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GCSE Mathematics |
RSH Oct-2003 |
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Higher Tier May 2002 Paper 2 |
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1 |
a) |
Increase = 3 500 000
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b) |
(1.04)³ ´ 5000 = £5624.32 |
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2 |
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15 - 4x = 21 \ 15 - 21 = 4x \ 4x = -6 \ x = -1.5 |
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3 |
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x = 2.5 too low x = 2.6 too high x = 2.55 too low \ x = 2.6 (to 1 d.p.) |
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4 |
a) |
Frequency Polygon points at (9.5, 20), (29.5, 45), (49.5, 24), (69.5, 9), (89.5, 2) |
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b) |
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5 |
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AC² = 8.7² - 5.4² = 46.53 \AC = 6.8 |
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6 |
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7 |
a) |
2.886 x 10-8 |
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b) |
6.855 ´ 105 |
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8 |
a) |
8x7y7 |
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b) |
x² - x - 30 |
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c) |
h² = t - d \ d = t - h² |
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9 |
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10 |
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CB=13.5 ´ sin 62° = 11.9 m \BD=11.9 - 4.7 = 7.2 m
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11 |
a) |
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b) |
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c) |
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12 |
a) |
m µ r³ \ m = kr³ When r = 2, m = 80 \ 80 = k (2³) \ 8k = 80 \ k = 10 \m = 10r³ |
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b) |
(i) m = 10 (4³) = 640 g (ii) 270 = 10 r³ \ r³ = 27 \ r = 3 cm |
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13 |
a) |
ÐAOC = 72° Angle at centre is double angle at circumference |
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b) |
ÐOXC = 18° DOXC is a right-angled triangle |
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c) |
ÐADC = 144° ABCD is a cyclic quadrilateral |
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14 |
a) |
Not random, could be a year group eating first or a group of friends |
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b) |
Take a stratified sample to get a proportional number from each year group / gender |
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15 |
a) |
(x - 4)(x + 4) |
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b) |
2x² + 5x - 12 = (2x - 3)(x + 4)
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16 |
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Error = 0.5 mm AB(max) = 3.45 cm, BQ(max) = 4.25 cm AQ(max)² = 3.45² + 4.25² = 29.965 \ AQ(max) = 5.47 cm PQ(max)² = AQ(max)² + AP(max)² = 29.965 + 2.65² = 36.9875 \PQ(max) = 6.08 cm |
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17 |
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Number of employees = 358 Management , Sales = 10, S/ware = 3, H/ware = 3, Admin = 2 |
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18 |
a) |
Similar shape translated down y-axis, cuts y-axis at (0, -1) |
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b) |
Similar shape translated left along x-axis, touches x-axis at (-4, 0) |
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c) |
(i) and (ii) |
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19 |
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SQ² = 8.6² + 10.8² - 2(8.6)(10.8) cos 38° = 44.22 \SQ = 6.65 cm ÐQPS = 74°
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20 |
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21 |
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Mean = 43.5; Standard deviation = 11.68 |
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22 |
a) |
Area of front and back = 3x + 3x = 6x Area of sides = 3(x - 1) + 3(x - 1) = 6x - 6 Area top and bottom = x(x - 1) + x(x - 1) = 2x² - 2x \Surface area = 2x² + 10x - 6 But surface area = 63 \2x² + 10x - 6 = 63 or 2x² + 10x - 69 = 0 |
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b) |
(i)
To give x = 3.88 or - 8.88 (ii) Length = 3.88 cm, Width = 2.88 cm and Height = 3 cm (ignore negative x) |
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