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GCSE Mathematics Higher Tier Solutions |
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June 2004 Paper 2 |
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1. |
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[3] |
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2. |
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1 share = 8000 ÷ 25 = £320 Bob: 9 ´ 320 = £2880; Viv: 5 ´ 320 = £1600; Mary: 11 ´ 320 = £3520 |
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3. |
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3000 ´ 1.043 = £3374.59 |
[3] |
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4. |
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12x - 21 = 4x + 15 \ 8x = 36 \x = 4.5
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[3] |
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5. |
a. |
V = pr²h = p ´ 2.6² ´ 95 = 2017.5 cm3 |
[3] |
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b. |
Density = mass ÷ volume = 8600 ÷ 2017.5 = 4.26 g/cm3 |
[3] |
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6. |
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4.7 (-4.077) too low 4.8 (1.99) too high 4.75 (-1.07813) too low x = 4.8 (1 d.p.) |
[4] |
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7. |
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PR² = 16.4² + 9.5² = 359.21 PR = 18.95 m |
[3] |
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8. |
a. |
1.49 ´ 108 |
[1] |
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b. |
(5.98 ´ 1024) ÷ 81 = 7.38 ´ 1022 |
[3] |
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9. |
a. |
x² + 2x - 35 |
[2] |
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b. |
8n + 4x = 6x -5 8n = 2x - 5 n = (2x - 5)/8 |
[3] |
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c. |
5x(y - 3x) |
[2] |
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10. |
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[4] |
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11. |
a. |
Height=54 ´ tan 43° = 50.36 m |
[3] |
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b. |
Tan EBC = 50.36/36 = 1.3988 EBC = Tan-1(1.3988) = 54.4° |
[3] |
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12. |
a. |
0.1 and 0.9 on first branch (or 1/10 and 9/10) 0.1 and 0.9 on second branch |
[2] |
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b. |
0.1 ´ 0.9 + 0.9 ´ 0.1 = 0.18 (or 18/100) |
[2] |
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13. |
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Any value between 5.5 and 5.7 |
[5] |
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14. |
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(5x - 3)(2x - 1) x = 3/5 and ½ |
[3] |
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15. |
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x = 1.22 and -0.55 |
[3] |
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16. |
a. |
13 and 11 |
[1] |
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b. c. |
(3.4, 13.2) |
[1] [2] |
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17. |
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[3] |
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18. |
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A = 145.6° |
[3] |
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19. |
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Volume of sphere = 4/3 ´ p ´ 6.53 = 1150.35 Volume of cone = 1/3 ´ p ´ r² ´ 9.4 = 9.84r² 9.84r² = 1150.35 r² = 116.9 \r = 10.8
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[5] |
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20. |
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4.4 |
[3] |
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21. |
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[5] |
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22. |
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Area of sector = 100/360 ´ p ´ 4.6² = 18.46 Area of triangle = ½ ´ 4.6 ´ 4.6 ´ sin 100° = 10.42 Area of shaded region = 18.46 - 10.42 = 8 cm
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[6] |
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23. |
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Distance = 73 ± 0.5 Time = 2.4 ± 0.05 Greatest average speed = greatest distance ÷ least time = 73.5 ÷ 2.35 = 31.3 mph |
[3] |
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24. |
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[2] |
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25. |
a. |
Plot point (1, 48), (4, 81), (9, 148), (16, 236), (25, 348)
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[2] |
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b. |
Estimate y intercept to give b between (30 and 40) Estimate gradient of line to give a = 12.5 (approx) |
[3] |
