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Slide 1 Course code 10NMB01 GCSE Mathematics Linked Pair Pilot – Beginning to teach 10NMB01 Presented by Edexcel Principal Examiners

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Slide 2 Course code 10NMB01/02 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

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Slide 3 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)

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Slide 4 Course code 10NMB01/02 Session 2 Examination Timetable Applications - Final dates Please note, first certification of this qualification is in June 2011 (until June 2013) 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)

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Slide 5 Course code 10NMB01/02 Session 2 Examination Timetable Methods - Final dates 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) Monday 13 June

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Slide 6 Course code 10NMB01/02 Session 2 Examination Timetable Methods - Final dates 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) Monday 21st June

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Slide 7 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

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Slide 8 Course code 10NMB01/02 Session 3 Spreadsheets – initial examples were judged to be inadequate!

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Session 3 Slide 9 Training from Edexcel ABCDEF 1 Length (m)Width (m)Area Wool £20 per m ² Nylon £15 per m ² Sisal £10 per m ² 2 43 3 54 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.

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Slide 10 Course code 10NMB01/02 Session 3 Flowcharts – what symbols are required? Process Decision Start/Stop Input/Output

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Slide 11 Course code 10NMB01/02 Session 3 Currency calculations at F Tier Financial Calculations at F tier (Personal Finance)(Index Numbers)

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Slide 12 Training from Edexcel Session 3 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. Currency calculations at F Tier

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Slide 13 Training from Edexcel 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? Session 3

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Slide 14 Course code 10NMB01/02 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

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Session 3 Similar Triangles at F tier Slide 15 Training from Edexcel 4 cm 6 cm 8 cm y cm 60 o 40 o xoxo These two triangles are similar. (a) Write down the value of x (b) Find the value of y

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Slide 16 Training from Edexcel Session 3 H Tier Intersecting chords – resource material Linear Programming – resource material

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Slide 17 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

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Slide 18 Training from Edexcel Session 4 New material at F Tier – Unit 2 Risk Here is some information about injuries in some sports SportNumber of games Number of injuries Football34837 Rugby24721 Extreme Ironing9611 Which sport caries the greatest risk of injury?

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Session 4 Slide 19 Training from Edexcel New material at F Tier – Unit 2 SportRel Freq Football0.106 Rugby0.085 Extreme Ironing0.115

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

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Slide 21 Training from Edexcel Session 4 New material at H Tier Risk Estimate of cost of breakdown = 0.15 × £120 = £18

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Session 4 Risk Slide 22 Training from Edexcel High Wind Gale Damage No damage Damage No damage 0.70 0.30 0.005 0.995 0.04 0.96 The probability tree has been used to show the structure of the problem so that the probability of damage on any high wind day can be found. The red figures have been calculated by subtraction from 1 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

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Slide 23 Training from Edexcel Session 4 New material at H Tier Midpoint theorem, its converse and the intercept theorem

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Slide 24 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.

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Slide 25 Training from Edexcel Session 4 Midpoint – a bit more challenging P QR S T XY 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

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Slide 26 Training from Edexcel Session 4 New material at H Tier – Exponential growth and decay Key idea – y =ab x Key idea - compound interest formula Applied to population growth and decay, radioactivity, decay of chemicals in the body and compound interest.

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Session 4 Exponential Growth/decay Slide 27 Training from Edexcel 2 4 6 8 1010 2468 1010 0 Time (t hours) Mass (grams) Equation of graph is m = 9×0.8 x The mass, m grams, of a radioactive substance decreases exponentially as shown in this graph. ( a) Work out the original mass of the substance. (b) Work out the mass of the substance after 6 hours. (c) (i) Work out the multiplier. (ii) Work out the percentage rate of decrease.

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Slide 28 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.

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Session 4 Gradients Slide 29 Training from Edexcel 8.[A] The graph shows the distance, y m, that a car has travelled during t seconds 10 20 30 40 50 60 70 80 90 100 102030405060 O x y (a) Calculate an estimate of the speed of the car at t = 20. (b) Calculate the average speed of the car between t = 10 and t = 50.

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Slide 30 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

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Slide 31 Training from Edexcel Session 4 Area under a curve 4. [A] 2020 4040 6060 8080 10 0 12 0 14 0 16 0 18 0 1010 2020 3030 4040 0 t Velocity m/s The graph gives information about the velocity of a particle during the first 40 seconds of its motion. (a)Calculate an estimate for the distance travelled during the first 40 seconds. (b) State, with a reason, whether your answer to (a) is an overestimate or underestimate of the true distance travelled

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Slide 32 Training from Edexcel Session 5 Scheme of Learning F Tier Methods

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Slide 33 Training from Edexcel Session 5 Scheme of Learning H Tier - Methods

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Session 5 Planning and strategy Slide 34 Training from Edexcel 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?

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Slide 35 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

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Slide 36 Training from Edexcel Session 6 Exemplification booklets

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Slide 37 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 M1M2A1A2 Solve simple quadratic equations by factorisation and completing the square

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Slide 38 Training from Edexcel Session 6 Book Chapters in the LP book 1 Mid-point/intersecting chordMethodsUnit 2H 2 Linear programmingAppsUnit 1H 3 Quadratic sequencesMethodsUnit 1H 4 Venn diagramsMethodsUnit 1F + H 5 Probability/Venn diagramsMethodsUnit 1F + H 6 Exponential growth/decayAppsUnit 2H 7 Area under curves AppsUnit 2H 8 GradientsAppsUnit 2H 9 Fin. and Bus. AERAppsUnit 1F + H 10 FlowchartsAppsUnit 1F + H 11 SpreadsheetsAppsUnit 1F + H 12 Time series/Moving averagesAppsUnit 1F + H 13 Prob (Risk)AppsUnit 2F + H

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Session 6 Venn diagrams Methods Unit 1F + H Slide 39 Training from Edexcel 1. Some boys were asked if they played football or rugby. The Venn diagram shows this information. F R 7 196 3 (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?

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Session 6 Probability and Venn Diagrams Slide 40 Training from Edexcel 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)

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Slide 41 Course code 10NMB01/02 Session 6 Further practice material Functional skills scenarios. Tiling problems – carpet and wall – area, costs, percentages, conversion of units

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Session 6 Functional Skills Slide 42 Training from Edexcel Tiling Here is a scale drawing of Jim’s floor. Each centimetre square on the scale drawing represents 1m 2 Jim wants to put carpet tiles on all his floor. Each carpet tile is 1 m 2 and costs £7.99 Work out how much it will cost Jim to put carpet tiles on all his floor.

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Session 6 Functional Skills Slide 43 Training from Edexcel 2 m 60cm 2 m 60 cm Jim wants to tile this part of a wall. 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.

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Slide 44 Course code 10NMB01/02 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

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Other Goodies Slide 45 Training from Edexcel Mixed up proofs Autograph demos Compound Int at F

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Mixed up proofs Slide 46 Training from Edexcel Step 1Square of (n+1)th term = (3n+2) 2 2Difference of the terms = 18n + 3 3Difference of the terms = (9n 2 +12n+4) - (9n 2 -6n+1) 4(n + 1)th term = 3n-1 +3 = 3n+2 5Difference of the terms = 3(6n+1) 6Square of nth term = (3n -1) 2 7Since 6n + 1 is an integer, the difference is a multiple of 3 8Difference of the terms = 9n 2 +12n+ 4 -9n 2 +6n-1 9nth term = 3n -1 10Difference of the terms = (3n+2) 2 - (3n -1) 2 Here are the first 5 terms an arithmetic sequence 2581114 Prove that the difference between the squares of consecutive terms is always a multiple of 3.

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Slide 47 Course code 10NMB01/02 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

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Slide 48 Training from Edexcel Results Plus Free! Especially useful for a unitised examination

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