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Insert one pair of brackets to make the statement correct.
$5 - 2 + 3 \times 2 = -5$
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Let \( \mathbf{p} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} \) and \( \mathbf{q} = \begin{pmatrix} 1 \\ 6 \end{pmatrix} \)
Find \( 2\mathbf{p} - 3\mathbf{q} \).
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Write 0.72 as a fraction in its lowest terms.
Answer ...................................... [1]
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The mean of a list of 9 numbers is 6.
When a 10th number is included in the list the mean is 5.5.
Find the value of this 10th number.
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Find the length of the hypotenuse of the triangle.
Answer ............................................. cm
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Solve the simultaneous equations.
$$\begin{align} u - w &= 9 \\ 3u + w &= 19 \end{align}$$
\text{Answer } u = \text{..................................................}
w = \text{.................................................. [2]}
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The scale of a map is 1 : 250 000.
Find the actual distance, in kilometres, between two cities which are 42 cm apart on the map.
Answer ....................................................... km
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| x | < 4 and x is an integer. Find the smallest possible value of x.
Answer .............................................................. [1]
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The first 4 terms of a sequence are 20, 13, 6 and -1.
Find
(a) the next term,
Answer(a) ............................................... [1]
(b) the nth term.
Answer(b) ............................................... [2]
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Make $u$ the subject of the formula.
$v^2 = u^2 + 2as$
Answer $u =$ .......................................................
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Factorise completely.
$2a - b + 2ax - bx$
Answer ........................................ [2]
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Find the exact value of
(a) $3^{-3}$,
Answer(a) .................................................. [1]
(b) $16^{\frac{3}{4}}$,
Answer(b) .................................................. [1]
(c) $\cos 30^\circ$.
Answer(c) .................................................. [1]
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On each Venn diagram, shade the region indicated.
$$ (A \cup B)' $$
$$ (C \cup D) \cap E' $$
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Find the equation of the straight line passing through $(-2, -4)$ and $(2, 0)$.
Answer $\text{.....................}$ [3]
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Rationalise the denominator.
$$ \frac{3}{\sqrt{5} + 2} $$
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(a) Factorise $3y - y^2$.
(b) Simplify $\frac{3y - y^2}{9 - y^2}$.
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Find the value of
(a) $\frac{\log 4}{\log 8}$, Answer(a) .......................................................... [2]
(b) $\log_{4}8$. Answer(b) .......................................................... [1]
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g(x) = \frac{2x+1}{x-1}, \; x \neq 1
Solve the equation \; g^{-1}(x) = 2.
Answer \; x = \text{..................................................} \; [1]
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