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GCSE Higher June 2013 Non-Calculator

GCSE Higher June 2013 Non-Calculator . Good morning year 11 Once you’ve sat down we’ll begin. GCSE Higher June 2013 Non-Calculator . Before you start the questions, write all the formulas you need on to the formula sheet. GCSE Higher June 2013 Non-Calculator . Q1

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GCSE Higher June 2013 Non-Calculator

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  1. GCSE Higher June 2013 Non-Calculator Good morning year 11 Once you’ve sat down we’ll begin

  2. GCSE Higher June 2013 Non-Calculator Before you start the questions, write all the formulas you need on to the formula sheet

  3. GCSE Higher June 2013 Non-Calculator Q1 Popular question – the answers are there you just need to move the decimal point. Use an estimate (2 x 200=400) 331.705 (300,000 ÷ 2 = 150,000) 179,300

  4. GCSE Higher June 2013 Non-Calculator Q2 Find each separately 15% - 10% = 24, 5% = 12 so 15% = 36 ¼ is 60 so ¾ is 180 Total so far is 216 so 24 don’t know Or ¾ is 75% plus 15% = 90% leaving 10% which is also 24

  5. GCSE Higher June 2013 Non-Calculator Q3 do as comes first 2 4,7,8 3 5,8,8,3,0,7,3 4,5,1,4,1,2 So you have 4,7,8 0,3,3,5,7,8,8 1,1,2,4,4,5 Don’t forget the key and the units

  6. GCSE Higher June 2013 Non-Calculator Q4 6 + 3t 6x2 + 15x m2 + 13m + 30

  7. GCSE Higher June 2013 Non-Calculator Q5 Factor tree which will give 3 x 5 x 5 x 7 Can be written with powers

  8. GCSE Higher June 2013 Non-Calculator Q6 If the mean is 10 then they must add to 40 The total is 33 The other must be 7

  9. GCSE Higher June 2013 Non-Calculator Q7

  10. GCSE Higher June 2013 Non-Calculator Q7b Note single transformation which is Rotation of 180° with centre of (0,1)

  11. GCSE Higher June 2013 Non-Calculator Q8 As an estimate use 20 litres and 300 days So number of bottles in a day = 40 So total is 300 x 40 = 12 000 Not asked but actual is 12152

  12. GCSE Higher June 2013 Non-Calculator Q9 You can do counts of both Matt: 50,100,150,200,250,300,350,400 Dan: 80,160,240,320,400 So they meet after 400 seconds Or find the LCM of 50,80 which is 400 Answer is how many laps though which is 8 for matt and 5 for dan - RTFQ

  13. GCSE Higher June 2013 Non-Calculator Q10 Perimeter is length around outside (yes Rose a snail trail!) Add to get 2(4 + 3x + x + 6) = 8x + 20 So 8x + 20 = 32 8x = 12 x = 1.5

  14. Ian went at 66 km/h which for 20 mins is 22 km so we can draw his line which is in red and is below Debbie’s line which means she is faster or find Debbie’s speed – she does 25 km in 20 mins so will do three times that in an hour so her speed is 75km/h Remember it’s a * question GCSE Higher June 2013 Non-Calculator Q11

  15. Make a table if you want but you only need three points for a straight line so X = 0 y = 0 + 5 = 5 X = 2 y = 1 + 5 = 6 X = 4 y = 2 + 5 = 7 GCSE Higher June 2013 Non-Calculator Q12

  16. Draw a cricle of 5 cm from the point C and then a line on a bearing of 037 (bearings – clockwise from North) The line goes inside the circle so the ship will get too close GCSE Higher June 2013 Non-Calculator Q13

  17. GCSE Higher June 2013 Non-Calculator Q14a b 8x – 3 ≥ 6x + 4 8x – 6x ≥ 4 + 3 2x ≥ 7 x ≥ 3.5

  18. GCSE Higher June 2013 Non-Calculator Q15 500 sheets will be 500 x 9 x 10-3 high Which is 500 x 0.009 which is 4.5 cm As the tray is only 4 cm deep then NO

  19. GCSE Higher June 2013 Non-Calculator Q16 Reverse percentage ( what was it before) 30% off means 70% in sale 70% = £350 10% = 350 ÷ 7 = 50 100% = 50 x 10 = £500

  20. GCSE Higher June 2013 Non-Calculator Q17 Shape is a PRISM (formula sheet) Cross section is a trapezium(formula sheet) CSA = ½ (1.3 + 0.5) x 2 = 1.8 Volume = CSA x width = 1.8 x 1 = 1.8 In first 30 mins it drops 20 cm which is a cuboid so its volume would be 0.2 x 1 x 2 = 0.4 so it can pump 0.8 in an hour Time then is 1.8 ÷ 0.8 = 18 ÷ 8 = 2 ¼ hours How much more time = 2 ¼ - ½ which is 1 ¾ hours RTFQC

  21. GCSE Higher June 2013 Non-Calculator Q18 eliminating the x eqn 1 x 3 12x + 21y = 3 ③ eqn 2 x 4 12x + 40y = 60 ④ Subtract ④-③ 19y = 57 y = 3 Put y=3 in eqn 1 4x + 21 = 1 4x = -20 x = -5 Check with eqn 2 3 x -5 + 10x 3 = -15 + 30 = 15 OR

  22. GCSE Higher June 2013 Non-Calculator Q18 eliminating the y eqn 1 x 10 40x + 70y = 10 ③ eqn 2 x 7 21x + 70y = 105 ④ Subtract ③ - ④ 19x = -95 x = -5 y = 3 Put x=-5 in eqn 1 -20 + 7y = 1 7y = 21 y = 3 Check with eqn 2 3 x -5 + 10x 3 = -15 + 30 = 15

  23. GCSE Higher June 2013 Non-Calculator Q19 turn all into decimals 5-1 = 1/5 = 0.2 50 = 1 So order is -5, 5-1 , 0.5, 50

  24. Easiest way is to find the area of the three triangles and subtract from rectangle • MD=MC= 2x and AN is 3x • Δ NMD has sides of x and 2x so area is x² • Δ BMC has sides of 4x and 2x so area is 4x² • Δ ANB has sides of 3x and 4x so area is 6x² • Total white area is 11x² • Grey area is area of square (16x²) minus white which gives 5x² GCSE Higher June 2013 Non-Calculator Q20

  25. GCSE Higher June 2013 Non-Calculator Q21 Cumulative frequencies 4,9,25,52,57,60 Median is 172 cm LQ= 166, UQ = 177, IQR = 11 cm

  26. GCSE Higher June 2013 Non-Calculator Q22 - similar shapes Lengths of AC and DF show the lengths are twice which means that areas will be four times bigger and volumes eight times Δ DEF will have an area of 4 x 10 = 40 Prism Q’s length will be twice as long so 30cm The volume will then be 30 x 40 (formula sheet) which gives 1200cmᶾ

  27. GCSE Higher June 2013 Non-Calculator Q23 simplify – the hint is to factorise the top and the bottom Top 4(x + 5) already so (x + 5) must be in the bottom Bottom x² + 2x – 15 = (x – 3)(x + 5) So simplified is

  28. GCSE Higher June 2013 Non-Calculator Q24 class width 10 5 5 10 15 frequency d 1.2 3 2.6 1.8 0.2

  29. GCSE Higher June 2013 Non-Calculator Q24

  30. GCSE Higher June 2013 Non-Calculator Q25 multiply the (x + a)² + b = x² + 2ax + a² + b If this is to be x² - 8x + 21 then matching give that The x’s must be the same so 2a = -8 so a = -4 Numbers on end must match so a² + b = 21 so 16+b=21 so b=5 So x² - 8x + 21 = (x – 4)² + 5 This is lowest when bracket is 0 so x = 4 and it will b 0 + 5 = 5 So M is (4,5)

  31. GCSE Higher June 2013 Non-Calculator Q26 to make £2.50 she could have (5 x 50p) or (3x50P and £1) or (50p and 2 x £1) and only the last is 3 coins P( £1 then £1 then 50p) = 3/10 x 2/9 x 7/8 = 42/720 P( £1 then 50p then £1) = 3/10 x 7/9 x 2/8 = 42/720 P(50p then £1 then £1) = 7/10 x 3/9 x 2/8 = 42/720 You can say all three the same Overall P = 126/720 = 63/360=21/120=7/40

  32. NQ + QR = NR From the first part and the ratio NQ =2/5 of SQ QR = PS = b All together makes NR = 2/5(a – b) + b Which is 2/5 a + 3/5 b GCSE Higher June 2013 Non-Calculator Q27 PS + SQ = PQ so SQ= PQ-PS which gives a - b

  33. GCSE Higher June 2013 Non-Calculator From the graph ¼ the way through the cycle so 90° y = 2 Cos x just doubles all the y values Q28

  34. GCSE Higher June 2013 Non-Calculator Grade boundaries (out of 100) U 0 to 11 D 12 to 23 C 24 to 42 B 43 to 62 A 63 to 79 A* 80 or more

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