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GCSE Mathematics Higher Tier Solutions |
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June 2004 Paper 1 |
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1. |
a. |
w9 |
[1] |
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b. |
12m + 3 - 8m - 12 = 4m - 9 |
[2] |
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2. |
a. |
4n - 3 |
[2] |
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b. |
(n + 1)(n + 3) |
[2] |
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3. |
a. |
22 ´ 33 ´ 5 |
[3] |
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b. |
3 ´ 5 or 15 |
[1] |
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4. |
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[3] |
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5. |
a. |
Reflection in the line y = -x |
[2] |
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b. |
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[2] |
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6. |
a. |
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[1] [1] [2] |
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7. |
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3x + 4y = 2 (1) 5x + 6y = 6 (2) (1) ´ 5 15x + 20y =10 (3) (2) ´ 3 15x + 18y = 18 (4) (3)-(4) 2y = -8 \y = -4 Into (1) 3x - 16 = 2 \3x = 18 \x = 6 |
[4] |
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8. |
a. |
Least mass = 9.5 kg Greatest mass = 10.5 kg |
[2] |
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b. |
(i) Least mass
in 100 blocks = 9.5 ´
100 kg = 950 kg (ii) 950 + 5 ´
9.5 = 997.5
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[5] |
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9. |
a. |
3a6b |
[2] |
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b. |
(x + 5)(x - 4) |
[2] |
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10. |
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Length, Volume, None, Area |
[2] |
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11. |
a. |
8x £ 18 \ x £ 18/8 (9/4 or 2.25) |
[2] |
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b. |
2 |
[1] |
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12. |
a. |
[2] |
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b. |
[2] |
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13. |
a. |
Clinic B by 4 minutes |
[2] |
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b. |
Clinic A, 34 people still waiting but only 8 still waiting at clinic B |
[2] |
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14. |
a. |
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[2] |
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b. |
(i) 1 (ii) 0 |
[1] [1] |
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c. |
105° or -105° |
[1] |
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15. |
a. |
w µ f² \w = kf² 100 = k ´ 25 \k = 4 \w = 4f² |
[3] |
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b. |
w = 4 ´ 4² = 64 |
[1] |
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c. |
1600 = 4f² \f² = 400 \f = 20 (or -20) |
[2] |
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16. |
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[5] |
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17. |
a. |
42° Tangent meets radius at 90°, radius is perpendicular to tangent |
[3] |
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b. |
48° Alternate segment or angle at centre twice angle at circumference |
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18. |
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[2] |
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19. |
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1/3 |
[2] |
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20. |
a. |
3x8y-2 |
[2] |
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b. |
16x12y8 |
[2] |
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c. |
12y² |
[2] |
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d. |
2x |
[1] |
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21. |
a. b. |
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[2] [2] |
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c. |
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[2] |
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22. |
a. |
(i) x (ii) x+y (iii) ½ (8x + y) + x – ½ (4x + y) = 3x |
[1] [1] [2] |
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b. |
Parallel and three times longer |
[2] |
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23. |
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Area = 1.5 + 3.5 + 3.5 + 1.5 = 10 |
[3] |
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24. |
a. |
0.4 ´ 0.4 = 0.16 (or 4/10 ´ 4/10 = 16/100) |
[2] |
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b. |
1 - P(no black) = 1 - (0.6 ´ 0.6) = 0.64 |
[3] |
