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GCSE Mathematics |
RSH Oct-2003 |
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Higher Tier May 2002 Paper 1 |
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1 |
a) |
700 = 2² ´ 5² ´ 7 |
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b) |
(2² ´ 5² ´ 7) ´ 7 = 2² ´ 5² ´ 7² = (2 ´ 5 ´ 7)² is a perfect square \700 ´ 7 = 4900 is the smallest multiple of 700 which is a perfect square. |
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2 |
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16x - 5 = 3(4x + 7) \16x - 5 = 12x + 21 \16x - 12x = 21 + 5 \4x = 26 \ x = 6 ½ |
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3 |
a) |
Octagon: side = x \ Perimeter = 8x Pentagon: side = x + 6 \ Perimeter = 5(x + 6) Perimeter of Octagon = Perimeter of Pentagon + 3 \8x = 5(x + 6) + 3 |
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b) |
8x = 5(x + 6) + 3 \8x = 5x + 30 + 3 \3x = 33 \ x = 11 \Length of side = 17 cm |
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4 |
a) |
9 shares = £270 \ 1 share = £30 Jill’s 5 shares = 5 ´ £30 = £150; Alan’s 4 shares = 4 ´ £30 = £120 |
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b) |
Alan’s 4 shares = £136 \ 1 share = £34 Profit is 9 shares in total \ Profit = 9 ´ £34 = £306 |
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5 |
a) |
Image has coordinates A`(-4, 2), B`(-2, -3), C`(3, 1) |
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b) |
Image has coordinates (-3, 0), (-3, 3) and (-2, 3) |
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6 |
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70 out of 180 had brown eyes There are 1650 pupils in the school Estimated number with brown eyes = |
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7 |
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8 |
a) |
3xy(y-2) |
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b) |
(x + 4)(x - 2) |
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9 |
a) |
Values: 12, 68, 112, 132, 148, 156, 160 |
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b) |
Graph |
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c) |
Interquartile range 34×5 - 16 = 18×5 |
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d) |
60% of 160 = 96 |
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10 |
a) |
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b) |
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11 |
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Volume; Length; Volume; Area |
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12 |
a) |
35 - 7 > 2n + 3n \ 5n < 28 \ n < 5×6 |
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b) |
3n > 1 \n > \ < n < 5×6 Integer values of n: 1, 2, 3, 4, 5 |
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13 |
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a(3t - 2p) = p(3b - w) - w \3at –2ap = 3pb - pw - w \ 3at + w = 3pb - pw + 2ap \3at + w = p(3b - w + 2a) \ |
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14 |
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Ratio of radii is 1 : 2 \Ratio of volumes is 1 : 2³ or 1 : 8 \Volume of large cylinder = 8 ´ 200 = 1600 cm³ |
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15 |
a) |
(i) Gradient at x = ½ is approx. = 0 (ii) Gradient at x = 1 is approx. = 1 |
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b) |
Graph |
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c) |
x² - x - 5 = - x² \2x² - x - 5 = 0 Solution is where y = x² - x - 5 meets y = -x² i.e. at x = -1.35 and x = 1.8 |
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16 |
a) |
Graph of y = sin x |
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b) |
Minimum value of y is -1 Maximum value of y is 1 |
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17 |
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Values: 1.8, 4, 2.5, 0.5 |
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a) |
Histogram |
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b) |
Area for heights at least 142cm = (4 ´ 8) + 25 + 10 Estimate is 67 children |
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18 |
a) |
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b) |
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c) |
(i) ¼ (ii) 25 |
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d) |
(i) 4³y6x9 (ii) a6 |
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19
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Mean = 76.8 - 1 = 75.8p Standard Deviation unchanged at 2.8p |
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20 |
a) |
(i) OP = 1/3 x (ii) OR = 1/6 y (iii) YX = x - y |
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b) |
Proof |
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c) |
ZX is parallel to RP and is six times longer |
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21 |
a) |
0.7 ´ 1 + 0×3 ´ 0×2 = 0×7 + 0×06 = 0×76 |
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b) |
76 correct in every 100 \38 correct in every 50 \114 correct in every 150 |
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