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A cuboid has a square base of side 10 cm and a volume of 1200 cm^3.
Work out the height of the cuboid.
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p = \begin{pmatrix} 3 \\ -1 \end{pmatrix} \quad q = \begin{pmatrix} 1 \\ -2 \end{pmatrix}
(a) Find \ \mathbf{p+q}. \ \begin{pmatrix} \ \ \ \ \ \ \ \ \end{pmatrix} \ [1]
(b) \ \mathbf{A} \ is \ the \ point \ (2,7).
The \ point \ \mathbf{A} \ is \ translated \ to \ the \ point \ \mathbf{B} \ by \ the \ vector \ \mathbf{p+q}.
Find \ the \ coordinates \ of \ \mathbf{B}. \ (\ \, \,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ) \ [2]
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Work out $\frac{3}{4} \div 2\frac{1}{2}$.
Give your answer as a fraction in its lowest terms.
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A truck of length 10 m passes a gate of length 2 m. The speed of the truck is 8 m/s.
Find the time the truck takes to completely pass the gate.
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Find the volume of a cone with radius 3 cm and perpendicular height 8 cm. Give your answer in terms of $\pi$. .......................................$\text{cm}^{3}$ [2]
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Work out the value of $x$.
$x = \text{...........................}$
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Simplify.
(a) \( \frac{15w^{15}}{3w^3} \) .............................................................. [2]
(b) \( (125y^6)^{\frac{2}{3}} \) .............................................................. [2]
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Rearrange the formula to write $h$ in terms of $\pi$, $r$ and $A$.
$A = 2\pi rh + 3\pi r^2$
$h = \text{.................................}$ [2]
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A, B \text{ and } C \text{ are points on a circle.}
T\!A \text{ is a tangent to the circle at } A.
C\!A = C\!B \text{ and angle } B\!A\!T = 70^\circ.
\text{Work out the value of } x.
\text{x = ....................................................}
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When Jack sells a computer for $264 he makes a profit of 20%.
Work out the price Jack paid for the computer.
$ ...........................................
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y is inversely proportional to \(\sqrt{x}\).
When \(x = 9\), \(y = 2\).
Find \(y\) in terms of \(x\).
\(y = \text{...............................}\) [2]
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3 \log y = 2 \log x - \log w
Find $y$ in terms of $x$ and $w$.
$y =$ ......................................... [3]
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Rationalise the denominator.
\( \frac{9}{\sqrt{7} - 2} \)
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In the diagram, the graph passes through the point (4, 2).
Write down the equation of the graph.
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Write as a single fraction in its simplest form. $$ \frac{1}{x-3} - \frac{2}{x} $$
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