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GCSE Mathematics Higher Tier Solutions |
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June 2003 Paper 1 |
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1. |
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[3] |
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2. |
a. |
4 |
[1] |
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b. |
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[3] |
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c. |
Solution: x=-0.886, y=3 Solution: x=3.386, y=3 |
[2] |
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d. |
2x² - 5x - 3 = 3 which re-arranges to 2x² - 5x - 6 = 0 |
[1] |
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3. |
(i) (ii) |
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[3] |
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4. |
a. |
5x - 6 = 30 - 3x \ 8x = 36 \ x = 36/8 or 9/2 or 4 ½ or 4.5 |
[3] |
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b. |
8y - 12 - 3y - 15 = 5y - 27
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[2] |
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5. |
a.
b. |
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[2]
[2] |
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6. |
a. |
Least capacity = 245 ml Greatest capacity = 255 ml |
[2] |
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b. |
20 ´ largest jug = 20 ´ 255 = 5100 ml
(5.1 litres = 5100 ml; 1/10 th of a litre = 100 ml) Bucket: least capacity = 5100 - 50 = 5050 ml Smallest bucket with largest jug will not always fit. |
[5] |
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7. |
a. |
x² - 4x - 3x + 12 = x² - 7x + 12 |
[2] |
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b. |
2n + 5 = 24 - 9t \ 9t = 19 - 2n \ t = (19 - 2n)/9 |
[3] |
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c. |
(i) (x + 9) (x - 2) (ii) x = -9, 2 |
[3] |
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8. |
a. |
Angle B = 35°, angle F = 81° Angles the same in both triangles \ triangles are similar |
[1] |
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b. |
Ratios The three corresponding sides are not in the same ratio \ triangles are not similar. |
[3] |
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9. |
a. |
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[2] |
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b. |
0.6 ´ 0.9 + 0.4 ´ 0.8 = 0.54 + 0.32 = 0.86 (fractional equivalents accepted) |
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10. |
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Length, none, area, volume |
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11. |
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[3] |
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12. |
a. |
[3] |
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b. |
(i) when x = 2, y = 50 ÷ 4 = 12.5 (ii) when y = 0.5 0.5 = 50/x² \x² = 100 \x = 10 or –10 |
[1] [2] |
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13. |
a. |
142° Cyclic quadrilateral |
[4] |
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b. |
76° Angle at centre is double angle on circumference |
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c. |
49° Right angled triangle, Alternate angle |
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14. |
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Enlargement, scale factor –3, centre of enlargement (1, 4) |
[3] |
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15. |
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(2x - 9)(2x + 9) x = 4.5, -4.5 |
[3] |
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16. |
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Area of rectangle = (6x)(5x) = 30x² Area of circle = p(2x)² = 4x²p Area remaining = 4x²p - 30x² |
[4] |
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17. |
a. |
[2] |
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b. |
Any square number |
[1] |
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c. |
(i) Ö2 (any other similar value) (ii) p (any other similar value) |
[1] [1] |
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d. |
[2] |
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18. |
a. |
Area of bars = 2´10 + 4´10 + 3.5´10 + 1.25´20 = 20 + 40 + 35 + 25 = 120 |
[3] |
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b. |
20 |
[1] |
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19. |
a. |
Shift left by 6 |
[2] |
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b. |
Shift up by 6 |
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c. |
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[3] |
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20. |
a. |
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[3] |
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b. |
1/13 |
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21. |
a. |
Gradient of tangent at t = 25s in the range 0.3 to 0.6 |
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(i) 470 m (ii) 470 + 900 = 1370 m |
[3] [1] |
