest in education.                                  Of about 7-million children under six,                                    formed early last year to study the            the Life Orientation curriculum.”
      It’s a complex issue and there are many             only 16 percent enjoy some form of                                        successful literacy campaigns in Cuba,
    different views. But all agree that                   formal ECD.                                                               New Zealand and Venezuela. The                SMS your
    certain vital steps along the learning                  A lack of commitment is clear in the                                    report on its findings has not yet been       view and win
    journey can make or break a learner’s                 amount of education resources for this                                    released to the public.                       a CD!
    school career. Let’s look at two of these             sector. With the exception of the Free                                      In June 006, another committee was         SMS either “yes”
    vital areas:                                          State, ECD receives less than 1 percent                                   tasked to develop a strategy for a mass       or “no” with the
                                                          of provincial education budgets.                                          literacy campaign. Hopefully we’ll            key word “gay”
                                                                                                                                                                                  to 32545. You
    The first years are the key                                                                                                     know what these plans are by June this
                                                                                                                                                                                  must also
    Early Childhood Development (ECD) is                  Baby steps to fixing it                                                   year.                                         include your
    the first taste of formal learning for the            In 001, the DoE’s set out its policy for                                                                               name and
    birth to nine age group. The reason                   ECD. Providing an “introductory year”                                     at opposite ends, but living together         postal address so we can
    ECD is so critical is that it is between              for five year olds was a priority. Last                                   Education for the youngest and                send you a CD by “Cassie” if you are one
    birth and age three that the most brain               year, the DoE says about 400 000                                          education for the oldest may not seem         of the 10 lucky winners.
    development takes place. By age seven,                learners attended Grade R. It also says                                   to have much in common – but there’s a
    about 75 percent of brain development
    is complete. If children experience
                                                          it’s “working towards reaching the
                                                          target of 1-million learners [in Grade R]
                                                                                                                                    major link. Illiterate adults are also
                                                                                                                                    parents – and studies show that               it’s your democratic right!
    quality ECD during this key “brain                    by 010”.                                                                 education levels of parents, as well as a
                                                                                                                                                                                  Got a burning question you’d like
    wiring” development, research shows                     It’s a start, but there’s still no clear                                culture of reading in the home, have          to ask government bodies involved
    that they:                                            plan to meet the education needs of the                                   dramatic effects on children’s school         with education, training, job
    • Are usually physically and                          birth to five-year-olds. Only the Free                                    performance.                                  creation and youth development?
      emotionally healthier and achieve                   State and Limpopo have a government-                                        There are clear reasons for this.
      better in school; and                               funded programme for the under-fives                                      Uneducated parents will be less able to       Send it to us, and PYF will ask the
    • Are more likely to become skilled and               at the moment.                                                            monitor or support their children in          responsible people in government for
      productive adults.                                                                                                            their school work. Growing up without         an answer. Where possible, we’ll then
                                                          another #1 weakest link                                                   books – especially in your own                publish both the question and the
                                                                                                                                    language – makes it harder to learn           response in PYF.
    On the other hand, children who don’t                 Adult Basic Education and Training
                                                                                                                                                                                   SMS a maximum of 150 letters,
    receive good ECD:                                     (Abet) is how those past school-going                                     both reading and writing when children
                                                                                                                                                                                  together with the keyword “answer”,
    • Are more likely to fail and drop out of             age without at least a Grade 9 pass are                                   get to school. Sadly, 90% of young South
                                                                                                                                                                                  to 3545.
      school; and                                         supposed to access their constitutional                                   African children do not have any access        You can also write to:
    • Are more likely to have behavioural                 right to education.                                                       to books at all.                              Get some answers/PYF, PO Box 1654,
      and emotional problems, becoming                     To say Abet is limping along would be                                                                                  Saxonwold, 13; or
      adults involved in crime, violence and              inaccurate; in fact, it has totally                                       Next week: other reasons learners             email
      substance abuse.                                    collapsed. It is riddled with problems,                                   struggle to succeed.                          There is a R1 charge per SMS.

                               Kick-start your dreams!
                                        Win a Kinetic scooter and helmets                                                                                     Be a part of the action
                                               worth over R6 000!                                                                              The JSE/Liberty Life Investment Challenge will begin on
                                     Kinetic Sa and PYf will be giving away four Kinetic scooters,                                                    March 1st, so make sure you’re ready.
                                          together with protective helmets, in PYf this year.                                         All South African Grades 10 and 11         • Each team must register with the
                                    To stand a chance of winning this Super 70 Kinetic scooter and                                    learners can join in the fun, but if         JSE at a cost of only R120.
                                      two helmets, send us the answer to the following question:                                      you’re in Grade 12 you first have to get
                                              “What protective headgear must always be
                                                      worn when riding a scooter?”
                                                                                                                                      permission from your principal.            Register today!
                                             • SMS your answer with the key word “kinetic1”,                                                                                     Get a registration form by contacting
                                         together with your name and contact details, to 32545.                                       Rules of the game:                         the Challenge co-ordinators on
                                              • Or fax your answer, name and contact details                                          • Teams must be made up of four            (011) 520-7344 / (011) 520-7116 /
                                                          to PYF on (011) 214-7110.                                                     learners from the same school. A         (011) 520-7168. You can also fill one in
                                           • Or post your answer, name and contact details to
                                              Kinetic1/PYF, PO Box 1654, Saxonwold, 2132                                                school can enter as many teams as it     on the Investment Challenge website
                                    Entries for this first scooter competition must reach us by Friday                                  likes.                                   at
                                    March 2nd. The winner will be announced in PYF on March 14th.                                     • One teacher or mentor from the           Remember to include proof of payment
                                    There is a R1 charge per SMS. Johncom employees and their immediate families may not enter.         school must supervise each team.         when registering.
                                     The editor’s decision is final and there can be no correspondence regarding this competition
                                                                           SHiNE WHERE YoU aRE                                                                  POWER YOUR FUTURE
                                                                                                                                                                   Volume 2 Edition 3       7

Brightening the way                                                                           The bursaries are granted to
                                                                                            matriculants who are academically
                                                                                            strong, financially needy, and who wish
                                                                                                                                            to build a computer lab in Senwabarwana.
                                                                                                                                            “I saw a computer for the first time at
                                                                                                                                            university and I did not want those

for the next generation
                                                                                            to study in the science and technology          children to go through the same thing,”
                                                                                            fields.                                         he says. The lab is run by the local
                                                                                              One student is Donald Madibana,               school and also offers computer classes
                                                                                            currently in his third year of studying         to the broader community.
                                                                                            for a B.Engineering degree in Computers.         Moloto’s next ambition is to reach out
SUzaN CHaLa                                                      Grade 1 learners          “I can concentrate on my studies                to learners all over the country. “A lot of
                                                                 before their exams. I      knowing that I don’t have to worry              businesses that we approach for funding
                                                                 had an opportunity to      about finance,” he says.                        have encouraged us to do more,” he says.

     ll of us know                                               speak to the best            Madibana’s bursary covers his tuition,         It’s like a small flame that becomes a
     someone who can                                             learners in the school,    books, living expenses, and he also gets        roaring fire: one man’s passion to help
     do with a little                                            and when I asked them      an allowance.                                   his community has sparked the support
help, whether it’s a                                             what they wanted to do                                                     of others, and young lives are all the
neighbour, a school                                              after matric, they all     More than just money                            brighter because of it.
child or the old lady                                            wanted to go to            But these students get more than just
next door. But while                                             university. The trouble    financial support. “It is difficult to fit in    For more information:
most of us do nothing                                            is that none of them       at university, especially for people from
about it, Eric Moloto                                            knew how they were         the rural areas,” says Moloto. “First you
does.                                                            going to finance their     have to learn to use technology you’ve
  Now working as a                                               studies. Their parents     never seen before, and then there’s the
software developer in                                            couldn’t afford the fees   shift from a simple rural life to the fast,      Want to tell the whole world?
Pretoria, Moloto is                                              or even qualify for a      complex life in a city. There’s pressure
originally from                                                  bank study loan. That      to dress and behave in a certain way.           “Shine where you are” is a space to
Senwabarwana in           ORDINARY HERO: Eric Moloto             bothered me,” Moloto        “Now imagine all that pressure linked          celebrate the good and the brightest in
rural Limpopo. He’s                                              explains.                  to the fact that you now have a bank            education.
very familiar with the                                             The result was the       account with R10 000 in it – also a new           Whether you’re part of a school, college,
lacks that often go with being poor and        creation of the Moloto Foundation,           experience. You can under-stand that            university, or an education organisation, PYF
rural. “Many of the people that I went         which provides financial support to          some are tempted to grab this freedom           wants to know more about amazing events
to school with – some of them better           matriculants to take their studies           and ignore their studies,” says Moloto.         and education successes in your learning
students than me – are now working as          further.                                       Relationships have been fostered with         community.
domestic workers or in spaza shops. It                                                      learning institutions to make sure that           These could be individuals who’ve achieved
                                                                                                                                            the extraordinary, great music or theatre
makes me sad. I know that if they got          Gathering support                            these students get extra support should
                                                                                                                                            productions, or even memorable school trips.
an opportunity like I did, their lives         Moloto recruited people from similar         they need it. “We also encourage                We’d love to hear more about art or sporting
would be different,” he says. Moloto was backgrounds who’ve also built                      relationships between new students and          successes, or your favourite educator who
one of the lucky ones, getting a bursary successful careers, and with their                 older students funded by the foundation         just retired after a life-time of teaching.
to study for a BSc in Computer Science.        support, raised funds from corporate         so they can share experiences and offer
                                               companies for scholarships. In 005,         emotional support,” Moloto adds.                So, share your “Shine where you are” stories:
a home town in nowhere                         three students were financed to the                                                          Post: Shine/PYF, PO Box 1654,
Then in 004, a visit to his old home          tune of R50 000 a year to study at           a lab for the future                            Saxonwold, 2132
town inspired him to help. “I had been         higher education institutions. This          Another proud achievement of the                Fax: (011) 214-7110
                                                                                            foundation was raising almost R300 000          e-mail:
invited to give a motivational talk to         number has now grown to over 0.

            11s and

                                                                                                                                       advice you’ll
                                                                                                                       dge, skills and of your world
          IN TO THE
                                                                                                    For all the kno ake a big success
     TUNE                 L!                E
                                IN G C HANN
                                                                                                    ever need to  m

                          LEARN                                                                                                 Catch our new youth life skills
                                                                                                                                slot, LC4U, broadcast every
                                               Learning Channel is broadc
                                                                               ast on                                            Wednesday from 10.20am to
                                                                              to Fridays.
                                            SABC1, 10am - 12pm, Mondays                                                         11.00am. LC4U is packed with
                                                                            12 lessons as
                                            Don’t miss our regular Grade                                                     motivational advice from successful
                                                                            ts for Maths
                                              well as our new Grade 11 slo                                                   celebs and practical info about how
                                                                           siness Studies,
                                            Literacy, Life Orientation, Bu                                                    to make it in your chosen career;
                                                                             and English.
                                             Maths, Science, Life Sciences                                                   plus loads of opportunities for you
                                                                                                                            to let us know just how FAB you are!
                                                                                  We’re also introducin
                                                                                   new subject, Grade                            Enter our Shin
                                                                                   Business Studies, on                         Class of 2007
                                                                                    Wednesdays (10:00am                         and WIN R10,0
                                                                                                        l as                                   00 for your
                                                                                   to 10:20am), as wel                          class! Watch L
                                                                                  TeacherTime, a specia                          Wednesday fo
                                                                                                                                               C4U every
                                                                                                                                                r details
                                                                                  slot for your hard-w
                                                                                    teachers (Wednesday
                                                                                         11am to noon).
                                                                                                         Visit or phone
                                                                                        (011) 214-7100 for more info about our Grade 12 revision videos

                                                                    All our new FET lessons are
                                                                  accompanied by supporting learner
                                                                   worksheets, assessment activities
                                                                 and teacher notes – you can view or
                                                                download copies from
     Volume 2 Edition 3

                                          Money Smarts
                        Being financially literate means understanding how money works and managing
                        it so that it benefits you. in this series, we’ll bring you information and advice to
                                               help you make your money work for you

    How to manage a bank account
      f you have a bank account, the bank          transactions he has made during the          Questions                                      8. How much money did he have in his
      will send you a bank statement each          previous month. He needs to keep a           1. What was Modise’s account balance               current account at the end of August
      month. A bank statement gives you            careful check on this to make sure that         on July 31, 2001?                               2001?
    details of all your transactions to help you   he has kept track of how much money he       2. What method did he use to pay               9. What could Modise do to reduce the
    keep track of your money. Check your           has and to ensure the bank has not              Computer Clones on August 12 2001?              large amount of service fees on his
    bank statement each month so you know          made a mistake.                              3. Compare the difference between the              current account?
    exactly how you have spent your money.           He also has a part-time job at the Save       service fees charged for using his          10. Now, look at your own bank statement
                                                   Supermarket working on Thursday and             own bank’s ATM and those charged                (if you have one) and see how you
    activity: analyse a bank statement             Friday evenings from 5-9pm and all day          for using another bank’s ATM?                   could manage your account better.
    Analyse Thabo Modise’s bank                    Saturday. For this he receives R400 a        4. What is the difference between the
    statement below and then answer the            week, which is paid directly into his bank      service fees charged for using his
    questions about the statement.                 account. He is saving some of his               own bank’s ATM and those charged
      Thabo Modise works in Krugersdorp            money in a savings account for a                for using another bank’s ATM?
    at Safe Connections. His net wages             holiday and he pays yearly subscription      5. What is the difference between the
    (after all deductions) is R900 per week        to a computer club, called Computer             service fees charged for drawing            ON TOP OF THINGS:
    and it is transferred electronically to his    Clones. He pays rent of R850 at the end         cash at his bank’s ATM and those            Good account
    current account. His current account is        of each month. He has a cheque book             charged for drawing cash at a teller        management is vital
                                                                                                                                               for financial heath
    with a local bank. Every month the             and a bankcard. The cheques are                 inside the bank?
    bank sends him a statement of his              numbered and Thabo knows that he has         6. How much cash did he withdraw from
    account. This statement shows the              written cheques from 1052 to 1062.              ATMs in August 2001?
                                                                                                7. What is the total value of cheques
                                                                                                   taken from his account (debited) in
                                                                                                   August 2001?

                                                                                                How to reduce your bank service fees
                                                                                                How to reduce your bank service fees:              withdrawals because a charge is levied
                                                                                                If your bank offers alternative methods            every time you withdraw cash.
                                                                                                for the same service, use the cheaper          •   Some banks give rebates or an
                                                                                                method.                                            exemption of service fee if you keep a
                                                                                                • For example, electronic banking                  minimum balance in your account – so
                                                                                                   services are cheaper than transactions          find out what your bank’s policy is.
                                                                                                   at tellers.                                 •   Avoid paying penalty charges – for
                                                                                                • Use your own bank ATM wherever                   example when you have insufficient
                                                                                                   possible because other bank ATM                 funds for a debit order or you overdraw
                                                                                                   transactions will cost you more.                your account without permission.
                                                                                                • Telephone and Internet banking               •   Study your bank statement over time to
                                                                                                   transaction fees are the same as using          see what you pay for service fees and
                                                                                                   your bank ATM, but there is a monthly           take action if they are too high.
                                                                                                   charge for the Internet banking facility.   •   Remember, banks won’t offer you a
                                                                                                • Plan your cash withdrawals carefully,            reduction in fees – you will have to ask
                                                                                                   and try not to make many small                  for it!

                                                                                                Electronic banking
                                                                                                What is it?                                    How does it work?
                                                                                                Electronic banking (or e-banking)              Banking transactions can be made
                                                                                                involves the use of bankcards,                 electronically using a bankcard at an
                                                                                                telephones and computers to do your            ATM, a personal computer at home or
                                                                                                banking transactions and, by using the         by telephoning a consultant who uses a
                                                                                                Internet, making online payments to            computer at the bank. Balance enquiries
                                                                                                purchase goods and services.                   are shown or conveyed instantly,
                                                                                                This technology dates quickly, so              transactions are completed without
                                                                                                contact your bank to keep up to date           delay, and the account balance is
                                                                                                with new developments and the latest           updated immediately. Different accounts
                                                                                                in banking services!                           can also be linked to one card, so money
                                                                                                                                               can be transferred between accounts.
                                                                                                What does it offer?
                                                                                                Electronic banking, also known as direct
                                                                                                banking, was introduced to allow bank
                                                                                                customers to conduct their transactions
                                                                                                without the help of banking staff,
                                                                                                reducing the need for customers to visit
                                                                                                their bank. This option has moved many
                                                                                                customers out of busy banking halls to
                                                                                                the bank foyers (for ATM transactions),
                                                                                                as well as to offices and homes (for
                                                                                                telephone, Internet and television
                                                                                                banking). This means more people can
                                                                                                use banking services 24/7.                     YOUR CALL: The convenience of e-banking
 Volume 2 Edition 3   9
                                                                                                                                          POWER YOUR                                                                                                                                                       POWER YOUR
• Equations of motion • Velocity-time graphs                                                        Science                                                                                      Nutrition                                                                    Biology                      LEARNING
• Displacement-time graphs                                                                     Vol2 Edition 3 Page 1                      LEARNING                                                                                                                      Vol2 Edition 3 Page 1
Straight line graphs                                                               • Acceleration between t1 and t 2 is (v – u) / (t 2 - t1).                                                     Animals eat foodstuffs that are mostly in complex,            called peristaltic movements or peristalsis.
                                                                                   • Acceleration between t 2 and t3 is negative since the final velocity
In mathematics you met the                                                                                                                                                                        insoluble forms such as starch, proteins and lipids (fats).   When chyme (food + digestive juices) pushes up into the
                                                                                     (0) is less than v. (Slope m < 0).
graph of a linear function. It            Y – axis                                 • a (from t 2 to t 3) = (0 - v) / (t 3 – t 2).
                                                                                                                                                                                                  These foodstuffs must be converted into simple soluble        oesophagus it causes acid indigestion/heartburn.
                                       Dependent                                                                                                                                                  nutrients, which can be readily absorbed into the blood
is in the form y = mx + c,               variable                   The slope      • Total area under the graph is the displacement: u.(t 2 - 0) + ½ (t 2
                                       eg. velocity                 of the                                                                                                                        (transport system).
where, if y is plotted against                                      graph is         - t1).(v – u) + ½ (t 3 – t 2).(0 – v).                                                                                                                                     The liver performs the following functions:
x, m is the slope of the                                            given by       • At t3 the body is at rest (-ie. velocity = 0 m.s -1).                                                                                                                      • Detoxification of harmful substances.
graph and c is the y –                                              m = ΔX/ΔY
                                                                                                                                                                                                  Digestion is the process of breaking down food and            • Amino acid metabolism. (Deamination, which is the
intercept.                                                                         What can we deduce                    V                                                                        occurs by mechanical and chemical means.                        breaking down of amino acids into glucose and urea.
                                                                                   from this graph?                        -1
Most of the graphs of                                                  X – axis                                       (m.s )                                                                      Mechanical digestion includes:                                  Glucose is used by the body, and urea is excreted as
motion that you will                              Independent variable, eg. time   • This graph is similar in
                                                                                     shape to the previous one                 v                                                                  • Chewing (mouth – teeth);                                      waste by the kidneys.)
encounter are in this form.                                                                                                                                time
                                                                                     up to t 3. At t 3 the body                                                                                   • Bolus formation;                                            • Glucose is stored as glycogen, and if not used by the
                                                                                                                               u                            (s)
  Occasionally we also meet graphs in the form: y = ax 2 + bx + c.                   has decelerated to rest.                  0       t1     t2 t3 t4                                            • Swallowing (tongue); and                                      body, it is converted to fat and deposited as adipose
  This is a curve known as a parabola. The graph of s vs t gives a                 • Now the body is                                                                                              • Peristalsis (oesophagus, small intestine and large            tissue.
 parabola since, as we see from Equation [3] below, the relationship                 increasing its velocity
                                                                                                                              -v                                                                    intestine).                                                 • Bile secretion – remember, the liver produces bile,
     between s and t is s = At 2 + Bt where A = ½ a and B = u.                       again, but in a negative
                                                                                     (or opposite) direction!                                                                                                                                                      and stores it in the gall bladder.
                                                                                   • Acceleration from t 3 to t 4 is (– v – 0) / (t 4 – t3).                                                      Roughage and water help the
By using four equations of motion we can describe a body
                                                                                   • The accelerations from t 2 to t 3 and t 3 to t 4 are the same (– v / Δt)                                     mechanical process. Chemical
moving with a constant acceleration in a straight line. We
can deduce other information too.                                                    but from t 3 to t 4 , a and v are in the same direction. Hence speed                                         digestion is achieved by the
                                                                                     is increasing (but in the opposite direction).                                                               hydrolytic action (the addition
[1] v = u + at                                                                     • Displacement from t 3 to t 4 is decreasing because the body is                                               of water because it is a catabolic
(v vs t ; m (slope) = a (a = Δv/Δt) ; c (constant) = u)                              returning along the same line.
                                                                                                                                                                                                  reaction) of enzymes -eg.
[2] s = (v + u)/2 . t                                                              • The two triangles from (t 2 to t 3) and (t 3 to t 4) are equal in size but
                                                                                     have opposite signs, so they “cancel”. What are the displacements?
                                                                                                                                                                                                  • Salivary amylase (mouth);
(not a graph to plot as such, but it helps us to get other                                                                                                                                        • Gastric juice (stomach);
information)                                                                                                                                                                                      • Pancreatic juice (pancreas);
                                                                                   Drawing and interpreting displacement – time
[3] s = ut + ½ at 2                                                                                                                                                                                 and
                                              2                                    graphs of motion
(if u = 0 (ie. c= 0), the graph for s vs t gives a slope m = ½ a)                                                                                                                                 • Succus entricus (small
                                                                                   What can we                 s                                                                                    intestine).
[4] v2 = u2 + 2as                                                                  deduce from this
                                2                                            2                                (m)

                                                                                                                                                                  Cut out and file per subject
(if we draw this we get v vs s; m (slope) = 2a; c (constant) = u )                 graph?
                                                                                   • The graph begins                                                                                             Secretions of these digestive
Drawing and interpreting velocity – time                                             at the origin so                      Slope:                                                                 juices is initiated by reflex
graphs of motion                                                                     the body starts                       m = Δs /Δt               Y                                             stimulation and hormones.
                                                                                                                                                                                                                                      Line diagram representing
                                                                                     from rest with zero                                                                                          Gastrin is a hormone that
                                                                                                                                               X                                                                                      the digestive system
A. Look at Equation [1] which relates v to t:                                        displacement.                                                  t (s)
                                                                                                                  0          t1      t2  t3                                                       stimulates the secretion of
What can we deduce from                                                            • From 0 to t1 the
                                        Velocity                                                                                                                                                  gastric juice into the stomach. Secretin stimulates the
                                             -1 v                                    displacement                                                                                                                                                               • Storage of vitamins B12, E, A, K and D and also iron.
this graph?                              (m.s ) v                                                                                           P
• If the graph begins at the origin                         Slope:                   increases steadily.                                                                                          secretion of the pancreatic juice into the small intestine.     Bile is produced by the liver, but stored in the gall
                                                            m = Δv /Δt (= a)         Velocity is constant and positive.                                                                                                                                           bladder. The bile passes through the cystic duct to
  then the body started from
  rest. [In this graph, u ≠ 0.]                                                    • From t1 to t 2 the body’s displacement from the origin is s and it                                           The human alimentary canal is differentiated into a series      the gall bladder. From the gall bladder, the bile duct
                                                 u                                   remains stationary.
• The two shaded areas under                                                                                                                                                                      of special regions: the mouth, oesophagus, stomach,             joins the pancreatic duct leading from the pancreas,
  the graph tell us the body’s                                                     • From t 2 to t 3 the body moves with constant velocity back to the
                                                                                                                                                                                                  duodenum jejunum, ileum and colon. The salivary                 to form the common bile pancreatic duct which
  displacement in time (t).                        0       t         Time            origin (-i.e. v < 0).
• If the body had carried on at                                        (s)         • The body continues past the origin with the same velocity to                                                 glands, pancreas and liver are called associated glands         enters at the duodenum (the first portion of the
  its initial velocity (u), it would have been displaced by ut.                      point P and then returns to the origin.                                                                      -i.e. they help with the digestion process.                     small intestine).
• Since it has accelerated, the additional displacement is                         • From X to Y the body accelerates -i.e. the velocity (the slope of a
  represented by the shaded triangle whose area is:                                  tangent to curve XY) increases.                                                                              There are three pairs of salivary glands: the parotid, the    Bile has functions as well:
  ½ b x h = ½ t x (v – u) = ½ t x at = ½ at 2                                                                                                                                                     submandibular and the sublingual glands. All three pairs      • It emulsifies fats -ie. it breaks the fats up into little
• Now we see that the shaded area is (ut + ½ at 2).
                                                                                                                                                                                                  produce saliva. Saliva contains salivary amylase which          particles to increase the area for the enzyme lipase
• This is displacement (s) given by Equation 3!                                     You now know:
                                                                                                                                                                                                  begins to work on cooked starch in the mouth.                   to work on.
B.                                                                                  • Four equations of motion on a straight line with a
       V                                      What can we deduce                                                                                                                                                                                                • Bile neutralises acidity from the stomach, to prevent
         -1                                                                           constant acceleration.
     (m.s )                                   from this graph?                                                                                                                                    The food passes through the pharynx and into the                enzymes in the small intestine (where pH is alkaline)
              v                               • A body starts moving at             • v – t and s – t graphs and the meanings of lines on
                                                                                                                                                                                                  oesophagus. No digestive juices are present in the              being denatured.
                                                t = 0 with initial velocity u.        them (having positive, negative or zero gradients)
                                              • At time t1 it accelerates.
                                                                                                                                                                                                  oesophagus. The food, now called a bolus, passes by           • Bile assists peristalsis.
              u                                                                       and the area under a v – t curve.
                                                a is positive since the                                                                                                                           contractions into the stomach. These contractions are         • It also acts as an antiseptic in the digestive system.
                                                                                    • How to interpret s – t and v – t graphs that show the
                                                final velocity (v) is greater
                  0   t1   t2       t3 time                                           motion of a body.
                                        (s)     than initial velocity (u).
Nutrition                                                                      Biology              POWER YOUR
                                                                                                                                                   • Falling bodies                                                                  Science                        POWER YOUR
                                                                      Vol2 Edition 3 page 2                                                        • Vertical projectile motion                                                 Vol2 Edition 3 Page 2               LEARNING
 Absorption of digested food takes place mainly            with the water, mineral salts and the water soluble
 through the villi. Villi are 1 mm long finger-like        vitamins B and C. The undigested food passes
                                                                                                                                                    Bodies falling near the earth: points to bear                      When a body is thrown upwards vertically and falls
 projections, located in the small intestine.              through the colon and into the rectum until it is
                                                                                                                                                    in mind …                                                          back to the ground …
                                                           defecated.                                                                               •   When a body falls it                                                                         … and its graph of motion
                                                                                                                                                                                                                       the diagram
 They are well suited for their function:                                                                                                               accelerates towards the earth                                                                looks like this:
                                                                                                                                                                                                                       looks like this:
 • The villi and microvilli increase the surface area      Each nutrient is kept at a constant level in the body                                        (we say “downwards”) in a
   for absorption.                                         by homeostasis. This process maintains the control of                                        straight line.
                                                                                                                                                                                                       [g=10 m.s-2]                 C v = 0 m.s
 • They have a single layer of columnar epithelial cells   glucose in the blood. The balance between insulin and                                    •   The distance of fall is h; the                                                                       V
   for easy diffusion of the nutrients.                    glucagon (both hormones) is maintained by a negative                                         time of fall is t; and the velocity h (m)                                                          (m.s )
 • Villi are kept moist by goblet cells in the columnar    feedback system. The pancreas is the only organ                                              it attains after t is v m.s-1.                                                                    v = +v
   epithelial cells, which secrete mucous.                 in the body that is both an endocrine gland and an                                       •   Bodies accelerate                                                                                               D
 • Villi ensure that the absorptive surface is in close    exocrine gland, which means that part of the pancreas                                        “downwards” because they                                      +
                                                                                                                                                                                                                      +                                   v=0
                                                                                                                                                                                                         t (s)                                                          C
   contact with the chyme (food).                          secretes digestive enzymes and part of it secretes                                           experience the “downward”                                                                                                (s)
 • They have an efficient transport system, because of     hormones. The Islets of Langerhans are the special                                           force that we call “the force of                               u = -v                         A
                                                                                                                                                                                                                                                      A   u = -v    B
   the capillary network in each villus.                   endocrine cells in the pancreas. They can be divided                                         gravity”.                                        v m.s                  A       F   v = +v
                                                           into the alpha cells which secrete glucagon and the                                      •   To a good degree of accuracy,
 Absorbed nutrients (glucose, amino acids, water,          beta cells which secrete insulin. Glucagon causes the                                        the acceleration due to
 mineral salts and vitamins) are transported by the        liver (the target organ) to convert stored glycogen to                                       gravity (g) can be taken as a                                 A When a body is thrown upwards its initial velocity is
 hepatic portal vein to the liver, where the liver will    glucose, which raises the blood sugar content. Insulin                                       constant, equal to 10 m.s-2.                                    negative (if we have chosen downwards as positive).
                                                                                                                                                                                                                        The magnitude of the velocity is at a maximum.
 perform its functions. Fatty acids and glycerol           causes the liver (the target organ) to convert glucose                                   •   This means that a falling body increases its downward
                                                                                                                                                                                                                        As soon as a body starts moving upwards it is decelerated
 molecules (from the break down of lipids) are too large   to glycogen and to then store it, thereby lowering the                                       velocity at a rate of 10 m.s-1 for each second it falls.
                                                                                                                                                                                                                        by gravity.

                                                                                                                    Cut out and file per subject
 to pass into the capillary network, so they move into     blood sugar content.                                                                     •   When a body is dropped (-ie. when it falls from rest)
 the lacteal – located in the centre of the villus. The                                                                                                 it has an initial, downwards velocity of u = 0 m.s-1.         B The slope of the graph on the right is positive and has a
 substance in the lacteal is then called chyle, which      A balanced diet contains nutrients in the correct                                        •   If a body is thrown downwards, both the downward                constant value.
 flows into the lymph system, and enters the general       quantities for good health.                                                                                                                                  The value of the acceleration is 10 m.s-2, -ie. “g”.
                                                                                                                                                        acceleration and its initial velocity must be taken into
 blood system at the junction of the left subclavian and                                                                                                account.                                                      C At the top of its flight the body will have decelerated to
 jugular veins.                                            Unbalanced diets result in malnutrition.                                                                                                                     zero velocity.
                                                           Examples of malnutrition are:                                                            Three of the equations for motion in a straight line with           Even when v = 0 m.s-1, the acceleration (g) remains
 The colon (large intestine) does not perform any          • Obesity (much fat – because of overeating);                                            constant acceleration (a) can be re-written as:                     constant, downwards. (THIS IS IMPORTANT!)
 digestive function as there are no enzymes present.       • Anorexia (very thin – starvation); and                                                                                                                   D The slope of the graph (acceleration due to gravity, g) is
 The main function of the colon is to absorb water and     • Kwashiorkor (lack of proteins).                                                        [1] v = u + gt      (v = gt if u = 0 m.s-1)                         the same as at B.
                                                                                                                                                    [2] h = ut + ½ gt 2 (h = ½ gt 2 and t = 2gh if u = 0 m.s-1)       E The area under the graph from where initial velocity (u)
                                                                                                                                                    [3] v2 = u2 + 2gh (v2 = 2gh if u = 0 m.s-1)                         is -v to where v = 0 (at C) is equal to the area from C to F.
  Longitudional section                                                                                                                                                                                                 Upward displacement (which is negative -ie. from the
  through a villus (located in                                                                                                                                                                                          bottom to the top) is given by the area of the shaded
  the small intestine)
                                                                                                                                                    The velocity – time graph for a falling body
                                                             single layer of                                                                                                                                            triangle on the left.
                                                             columnar epithelium                                                                    A. When it is dropped (from rest):
          Microvilli (increase                               (for easy diffusion of                                                                                                                                     Downward displacement (which is positive -ie. from
          the surface area)                                  nutrients)                                                                             Velocity                                                            the top to the bottom) is given by the area of the shaded
                                                                                                                                                         -1 v
                                                                                                                                                     (m.s )
                                                                                                                                                                                                                        triangle on the right.
                                                              goblet cells
                                                              (secrete mucous)                                                                                                                                        F When the body reaches the ground again (or the level
                                                                                                                                                                               Slope (m)                                from which it was projected upwards in the first place) the
                                                              nerve                           Remember to learn                                                                = Δv /Δt (= g)
                (contains chyle and flows                                                                                                                                                                               magnitude of the velocity (+v) is the same as the initial
                into lymph vessel)                                                              your digestive                                                                                   [Remember: the         velocity (u = -v) with which it was thrown.
                                                               arteriole (O blood)                                                                              -1
                                                                                                enzyme table                                        u = 0 m.s
                                                                                                                                                                                                 area under the
        Crypt of Lieberkühn                                      Brunner’s gland
                                                                                                                                                                     0     t             time
        (secretes succus entericus)                                                                                                                                                       (s)                             Time taken for the upward flight = time taken for the
                                                                 (secretes succus                                                                                                                velocity – time
                                                                 entericus)                                                                         B. When it is thrown downwards:              graph gives the          downward flight. (NOTE THE SYMMETRY!)
                 (CO2 blood back                                Artery - from Aorta                                                                             v                                distance of fall.]
                 to vein)                                       (constant supply of
                                                                blood).                                                                                                                                                 You now know:
                 muscle tissue
                                                                Lymph vessel - joins                                                                                                             [When a falling        • Equations of motion for bodies under the effect of
                                                                rest of circulation at                                                                                                           body reaches             the force of gravity; and
             Vein                                               junction of subclavian and
             (flows into superior mesentric vein,                                                                                                               u                                the ground, its        • Velocity – time graphs for bodies that were dropped
                                                                jugular veins
             to hepatic portal vein, through liver                                                                                                                                               velocity is at a         or thrown upwards and allowed to fall back to the
             and into the Inferior Vena Cava)
                                                                                                                                                                     0     t             time    maximum.]                same level.
                                                                                                                 POWER YOUR                                         Word meanings –                                                                                                      POWER YOUR
Trigonometry: Compound angle identities – HG                        Mathematics                                  LEARNING                                           Literal & figurative meanings
                                                                                                                                                                                                                                                          English                        LEARNING
                                                                              Vol2 Edition 3 Page 1                                                                                                                                                Vol2 Edition 3 Page 1
  1. cos (A – B) = cos A cos B + sin A sin B             METHOD:
                                                         Use a unit circle (r = 1)                                                                                                                                                         The reason so many successful and rich people are able
                                 y                       co-ordinates Q(cos A; sin A)
                                                                                                                                                                       Welcome once again to                                             to have overweening power is that people surround them
                                                         co-ordinates P(cos B; sin B)                                                                                                                                                    with a foofaraw of flattery.
                                                                                                                                                                       Power Your Future!                                                  By all accounts, Anna Winter, the editor of American
         Q                                               By the distance formula:                                                                                      As we said at the begining of the series, the focus for the       Vogue, is a monster, who demands that people keep their
(cosA; sinA)                                             PQ 2 = (cosB – cosA) 2 + (sinB – sinA) 2                                                                      English articles for this year is on READING SKILLS and           eyes lowered if they meet her by accident in the building.
                                                              = cos2B – 2cosA cosB + cos2A + sin2B – 2sinA sinB + sin2A                                                the LANGUAGE component of your exams.                               She has breakfast ordered from a chic downtown
                                          (cosB; sinB)                                                                                                                                                                                   restaurant. When she wants it, it has to be there. So, never
                                 A                            = (cos2B + sin2B) + (sin2A + cos2A) – 2sinA sinB – 2cosA cosB
                                                              = 2 – 2sinA sinB – 2cosA cosB                                                                            In the last two editions, we have been looking at an article      quite knowing when this might be, breakfasts are ordered
                             A–B     B                                                                                                                                 published in Sunday Times Lifestyle on October 23 2005.           every twenty minutes, so there is always one ready.”
                                                         By the cos rule:
                                                   x                                                                                                                   The title of the article is, “Oh, you do flattery so well”. Let
                             0                           PQ 2 = 12 + 12 – 2(1)(1) cos (A – B)
                                                                                                                                                                       us examine paragraphs 8–12.                                       What skills do you need to be able to read these
                                                                     2 – 2 sin A sin B – 2 cos A cos B = 2 – 2 cos (A – B)
                                                                                                                                                                                                                                         paragraphs and understand the writer?
                                                                                           cos (A – B) = cos A cos B + sin A sin B
                                                                                                                                                                         “The thing about flattery is that it offers maximum             • A recognition of figures of speech, especially antithesis;
                                                                                                                                                                       rewards for minimum effort.                                       • A recognition of vocabulary;
  Now we can use the above proof to derive                                                                                                                               A competent flatterer stops at nothing. They tell ugly          • A recognition of the ability to guess from context;
  the other compound angle formulae.                                                  SUMMARY
                                                                                                                                                                       people they are beautiful, old people they look young and         • Punctuation; and
                                                                             Know these formulae:
                                                                                                                                                                       compliment the stupid on their brains.                            • A recognition of common errors.
  2. cos(A+B) = cosA cosB – sinA sinB
     Proof: cos (A + B)                                               cos (A ± B) = cosA cosB Ŧ sinA sinB
                                                                                                                                                                     FIGURES OF SPEECH                                                   The words “maximum” and “minimum” are an example of
          = cos(A – (-B))                                                                                                                                            In our first article, we said the following :                       antithesis. The writer is pointing out that it is easy to flatter
          = cosA cos(-B) + sinA sin(-B)                               sin (A ± B) = sinA cosB ± cosA sinB                                                                                                                                (flattery requires “minimum effort”) but the person who
          = cosA cosB + sinA (-sinB)                                                   tanA ± tanB                                                                    FIGURES OF SPEECH are a special use of language                    flatters another is richly rewarded; the flatterer gets
          = cosA cosB – sin A sin B                                   tan (A ± B) = 1 Ŧ tanA tanB                                                                     that creates a meaning beyond the literal meaning. The             “maximum rewards”.
                                                                                                                                                                      most common figures of speech are the SIMILE and the
  3. sin(A – B) = sinA cosB – cosA sinB                                                                                                                               METAPHOR.                                                          Now look at the second paragraph in the article:
     Proof: sin(A – B) = cos [90° – (A – B)]
                       = cos(90° - A + B)                                                                                                                            When we use figures of speech, we are using words out of                “They tell ugly people they are beautiful, old people they
                                                                     Example 1:                                                                                      their literal meaning or out of their ordinary use in order to:       look young and compliment the stupid on their brains.”
                       = cos [(90° + B) – A]

                                                                                                                                     Cut out and file per subject
                                                                     Use the compound angle formulae to prove that                                                   • Add beauty;
                       = cos(90°+B) cosA+sin(90°+B)sinA                                                                                                                                                                                  Where do you find more examples of antithesis? Here they
                                                                     sin (90° + θ) = cosθ                                                                            • Add emotional intensity; and
                       = -sinB cosA + cosB sinA                                                                                                                                                                                          are: “ugly” and “beautiful”, “old” and “young”, the “stupid” and
                                                                     Solution:                                                                                       • Transfer the writer’s sense impressions by comparing
                       = sinA cosB – cosA sinB                                                                                                                         or identifying one thing with another that has a meaning          “brains”.
                                                                     sin (90° + θ) = sin 90° cosθ + cos90° sinθ
                                                                                   = cosθ(1) + 0(sinθ)                                                                 familiar to the reader.
  4. sin(A + B) = sinA cosB + cosA sinB                                                                                                                                                                                                  VOCABULARY
                                                                                   = cosθ
     Proof: sin(A + B) = cos [90° - (A + B)]                                                                                                                         Figures of speech are also a means of concentration; they           There is a very unusual word in the extract below: “foofaraw”.
                        = cos [(90° - A) – B]                                                                                                                        enable the writer to convey an image with the power of              It is unlikely that a school dictionary will have this word, so let
                                                                     Example 2                                                                                                                                                           us practise another important reading skill: LOOKING AT A
                        = cos(90°-A) cosB+sin(90°- A)sinB                                                                                                            just a few words, where a great many would otherwise be
                                                                     Find tan 15° without a calculator                                                                                                                                   WORD IN CONTEXT.
                        = sinA cosB + cosA sinB                                                                                                                      required.
  5. tan(A + B)                                                      tan 15° = tan (60° - 45°)                                                                       Some important figures of speech are: simile, metaphor,             When you look at a word in its context, you are guessing
     Proof:                                                                      tan60° – tan45°                                                                     personification, hyperbole, and symbol.                             what it means. You do not actually KNOW; you simply make
                                                                              = 1 + tan60° tan45°
                                                                                                                                                                                                                                         an intelligent GUESS. Let us read the sentence in which this
           sin(A + B)
       = cos(A + B)                                                           = 3-1                                                                                  In this extract, we find ANTITHESIS.                                word appears, and guess its meaning:
         sinA cosB + cosA sinB                                                    1+ 3
       = cosA cosB – sinA sinB ( cosA cosB)                                                                                                                           ANTITHESIS is a figure of speech in which a thought                   “The reason so many successful and rich people are able
          tanA + tanB                                                Example 3                                                                                        is balanced with a contrasting thought in parallel                  to have overweening power is that people surround them
       = 1 – tanA tanB
                                                                     Simplify without a calculator:                                                                   arrangements of words and phrases.                                  with a foofaraw of flattery.”
                                                                     cos 79° cos 311° + sin 101° sin 49°                                                              Examples:
  6. tan(A – B)                                                                                                                                                       – “He promised wealth and provided poverty.”                       It seems that this word means a “confusing cloud”. Flattery
     Proof:                                                                                                                                                           – “Willing to wound, and yet afraid to strike.” (from Pope’s       surrounds these people, so it must be like a cloud
                                                                             = cos 79° cos 49° + sin 79° sin 49°                                                                                                                         surrounding a mountain. The cloud of flattery is designed to
                                                                                                                                                                         An Epistle to Dr Arbuthnot)
           sin(A – B)                                                        = cos (79° - 49°)
       = cos(A – B)                                                                                                                                                                                                                      trick the person into believing whatever insincere
                                                                             = cos 30°                                                                               In the first paragraph of “Oh you do flattery so well”, Lin         compliments are paid to them, so we guess that the meaning
           sinA cosB – cosA sinB
       = cosA cosB + sinA sinB ( cosA cosB)                                       3                                                                                  Sampson writes: “The thing about flattery is that it offers         is a “confusing cloud” or “deliberately deceitful mist”. We
               tanA – tanB
                                                                              =   2                                                                                                                                                      could be wrong, but we have at least TRIED.
                                                                                                                                                                     maximum rewards for minimum effort.”
       = 1 + tanA tanB
Word meanings –                                                                     English                      POWER YOUR
                                                                                                                 LEARNING                                                                                                             Mathematics                                  POWER YOUR
Literal & figurative meanings                                                Vol2 Edition 3 Page 2
                                                                                                                                                                    Trigonometry: Compound angle identities – HG
                                                                                                                                                                                                                                               Vol2 Edition 3 Page 2               LEARNING
 Guessing from context is an important skill to develop.            • The “When ...” clause is another SUB-ORDINATE                                                  Example 4
 You do not always have a dictionary beside you, and                  ADVERBIAL CLAUSE, which is usually separated from                                              Prove that
                                                                                                                                                                                                                                             SUMMARY                    NB: Don’t
 sometimes, in an exam, you are asked to give a meaning of            the rest of the sentence by a comma.                                                            3 sin (x + 60°) – sin (x + 30°) = cosx
                                                                                                                                                                                                                                            Learn these:                confuse these
 a word that you do not know. Looking at the context helps                                                                                                           Solution:
 you to write something instead of leaving the answer blank.        The paragraph ends:                                                                                                                                                sin2A = 2 sin A cos A            sin2θ+ cos2θ = 1
                                                                      “So, never quite knowing when this might be, breakfasts are                                                                                                                                          -sin2θ - cos2θ = -1
                                                                                                                                                                      3 (sinx cos60° + cosx sin60°) – (sinx cos 30° + cosx sin 30°)
 PUNCTUATION                                                        ordered every twenty minutes, so there is always one ready.”                                           1        3           3        1                             cos2A = cos2A - sin2A
 Punctuation marks include:                                                                                                                                          = 3 ( 2 sinx + 2 cosx) – ( 2 sinx + 2cosx)                              or 1 – 2 sin2A             cos2θ - sin2θ = cos2θ
 • Full stop      • Question mark            • Dash                 Why is there a pair of commas marking off “never quite                                           = 3 sinx + 3 cosx – 3 sinx – 1 cosx
                                                                                                                                                                       2         2          2        2                                       or 2cos2A – 1               sin2θ - cos2θ = -cos2θ
 • Comma          • Exclamation mark         • Hyphen               knowing when this might be”?
 • Semi-colon     • Inverted commas          • Colon                • This is a PARTICIPIAL PHRASE, which is separated from                                          = cosx                                                                         2 tanA
                                                                                                                                                                                                                                       tan2A = 1 – tan2A
 • Apostrophe                                                         the main part of the sentence by a comma.
                                                                                                                                                                     Example 5
 Punctuation is for the eyes and each punctuation mark              Finally, we have “so there is always one ready”. Can you                                         Prove that                                                       EXAMPLES
 has a meaning. In two of the paragraphs below, there are           recognise why there is a comma before this clause?                                               cos(A + B) cos(A - B) = cos2 B - sin2 A
 commas:                                                            • The “so ...” clause is another SUB-ORDINATE                                                    Solution:                                                        Example 1                 sin2A – 1
                                                                      ADVERBIAL CLAUSE, which is usually separated from                                              LHS                                                              Prove that cosA – sinA = sinA –cosA
    “By all accounts Anna Winter, the editor of American              the rest of the sentence by a comma.                                                           cos (A + B) cos (A – B)                                          Solution:
  Vogue, is a monster, who demands that people keep their
                                                                                                                                                                     =(cosA cosB – sinA sinB)(cosA cosB + sinA sin B)                 RHS
  eyes lowered if they meet her by accident in the building.        COMMON ERRORS                                                                                                                                                     2sinA cosA –1
                                                                                                                                                                     = cos2A cos2B - sin2A sin2B
    She has breakfast ordered from a chic downtown                  In your examination or class exercises, you are often asked                                                                                                         sinA –cosA
  restaurant. When she wants it, it has to be there. So, never      to find common errors made in writing and to correct them.                                       = cos2B(1 - sin2A) - sin2A(1 - cos2B)
                                                                                                                                                                                                                                         2sinA cosA – (sin2A + cos2A)
  quite knowing when this might be, breakfasts are ordered          There is an example of such an error in: “ ... so, never quite                                   = cos2B - sin2A cos2B - sin2A + sin2A cos2B                      =

                                                                                                                                     Cut out and file per subject
                                                                                                                                                                                                                                                  sinA –cosA
  every twenty minutes, so there is always one ready.”              knowing when this might be, breakfasts are ordered every                                         = cos2B - sin2A                                                     2sinA cosA – sin2A – cos2A
                                                                                                                                                                                                                                      =          sinA –cosA
                                                                    twenty minutes, so there is always one ready”.
 In an examination, you can be asked to discuss why the                                                                                                              Example 6                                                          sin2A –2sinA cosA +cos2A
                                                                                                                                                                                                                                      =         sinA –cosA
 writer has used a particular punctuation mark. Let us look         What is the mistake?                                                                             If cos(A – B) = a and cos(A + B) = b, prove that                    (sinA – cosA) 2
 carefully at the use of commas above:                              • According to the sentence, WHAT never quite knows when                                                       a+b                                                = sinA –cosA      = sinA – cosA
                                                                      Anna Winter wants her breakfast? Yes, the sentence says
                                                                                                                                                                     cosA cosB = 2
 The first example is actually a PAIR OF COMMAS. The                  that the breakfasts themselves do not know!                                                    Solution:
 commas are placed so that “the editor of American Vogue”
                                                                                                                                                                                                                                      Example 2
 is placed between commas. Why?                                     The mistake is that “knowing” is an adjective and it needs a                                     a + b cos(A – B) + cos(A +B)                                     Find the value of cos A if cos 2A = 0,62 (without a calculator)
 • Here, the commas are an example of PARENTHESIS                   noun or pronoun to describe. The participial phrase (“never                                        2 =            2                                               Solution:
                                                                                                                                                                       cosA cosB + sinA sinB + cosA cosB – sinA sinB
    (adding extra information between commas, brackets or           quite knowing when this might be”) must describe the FIRST                                       =                      2                                             cos2A = 0,62
    dashes). The extra information is about Anna Winter.            noun or pronoun that comes after it, and, in this sentence, it                                   = 2 cosA cosB                                                    2cos2A – 1 = 0,62
    We are told that she is the editor of American Vogue.           is the word “breakfasts”. Obviously this sentence makes NO                                                                                                            2cos2A = 1,62
                                                                                                                                                                     = cosA cosB
                                                                    SENSE. How do we correct it?                                                                                                                                            cos2A = 0,81
 The next comma comes after “monster”: “ ... is a monster,          • We must give the word “knowing” a subject. Here is one                                                                                                                 cos A = ±0,9
 who demands that people keep their eyes lowered”. Why is              way to correct the sentence:                                                                  FORMULAE FOR DOUBLE ANGLES
 it used?                                                                                                                                                                                                                             Example 3
 • “... who demands that people keep their eyes lowered ...” is        “As the waiters never quite know when she might want                                          1. sin 2A = sin (A + A)
                                                                                                                                                                                                                                      Express sin 3α in terms of sinα
    called a NON-DEFINING CLAUSE. This clause is telling              her breakfast, breakfasts are ordered every twenty minutes.”                                              = sin A cos A + sin A cos A
    us about Anna Winter. It is also adding extra information                                                                                                                   = 2 sin A cos A
    about her. The comma has the same meaning as “and”.             There is another error in the extract we have been                                                                                                                sin 3α = sin(2α+ α)
    Anna Winter is a monster AND she demands that people            examining. Can you find the mistake in these sentences?                                          2. cos 2A = cos (A + A)                                                 = sin2α cosα + cos2α sinα
    keep their eyes lowered.                                                                                                                                                    = cos A cos A – sin A sin A                                  = 2 sinα cosα cosα + sinα (1 – 2 sin2α)
                                                                       A competent flatterer stops at nothing. They tell ugly                                                   = cos2A - sin2A                                              = 2 sinα cos2α + sinα - 2 sin3α
 Note that Lin Sampson has not used a comma before the “if”           people ...                                                                                        NB: cos2A can be written in other ways. It depends on                = 2 sinα (1 - sin2α) + sinα - 2 sin3α
 clause: “if they meet her by accident in the building.” However,                                                                                                       what is needed.                                                      = 2 sinα - 2 sin3α + sinα - 2 sin3α
 this clause should be marked off with a comma. Why?                • “A competent flatterer” describes one person. It is                                                       cos2A - sin2A                                                = 3 sinα - 4 sin3α
 • It is a SUB-ORDINATE ADVERBIAL CLAUSE, which                       SINGULAR. “They” is a plural pronoun. This is called an                                                   = (1 – sin2A) - sin2A
    is usually separated from the rest of the sentence by a           ERROR OF CONCORD. (“Concord” means harmony; the                                                           = 1 – 2 sin2A (in terms of sin A)
    comma.                                                            two bits of the sentence do not fit together properly.) How                                                or                                      3. tan2A                  NB: Often you see 1 + sin2θ
                                                                      can we correct it?                                                                                                                                                           (More often than not you need to create a
                                                                                                                                                                                cos2A - sin2A                                = tan (A + A)
 There is another example of the same use of the comma in                                                                                                                                                                                          trinomial by changing 1 into sin2θ + cos2θ)
                                                                                                                                                                                = cos2A – (1 - cos2A)                        = tanA + tanA
 the next paragraph: “When she wants it, it has to be there.”        “Competent flatterers stop at nothing. They ...”                                                                                                          1 – tanA tanA          sin2θ + 2 sinθ cosθ + cos2 θ
 Why is there a comma here?                                                                                                                                                     = cos2A – 1 + cos2A
                                                                                                                                                                                = 2 cos2A – 1 (in terms of cos A)            = 2 tanA                 = (sinθ + cosθ) 2
                                                                                                                                                                                                                               1 – tan2A

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