2010 Nov UNIT 1F 43601F tsddcs

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					                                                                      time allowed: 1 hour    marks: 54

                                                                     2010 November UNIT 1F 43601F

Question 1 complete tally chart; fraction of days; simplify fraction; interpret percentage;
use probability words
Question 2 * complete pictogram; interpret key; read bar chart; compare results
Question 3 given small data set, find mode, median & mean; criticise a claim; discuss
sampling method
Question 4 * calculate percentage of an amount; compare ways of working it out
Question 5 read a scatter diagram; comment on a hypothesis; draw a scatter diagram to
support a hypothesis
Question 6 given a bag of counters, find probability; find number of counters
Question 7 * design observation sheet; find evidence to decide hypothesis
Question 8 share amount in given ratio
Question 9 find winnings for probability game
Grade boundaries




* The quality of written communication is specifically assessed in questions 2, 4 and 7

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                                                2010 November UNIT 1F 43601F

1 The table shows the weather in London each day for 40 days


                                                      10
                                                      18
                                                       4
                                                       8


 1(a) Complete the table                                               2 marks


 1(b) What fraction of the 40 days are sunny?         10
      Give your answer in its simplest form.           40


                                          answer         ¼             2 marks

                                                                                   2
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                                             2010 November UNIT 1F 43601F

1(c) In Manchester for the 40 days

   • 16 days are sunny
   • 50% of the days have rain
   • there is no snow

1(c) (i) Complete the table for Manchester



                                                               16
 50% of 40 days is 20                                          20
                                                                    0
 20 + 16 + 0 = 36                                                   4
 40 – 36 = 4

                                                                        3 marks
                                                                                    3
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                                               2010 November UNIT 1F 43601F



                            16
                            20
                             0
                             4



1 (c) (ii) One of the 40 days in Manchester is chosen at random.
           Use a suitable probability word to complete the sentences.

                                              impossible
The chance of choosing a day with snow is ……………………………………………

                                                 evens
The chance of choosing a day with rain is ………………………………………………

                                                                       2 marks

                                                                                   4
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                                               2010 November UNIT 1F 43601F

2* Nick takes four tests. The pictogram shows his scores.




 2(a) Nick scores 60% in English.   Complete the key.

                                                   20                 1 mark


 2(b) In which subject is his highest score?
                                      answer   Mathematics            1 mark

                                                                                  5
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                                        2010 November UNIT 1F 43601F

2 (c) Jen takes the same four tests.
      The bar chart shows her scores.




                                                                           6
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                                                2010 November UNIT 1F 43601F

2(c) (i) Nick wants to compare his scores with Jen’s scores.
Draw a suitable diagram that he can use.


                                                                   Jen
                                                                   Nick




                                                                       4 marks




                                                                                   7
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2 (c) (ii) Write down three facts comparing     2010 November UNIT 1F 43601F
their scores
                                                            Jen
                                                            Nick




  Fact: Jen scored higher than Nick in English, Geography and Science
  Fact: Nick scored higher than Jen in Mathematics
  Fact: both scored 40% or more in every test; they both had a highest
  score of 90%
                                                                                      8
                                                                        3 marks
                                                   time allowed: 1 hour    marks: 54

                                                  2010 November UNIT 1F 43601F

3 A company makes bags of toffees

The company checks that the bags contain
50 toffees.

3(a) The number of toffees in a sample of 11 bags is

         51    50   51    51    52     43    50     50       51       51     50

3(a) (i) Write down the mode
                                                  answer        51         1 mark
the mode is the data that occurs the most
3(a)(ii) Work out the median.        You must show your working
the median is halfway along the ordered list of data

         43    50    50    50    50     51   51     51     51        51    52

                                                  answer        51         2 marks 9
                                                  time allowed: 1 hour   marks: 54

                                                 2010 November UNIT 1F 43601F


3(a) The number of toffees in a sample of 11 bags is

         51     50   51   51    52    43    50    50       51      51     50

3(a) (iii) Work out the mean
the mean is calculated by adding all the data together, then
dividing the total by the number of items


51 + 50 + 51 + 51 + 52 + 43 + 50 + 50 + 51 + 51 + 50 = 550

550 ÷ 11 = 50                                    answer       50         3 marks




                                                                                 10
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                                                2010 November UNIT 1F 43601F

3(b) The company claims there are 50 toffees in a bag

3(b) (i) Give a reason why this claim seems fair.

         All the averages are 50 or bigger than 50                         1 mark




3(b) (ii) Give a reason why this claim seems unfair



         one of the sample bags only had 43 sweets in it                   1 mark




                                                                                    11
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                                             2010 November UNIT 1F 43601F


3(c) The company uses the first 11 bags produced each
Monday to check the contents.

State two ways this method of sampling can be improved


Take several samples during the week

Take bigger samples

Take samples at different times and on different days

Take every hundredth bag during production to be part of the sample


                                                                     3 marks

                                                                             12
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                                   2010 November UNIT 1F 43601F


4(a) * Work out 70% of £986

70% is the same as 0.7


70% of 986 = 0.7 × 986 =      answer   £690.20            2 marks
690.2




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                                                   2010 November UNIT 1F 43601F


    4(b) Circle the calculations that have the same answer as

                                      57% of 372       0.57 × 372 = 212.04
    A 58% of 371         No !


    B 5.7% of 37.20      No !

        57
    C          372      0.57 × 372 = 212.04
        100

    D 0.57 × 0.372       No !


    E 5.7% of 3720       0.057 × 3720 =                                    2 marks
                         212.04
                                                                                   14
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  5 Freddie and Priya both like music              2010 November UNIT 1F 43601F
  Freddie gives some songs a score out of 10
  The scatter diagram shows his results
  5(a) What fraction of the                     two scored 10 out of 10
  songs is given full marks?
                                                                 thirteen songs
    answer     2
                                                                 were scored
               13
                      1 mark

   5(b) How long is the song
   that is given a score of
   4?
   Give your answer in
   minutes and seconds.
time is 5 minutes and two sections

each section is 60 seconds ÷
5
              = 12 seconds

                               answer = 5 minutes and 24 seconds           2 marks
                                                                                 15
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                                                2010 November UNIT 1F 43601F

5(c) Freddie has this hypothesis
     He says, “The shorter the song, the more I like it.”

Comment on his hypothesis

the line of best fit
shows weak negative
correlation which
supports his hypothesis

shorter songs scored
high marks and long
songs scored low marks




                                                                               16
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                                                  2010 November UNIT 1F 43601F

  5(d) Priya also gives some songs a score out of 10.
       She has a different hypothesis.
       She says, “The longer the song, the more I like it.”
       Her hypothesis is strongly supported by the data she collects.

   Plot points on the grid to
   show how her scatter
   diagram may look

• a line of best fit would show
positive correlation
• shorter songs score low marks
and long songs score high marks
• the data points would be close
to the line of best fit
                        1 mark

                                                                                  17
                                                time allowed: 1 hour   marks: 54

                                               2010 November UNIT 1F 43601F

6(a) A bag contains 3 red, 5 white and 8 blue counters.
     One counter is chosen at random.

What is the probability of choosing a blue counter.

3 + 5 + 8 = 16 counters in the bag       probability =       8

8 of them are blue                                          16

                                              answer = ½               2 marks




                                                                               18
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                                                 2010 November UNIT 1F 43601F

6(b) A different bag contains only black counters, pink counters
and white counters.
When one counter is chosen at random, each colour is equally likely.

Write down two possible values for the total number of counters in
this bag

 three colours in the bag

 probability of each colour is ⅓

 number of counters in the bag must be a multiple of 3

                                    answer 6 and 24                      2 marks




                                                                                 19
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                                               2010 November UNIT 1F 43601F
6(c) Another bag contains only green counters and yellow
counters.
There are more than 10 counters in the bag.
When one counter is chosen at random, the probability of
choosing a green counter is ¾

Write down two possible values for the total number of
counters in this bag

probability of green = ¾  probability of yellow = ¼

number of counters in the bag must be a multiple of 4, bigger than 10

                                        answer 16 and 24              2 marks




                                                                              20
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                                                   2010 November UNIT 1F 43601F

7* This poster is put up in a school dinner hall

                         Coming soon
                     NEW healthy eating menu

The headteacher thinks the number of students who eat school dinners
will increase by 25%
7(a) Design an observation sheet the headteacher can use to see if she
is right

                     tallies                        total
         old menu
         new menu
                                                                          2 marks




                                                                                  21
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                                                2010 November UNIT 1F 43601F

7(b) The number of students who eat school dinners
increases from 78 to 91.

Is the headteacher correct?       [She thinks the number of
students who eat school dinners will increase by 25%]

Show clearly how you decide.


25% of 78 = 0.25 × 78 = 19.5

a 25% increase on 78 would have to be 20 students

91 – 78 = 13   only 13 extra students ate the new lunch menu

answer: this is not enough to be 25% increase                          3 marks



                                                                               22
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                                                2010 November UNIT 1F 43601F

8 Peter and Alice buy a set of golf clubs for their mother.
They pay in the ratio 4 : 3
Peter pays £224

How much does Alice pay?

                           Peter              Alice
                             4                  3

                           224                 168


 224 ÷ 4 = 56           56 × 3 =
                       168

                                   answer: Alice pays £168              3 marks


                                                                                23
                                               time allowed: 1 hour   marks: 54

                                              2010 November UNIT 1F 43601F

9 At the school fayre, I play a game 20 times.
                       Each go costs 50p.
                       Each time I win, I receive £1.50
                       The probability of winning is ⅕.

How much money do I expect to lose?


You pay 50p for each of 20 games         50p × 20 = £10

You expect to win ⅕ of the time

                ⅕ of 20 games = 4       Four prizes of £1.50 = £6


£10 − £6 = £4            You should expect to lose £4                 3 marks


                                                                              24
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                                                  2010 November UNIT 1F 43601F




Total: out of 54           actual ones used

             grade    G        F     E        D        C
              score   10      16    22    29          36




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