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(a) Insert one pair of brackets to make the statement correct.
$3 \times 7 + 2 + 9 = 36$ [1]
(b) Work out $(0.2)^3$. .........................................................[1]
(c) Write down a prime number between 80 and 90. .........................................................[1]
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581
Solve the equation. $$7 - 5x = -3$$
$x = \text{.......................}$ [2]
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545
(a) Work out \( \begin{pmatrix} 1 \\ 2 \end{pmatrix} - \begin{pmatrix} -5 \\ 3 \end{pmatrix} \). \( \begin{pmatrix} \quad \\ \quad \end{pmatrix} \) [1]
(b) \( P \) is the point \((-3, 6)\).
\( Q \) is the point \((0, 2)\).
Find the translation vector that maps the point \( P \) onto the point \( Q \).
\( \begin{pmatrix} \quad \\ \quad \end{pmatrix} \) [2]
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(a) Factorise.
$$2p^2 - pq$$
[1]
(b) Expand the brackets and simplify.
$$(p - 7)(p + 3)$$
[2]
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599
(a) Work out $\frac{11}{12} + \frac{3}{4}$.
Give your answer as a mixed number in its simplest form. ............................................................ [2]
(b) Simplify $\frac{a}{x} \div \frac{b}{2y}$.
Give your answer as a single fraction. ............................................................ [1]
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Rotate triangle $T$ $90^{\circ}$ clockwise about the point $(2, 1)$.
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The interior angle of a regular polygon is 140°.
Find the number of sides of this polygon.
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526
Rearrange this equation to make $x$ the subject.
$y = 7x + 2$
$x = \text{..............................}$ [2]
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538
$APB$ is a tangent to the circle at $P$.
Work out the value of $x$.
$x = \text{..........................}$
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573
f(x) = 3 \sin(4x^{\circ})
Find the amplitude and period of f(x).
Amplitude = .........................................
Period = .......................................... [2]
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500
y varies inversely as \( \sqrt{x} \).
When \( x = 9 \), \( y = 2 \).
Find \( y \) in terms of \( x \).
\( y = \text{..........................} \) [2]
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573
f(x) = x^{\frac{1}{7}}
Find f^{-1}(x).
f^{-1}(x) = \text{...............................} \ [1]
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513
Simplify.
(a) $\frac{3}{x+2} - \frac{2}{x-1}$ ....................................................... [3]
(b) $\frac{6x^2+x-12}{6ax-8a-3x+4}$ ....................................................... [5]
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564
