Linear Maths Edexcel Gcse Mock Paper Non Calculator

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					GCSE Mathematics Linked Pair Pilot –
Beginning to teach


 10NMB01
 Presented by
 Edexcel Principal Examiners




                                  Slide 1
Course code 10NMB01
Session 1 Aims

The purpose of this event is to:
• Review the GCSE Linked Pair in more detail
• Review differences between GCSE Linked Pair and GCSE
  Maths at unit 2 in particular
• Consider some teaching implications
• Review additional resources for GCSE Linked Pair
• Discuss and share entry practice



                                                Slide 2
Course code 10NMB01/02
Session 2
Examination Timetable Applications - Final dates

         Monday 6 June
         5AM1F Applications of Mathematics
         Unit 1 F Tier: Paper 1
         (Calculator) (1h 45m)

         5AM1H Applications of Mathematics
         Unit 1 H Tier: Paper 1
         (Calculator) (1h 45m)
                                                   Slide 3
Course code 10NMB01/02
Session 2
  Examination Timetable Applications - Final dates
     Friday 10 June

       5AM2F Applications of Mathematics
       Unit 2 F Tier: Paper 1 (Calculator) (1h 45m)
       5AM2H Applications of Mathematics
       Unit 2 H Tier: Paper 1
       (Calculator) (1h 45m)
       Please note, first certification of this
       qualification is in June 2011 (until June 2013)
                                                      Slide 4
Course code 10NMB01/02
Session 2
       Examination Timetable Methods - Final dates
       Monday 13 June
       5MM1F Methods of Mathematics
       Unit 1 F Tier: Paper 1
       (Non-Calculator) (1h 45m)

       5MM1H Methods of Mathematics
       Unit 1 H Tier: Paper 1
       (Non-Calculator) (1h 45m)

                                                     Slide 5
Course code 10NMB01/02
Session 2
       Examination Timetable Methods - Final dates
       Monday 21st June
       5MM2F Methods of Mathematics
       Unit 2 F Tier: Paper 1
       (Calculator) (1h 45m)

       5MM2H Methods of Mathematics
       Unit 2 H Tier: Paper 1
       (Calculator) (1h 45m)

                                                     Slide 6
Course code 10NMB01/02
Session 3
 Feedback on Unit 1 issues

 *Spreadsheets – modelling v testing v accessibility
 *Flowcharts – what symbols are required?
 Currency calculations at F Tier
 Financial calculations at F tier
 Similar triangles at F tier
 *Intersecting chords – resource material
 *Linear programming – resource material
 *Sets –Venn Diagrams – prob - required notation

                                                  Slide 7
Course code 10NMB01/02
Session 3

         Spreadsheets – initial examples were judged
         to be inadequate!




                                                       Slide 8
Course code 10NMB01/02
Session 3
                  1. Ronnie wants to buy some carpets.
                  She can buy 3 types of carpets, wool, nylon and sisal.
                  Complete the spreadsheet so that she can compare the costs of carpeting
                  some of the rooms in her house.



                                A           B         C        D          E           F
                                                            Wool £20   Nylon £15   Sisal £10
                        1   Length (m)   Width (m)   Area
                                                             per m²     per m²      per m²
                        2       4           3
                        3       5           4




                                                                                               Slide 9
Training from Edexcel
Session 3
         Flowcharts – what symbols are required?
         Process

         Decision

         Start/Stop


         Input/Output

                                                   Slide 10
Course code 10NMB01/02
Session 3

   Currency calculations at F Tier


   Financial Calculations at F tier
   (Personal Finance)(Index Numbers)




                                       Slide 11
Course code 10NMB01/02
         Session 3
           Currency calculations at F Tier
        5. £1 = €1.20

        A watch costs £50 in the UK. The same make of watch costs €63 in France. Work out the
        difference between the cost in the UK and the cost in France. Give your answer in £.


         9. £1 = $1.50
         Jim has £4000
         He wants to buy $ for a holiday.
         The agent will charge Jim 2% commission
         Work out how the largest number of $ Jim can get.




                                                                                                Slide 12
Training from Edexcel
             Session 3
               Financial Calculations at F Tier
            1. Jim earns £250. He gets a wage rise of 10%. Work out his new wage.




            20. Rail operators are allowed to raise fares by the cost of living index
            increase + 1%. In 2010, the cost of living increase was 4.5%.
            The fare from Bristol to London in 2010 was £120.

            What is the fare going to be in 2011?




                                                                                        Slide 13
Training from Edexcel
Session 3
• Sets –Venn Diagrams – Probability - required notation

F Tier – {1, 4, 7}, A′ ø,

H Tier - {1, 4, 7}, A′ ø,


No more than 3 sets for any Venn diagram at H tier
Generally 2 sets at F Tier


                                                   Slide 14
Course code 10NMB01/02
Session 3

• Similar Triangles at F tier

                                              8 cm
                        4 cm

                           60o          40o          60o          xo

                                 6 cm                      y cm



           These two triangles are similar.

           (a) Write down the value of x
           (b) Find the value of y


                                                                       Slide 15
Training from Edexcel
Session 3

• H Tier
• Intersecting chords – resource material

    Linear Programming – resource material




                                             Slide 16
Training from Edexcel
Session 3               Compound Interest at F Tier (and H Tier)


• Work out the amount an investment is worth
• given the number of years and interest rate

• Use multipliers to work out appreciation and
• depreciation




                                                           Slide 17
Training from Edexcel
Session 4
• New material at F Tier – Unit 2
      Risk
  Here is some information about injuries in some sports

         Sport             Number of   Number of
                           games       injuries
         Football          348         37
         Rugby             247         21
         Extreme Ironing   96          11


          Which sport caries the greatest risk of injury?
                                                        Slide 18
Training from Edexcel
Session 4
   New material at F Tier – Unit 2

       Sport             Rel Freq   Rel Freq

       Football              37     0.106
                             348
       Rugby                  21    0.085
                             247
       Extreme Ironing        11    0.115
                              96




                                               Slide 19
Training from Edexcel
Session 4
         New material at H Tier

• Risk

         Key idea is that of a cost – usually monetary

      The probability that my freezer will fail next year
      is 0.15 . It would cost £120 to fix it.
      Insurance costs £35. Should I take out insurance?

                                                         Slide 20
Training from Edexcel
           Session 4
           New material at H Tier
           Risk

          Estimate of cost of breakdown = 0.15 × £120
                                        = £18




                                                    Slide 21
Training from Edexcel
  Session 4                           Risk
A company generates electricity from an offshore site with wind turbines.
If a high wind becomes a gale the probability of
damage to the wind turbines increases.
The probability of damage in a gale is 0.04.
The probability of damage in a high wind is 0.005
The probability that a high wind becomes
a gale is 0.3

This site has 50 high wind days each year. Work out an estimate for the number of times
it will be damaged in a period of 10 years                                                          The probability tree
                                                                                          Damage    has been used to
                                                                             0.005                  show the structure of
                                                                                                    the problem so that
                                                                                                    the probability of
                                                         High
                                                                                                    damage on any high
                                                         Wind
                                          0.70                              0.995         No        wind day can be
                                                                                          damage    found.
                                                                                                    The red figures have
                                                                                                    been calculated by
                                                                                           Damage
                                                                              0.04                  subtraction from 1

                                          0.30           Gale


                                                                                          No
                                                                              0.96        damage
                                                                                                      Slide 22
  Training from Edexcel
Session 4

             New material at H Tier

             Midpoint theorem, its converse and the
             intercept theorem




                                                      Slide 23
Training from Edexcel
Session 4

• 5.[A] ABCD is a rectangle. K, L, M and N are the
  midpoints of AB, BC, CD and DA respectively. Use the
  midpoint theorem to show that the quadrilateral KLMN is
  a parallelogram.




                                                  Slide 24
Training from Edexcel
Session 4 Midpoint – a bit more challenging
                                      P
                        Y                                  X



                                                 T
                                  S




                              Q                        R




             S and T are the midpoints of PQ and PR.
             QTX is a straight line with QT = TX
             RSY is a straight line with RS = SY

             Prove (i) XPY is a straight line.
                   (ii) XY = 2QR
                                                               Slide 25
Training from Edexcel
Session 4
• New material at H Tier – Exponential growth and decay


     Key idea – y =abx

      Key idea - compound interest formula

    Applied to population growth and decay,
    radioactivity, decay of chemicals in the body and
    compound interest.
                                                    Slide 26
Training from Edexcel
  Session 4 Exponential Growth/decay

The mass, m grams, of a radioactive substance                 Mass
                                                              (grams)
decreases exponentially as shown in this graph.                         1
                                                                        0

                 Equation of graph is                                   8
                 m = 9×0.8x

                                                                        6


                                                                        4

  (a) Work out the original mass of the substance.
  (b) Work out the mass of the substance after 6 hours.                 2
  (c) (i) Work out the multiplier. (ii) Work out the percentage
  rate of decrease.
                                                                        0   2   4   6        8             1
                                                                                                   Time (t hours)
                                                                                                           0


                                                                                        Slide 27
  Training from Edexcel
Session 4
New material at H Tier – gradients of curves


 Key Idea – the gradient of a curve at a point is equal
 to the gradient of the tangent to the curve at that
 point

   No Calculus!

     Key ideas – gradients of the d/t graph and the v/t
     graph as well as water tanks.
                                                     Slide 28
Training from Edexcel
   Session 4 Gradients
     8.[A] The graph shows the distance, y m, that a car has             y
     travelled during t seconds                                         100

                                                                         90

                                                                         80

                                                                         70

(a) Calculate an estimate of the speed of the car at t = 20.             60
(b) Calculate the average speed of the car between t = 10 and t = 50.
                                                                         50

                                                                         40

                                                                         30

                                                                         20

                                                                         10


                                                                         O    10   20   30    40        50   60   x



                                                                                             Slide 29
Training from Edexcel
Session 4
• New material – Area under a curve


     Key idea – find an estimate for the area under a
     curve (the area between the curve and the x- axis)
     by using trapeziums to approximate the region

       No negative areas - use 4 or 5 trapeziums

        Key idea – area under a v/t graph

                                                    Slide 30
Training from Edexcel
Session 4 Area under a curve
                                                             Velocity m/s
                                                                       18
      4. [A]                                                            0
      The graph gives information about the velocity of a              16
      particle during the first 40 seconds of its motion.               0
                                                                       14
                                                                        0
      (a) Calculate an estimate for the distance travelled             12
          during the first 40 seconds.                                  0
                                                                       10
      (b) State, with a reason, whether your answer to (a) is an        0
      overestimate or underestimate of the true distance                8
                                                                        0
      travelled                                                         6
                                                                        0
                                                                        4
                                                                        0
                                                                        2
                                                                        0
                                                                        0   1   2          3   4   t
                                                                            0   0          0   0

                                                                                    Slide 31
Training from Edexcel
Session 5
• Scheme of Learning F Tier Methods




                                      Slide 32
Training from Edexcel
Session 5
• Scheme of Learning H Tier - Methods




                                        Slide 33
Training from Edexcel
Session 5 Planning and strategy

           Which groups/classes are following the
           course in your school – why this choice?
           What are the advantages and disadvantages?

         In what order are you teaching the course –
         why this choice?
         What are the advantages and disadvantages?


                                                        Slide 34
Training from Edexcel
Session 6
• Resource Review
         Includes
         Methods exemplification booklet
         Applications exemplification booklet
         Matching Doc to Spec A book from Edexcel
         Matching Doc from St Peter’s school
         Book chapters in the LP book
         Further Practice Material.
         New mock papers
         Functional skills - common scenarios
                                                    Slide 35
Training from Edexcel
Session 6
• Exemplification booklets




                             Slide 36
Training from Edexcel
Session 6
• Excel Matching spreadsheets


    Edexcel matchings to the Spec A books


     St Peter’s matchings – skill doc showing which
     skills are present where
                                            M1   M2   A1   A2
        Solve simple quadratic equations
        by factorisation and completing the
        square                              P




                                                                Slide 37
Training from Edexcel
Session 6
• Book Chapters in the LP book
 1 Mid-point/intersecting chord   Methods          Unit 2                H
 2 Linear programming                       Apps            Unit 1       H
 3 Quadratic sequences            Methods          Unit 1                H
 4 Venn diagrams                  Methods          Unit 1                F+H
 5 Probability/Venn diagrams      Methods          Unit 1                F+H
 6 Exponential growth/decay                 Apps            Unit 2       H
 7 Area under curves                        Apps            Unit 2       H
 8 Gradients                                Apps            Unit 2       H
 9 Fin. and Bus. AER                        Apps            Unit 1       F+H
 10 Flowcharts                              Apps            Unit 1       F+H
 11 Spreadsheets                            Apps            Unit 1       F+H
 12 Time series/Moving averages             Apps            Unit 1       F+H
 13 Prob (Risk)                             Apps            Unit 2       F+H
                                                                     Slide 38
Training from Edexcel
Session 6 Venn diagrams Methods Unit 1                                        F+H




                                                                               R
                                                                 F
  1. Some boys were asked if they played football or rugby.                                3
                                                                     19        6
  The Venn diagram shows this information.
                                                                          7




    (a) How many boys were asked if they played football or rugby?
    (b) How many boys played just rugby?
    (c) How many boys do not play football?
    (d) How many boys play both rugby and football?




                                                                                    Slide 39
Training from Edexcel
Session 6                Probability and Venn Diagrams

             3.   (a) On a Venn diagram

                   show the whole numbers from 1 to 12
             set E where E = {2, 4, 6, 8, 10, 12}
             set F where F = {1, 2, 3, 4, 6, 12}

             (b) A number is chosen at random from those in the Venn diagram.

             Find
             (i) P(E) (ii) P(F′) (iii) P(E ∩ F) (iv) P(E U F)




                                                                                Slide 40
Training from Edexcel
Session 6 Further practice material

   Functional skills scenarios.

  Tiling problems – carpet and wall – area, costs,
  percentages, conversion of units




                                                     Slide 41
Course code 10NMB01/02
Session 6 Functional Skills


    Tiling
    Here is a scale drawing of Jim’s floor. Each centimetre
    square on the scale drawing represents 1m2




    Jim wants to put carpet tiles on all his floor.
    Each carpet tile is 1 m2 and costs £7.99
    Work out how much it will cost Jim to put carpet tiles on all his floor.




                                                                               Slide 42
Training from Edexcel
Session 6 Functional Skills
                                                               2m




                                             2m                             2m




      Jim wants to tile this part of a wall.            60cm        60 cm
      He wants to use square tiles with an edge of 20 cm.
      The tiles are sold in boxes of 10.
      Work out the number of boxes he will need.




                                                                                 Slide 43
Training from Edexcel
Session 6 Mock papers
• New papers more like the standard of papers to be set

• F Tier Applications U1 and U2

• F Tier Methods U1 and U2

• H Tier Applications U1 and U2

• H Tier Methods U1 and U2




                                                   Slide 44
Course code 10NMB01/02
Other Goodies
     Mixed up proofs
     Autograph demos
     Compound Int at F




                         Slide 45
Training from Edexcel
 Mixed up proofs
Here are the first 5 terms an arithmetic sequence
           2            5          8          11       14
Prove that the difference between the squares of consecutive terms is always a multiple of 3.

          Step

          1             Square of (n+1)th term = (3n+2)2

          2             Difference of the terms = 18n + 3

          3             Difference of the terms = (9n2+12n+4) - (9n2-6n+1)

          4             (n + 1)th term = 3n-1 +3 = 3n+2

          5             Difference of the terms = 3(6n+1)

          6             Square of nth term = (3n -1)2

          7             Since 6n + 1 is an integer, the difference is a multiple of 3

          8             Difference of the terms = 9n2+12n+ 4 -9n2+6n-1

          9             nth term = 3n -1

          10            Difference of the terms = (3n+2)2 - (3n -1)2

                                                                                        Slide 46
Training from Edexcel
Ask the Expert

• Extensive consultation taught us that customers want access to
  experts to help with subject specific queries

• Ask the Expert will put customers in direct email contact with over
  300 senior subject examiners and verifiers

• Information on all our subject experts will be made available on the
  Edexcel website so customers can see who they are dealing with

• Ask the Expert will be complemented by online subject support
  information and teacher forums, enabling peer-to-peer support


                                                             Slide 47
Course code 10NMB01/02
Results Plus

• Free!
• Especially useful for a unitised examination




                                                 Slide 48
Training from Edexcel

				
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