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(a) Work out $16 - 8 \div 2 + 2 \times 4$.
Answer(a) ................................. [1]
(b) Work out $(8 \times 10^{-4}) \times (2 \times 10^{-3})$, giving your answer in standard form.
Answer(b) ................................. [2]
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Solve.
(a) $2x - 3(1 - 4x) = 2(11 - 3x)$
Answer(a) $x = \text{..............................................................}$ [3]
(b) $|4x - 3| = 11$
Answer(b) $x = \text{..............................................................}$ [2]
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x varies as the square of y.
When y = 4, x = 32.
Find x when y = 5.
Answer x = \text{.....................} [3]
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598
Two fair dice, each numbered 1, 2, 3, 4, 5, 6, are rolled and the total score is recorded. Find the probability that the total score is
(a) 12,
Answer(a) .................................................................[2]
(b) 13,
Answer(b) .................................................................[1]
(c) 7.
Answer(c) .................................................................[2]
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a = \begin{pmatrix} 5 \\ -12 \end{pmatrix}, \ b = \begin{pmatrix} 2 \\ -3 \end{pmatrix}
(a) Find \ a - 3b. [2]
(b) Work out \ |a|. [2]
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Factorise.
(a) $8ax - by + 2ay - 4bx$
Answer(a) .............................................................. [2]
(b) $3x^2 - 5x - 12$
Answer(b) .............................................................. [2]
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569
(a) Find the value of $6^0$.
Answer(a) ................................................ [1]
(b) Write $5^{-2}$ as a fraction.
Answer(b) ................................................ [1]
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588
A, B, C, and D lie on a circle, centre O.
AD is parallel to OC and angle $ADC = 108^{\circ}$.
Find
(a) angle $ABC$,
Answer(a) ............................................................... [1]
(b) angle $AOC$,
Answer(b) ............................................................... [1]
(c) angle $OCA$,
Answer(c) ............................................................... [1]
(d) angle $DAC$.
Answer(d) ............................................................... [1]
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In triangle $ABC$, $AB = \sqrt{48}$ cm, $AC = 8$ cm and angle $ABC = 90^\circ$.
Find
(a) $BC$,
Answer(a) \text{.............................} \text{ cm} [3]
(b) angle $BAC$.
Answer(b) \text{.............................} [2]
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The graph of $y = (x - h)^2 + k$ has a vertex at $(2, -3)$.
Find the value of $h$ and the value of $k$.
Answer $h =$ .........................................................
$k =$ ......................................................... [2]
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571
The table shows the marks of 70 students in an examination.
[Table_1]
On the grid below, draw a histogram to show this information.
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