GCSE Mathematics Higher Tier Solutions

November 2002 Paper 2

1.

6x - 30 = 4x + 1\2x = 31 \x = 15.5

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2.

a.

Frequency Polygon

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b.

  \ Mean price = 81.55 ´ 1000 = £81550

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3.

3000 ´ 0.85³ = £1842.38

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4.

Volume = 78 ´ 54 = 4212 cm³

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5.

a.

Least: 18.45 cm; Greatest: 18.55 cm

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b.

Least: 30 ´ 18.45 = 553.5 cm; Greatest: 30 ´ 18.55 = 556.5 cm

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6.

a.

15.2 - 10.6 = 4.6

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7.

In between 1.36 and 1.365

x = 1.36 (2 d.p.)

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8.

The original bill = 89.30 ÷ 1.175 = £76

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9.

a.

Tree diagram 1^st Branch 2/5 and 3/5; 2^nd Branch 2/5 and 3/5; 2/5 and 3/5;

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b.

c.

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10.

a.

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b.

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c.

    (i)  (x - 7)(x + 2)

    (ii)  x = 7 and x = -2

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11.

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12.

a.

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b.

When s = 5, h = 0.05 ´ 5² = 1.25 m

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c.

When h = 0.45, 0.45 = 0.05 ´ s²
\s² = 9 \ s = 3

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13.

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14.

a.

Zero

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b.

The solution is where the line y = 1 cuts x² - 3x - 4 = 0
i.e. at x = 4.2 and -1.19

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c.

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15.

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16.

a.

[1]

[2]

b.

(i)                 Groups not in proportion to sizes

(ii)               Easier / less calculation

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17.

a.

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b.

y axis at (0, -1)

x axis when 4x² - 1 = 0 or x² = ¼  \x = -½ and x = ½
i.e. at (-½, 0) (½ , 0)

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18.

Using the Cosine Rule to find TS

Then the Sine Rule to find ÐTSR

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19.

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20.

a.

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b.

Mean = 16.14 years

Standard Deviation = 1.34 years

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21.

a.

Let the radius BO = r

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b.

Using Area of a triangle = ½ abSinC

Area = ½ ´ 3.8 ´ 3.8 ´ sin 75° = 6.97 cm²

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