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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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Edexcel Gcse Maths, Michael Flowers, Trevor Johnson, GCSE Mathematics, Tony Tanner, GCSE Maths, FREE Super Saver, Foundation tier, Homework Book, Trevor Tanner

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Linear Maths Edexcel Gcse Mock Paper Non Calculator document sample

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