GCSE Mathematics Paper2

1 GCSE Bitesize examinations General Certificate of Secondary Education MATHEMATICS Higher Tier Paper 2 Calculator Marking scheme Unless otherwise stated, correct answers only should be accepted. 2 Answer all questions in the spaces provided. 1. 19.9 (3 marks) 2 marks for showing 19.87 or 19.870 2 marks for 16.27026787 + 3.6 1 mark for showing 7 . 2 3.6 1 2.50798724 41.421736 + + 2. 245g (2 marks) (1 mark for 21 12 140 × ) 3. (a) (i) 8 10 567 . 1 156700000 × = (ii) 4 10 41 . 3 000341 . 0 − × = (1 mark) (b) (i) 260000 10 6 . 2 5 = × (ii) 00902 . 0 10 02 . 9 3 = × − (1 mark) (c) 4 23 10 4 10 9 . 6 10 76 . 2 × = ×× − (2 marks) 1 mark for showing 7 10 x 6.81122449 or 8 10 x 9 0.68112244 4. c=2a−b (3 marks) 1 mark for showing 3c+b=2c+2a 5. 1.05 km (3 marks) 2 marks for showing an un-rounded number 1 mark for correct diagram, and 1 mark for showing 3.4 × cos72° or 3.4 sin 18 6. (a) 0.004 km (1 mark) (b) 30 000 ml (1 mark) (c) 800 mm2 (2 marks) 3 7. £194.05 (3 marks) 2 marks for showing £1793.05, or 1 mark for showing £267.05 8. (a) 27x6y9 (2 marks) 1 mark if 27 or x6 or y9 seen (b) 1 − x x (3 marks) 1 mark for x(x + 4) 1 mark for (x + 4)(x – 1) 9. Fast Coach is better. (2 marks) (i) It has a lower average journey time, so the trains get to Manchester quicker. (1 mark) (ii) It has a lower inter-quartile range of journey times, so it is more reliable. (1 mark) 10. (a) 58.8816 (2 marks) (b) 57.4425 (2 marks) 1 mark if 2 of 10.35, 10.44, 5.55, 5.64 seen 2 marks if 3 or 4 of 10.35, 10.44, 5.55, 5.64 seen 11. 3.8 (4 marks) 2 marks for working shown but incorrect conclusion. If no working shown, then only award 1 mark for answer) 4 12. (a) (3 marks) 3 marks for all correct, 2 marks for one error, and 1 mark for two errors. (b) 49 25 (2 marks) 1 mark for showing 49 16 49 9 + 5 13. Midpoint ⎟⎠ ⎞ ⎜⎝ ⎛ 2 , 23 (2 marks) 1 mark for showing ⎟⎠ ⎞ ⎜⎝ ⎛ + + − 23 1 , 2 5 2 Length 7.28 (2 marks) 1 mark for showing 2 2 2 7 + 14. 22.3° (4 marks) 1 mark each for showing correct substitution into cosine rule and/or correct simplification of cosine rule and/or cos A = 0.8 1 mark for 100 80 2 60 -100 80 cos 2 2 2 × ×+ = A 1 mark for cos A = 0.8 6 15. (a) Fill in the following table for the function: y=x2 −3x−3 (3 marks) (b) Plot the graph (2 marks) 1 mark for one error, 0 marks for more errors. (c) 3.8, –0.8 (3 marks) Accept answers ±0.2 (d) –1.4, 4.4 (3 marks) Accept answers ±0.2 x –2 –1 0 1 2 3 4 5 y 7 1 –3 –5 –5 –3 1 7 7 16. Ice-Cream Stall Weather Profit 0.78 Sunny 0.32 Break even 0.07 Dull 0.5 Loss 0.15 Raining 0.18 (2 marks) (b) No. They are not independent. The profit on ice-cream depends on good weather. (2 marks) For 2 marks must show ‘No’ and ‘not independent’ 17. (a) No. of those to survey Management 66 Administrative 120 Clerical 180 Semi-skilled 72 Un-skilled 162 (4 marks) 4 marks for showing actual number of those to be surveyed (column 1) 3 marks for showing these not rounded to a whole number 1 mark for showing the worked out percentages (column 2) or 1 mark for showing 12628 x 11/100 x 5/100 (b) Conduct the survey on-the-job to ensure that responses are in the context of the work. (1 mark) 1 mark for any sensible equivalent e.g. question people off-the-job so people are not scared of being overheard. 8 18. (a) xx x 3 3 8 2 2 + + (2 marks) 1 mark for showing : x x x x x 3 2 3 3 9 2 − + + b) x = -8.32 and x = -0.18 (3 marks) 1 mark for substitution into formula a ac b b x 2 ) 4 ( 2 − ± − = and showing a = 2 b = 17 and c = 3 1 mark for -8.3197 AND – 0.1803 19. 2a (1 mark) If the top angle is a then x = 2a If x = 2a then y = 360 – 2a because they make a full turn. (1 mark) Then z = half of this so 180 – a (1 mark) So, a + z = a +180 – a = 180. So opposite angles add up to 1800 (1 mark) 20. (a) Mid-price game: £ 12.49 (2 marks) (b) Full-price game: £ 27.99 (2 marks) 1 mark for showing 3m + 2f = £93.45 AND 5m + 3f = £146.42 1 mark for showing successful setting out to add or subtract. 9 21. (5 marks) 1 mark for each correct line 1 mark for shading 1 mark for complete accuracy 10 22. 24 . 35s A = (3 marks) 2 marks for not rounding the answer. 1 mark for showing 2 3 . 2 7 . 6 k = and/or 1 mark for showing k = 35.4 (b) s = 2.61cm (3 marks) 2 marks if not rounded to 2 significant figures. 1 mark for showing 24 . 35 2 . 5 s = and/or 1 mark for 2 . 5 4 . 35 2 = s 23. (a) 600 (1 mark) (b) 160 < h ≤ 170 (1 mark) (c) 160 < h ≤ 170 (2 marks) (d) 160.5 cm (3 marks) 1 mark for using midpoints (135, 145, 155, etc) (e) Cumulative frequency 40 100 280 480 570 600 1 mark if 3 correct (2 marks) (f) Definite points should be plotted at (130, 0), (140, 40), (150, 100), (160, 280), (170, (480), (180, 570) and (190, 600) and joined with a smooth curve. (2 marks) (g) 400 (380 – 420 acceptable) (1 mark)