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Given the equation $y = mx + c$:
(a) Find $y$ when $m = \frac{1}{2}$, $x = -2$ and $c = 4$. $y = \text{..............................}$ [2]
(b) Rearrange the formula to write $m$ in terms of $x$, $y$ and $c$.
$m = \text{..............................}$ [2]
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Solve.
$$6 - 2t = -12$$
$$t = \text{.....................} \; [2]$$
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540
Write down the inequality shown above. .......................................... [1]
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Danny stands to watch a train go past. The train has a length of 120 m and takes 3 seconds to pass.
Find the speed of the train
(a) in m/s, .................................................. m/s [1]
(b) in km/h. .................................................. km/h [2]
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Work out $\frac{5}{6} \cdot \frac{15}{16}$.
Give your answer in its lowest terms.
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(a) Simplify $\sqrt{98}$.
............................................. [1]
(b) Rationalise the denominator. $\frac{1}{3 - \sqrt{5}}$
............................................. [2]
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Solve the simultaneous equations.
$$3t - u = -5$$
$$3t + 2u = 1$$
$$t = \text{.......................................}$$
$$u = \text{.......................................}\,[2]$$
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Simplify.
(a) $12v^{12} \times 3v^{3}$ ...............................................[2]
(b) $(100x^{100})^{\frac{3}{2}}$ ...............................................[2]
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For the diagram, write down
(a) the number of lines of symmetry, ............................................... [1]
(b) the order of rotational symmetry. ............................................... [1]
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The volume of a sphere is $36\pi$ cubic centimetres.
Find the radius of the sphere. ..................................... cm [2]
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(a) $T, U, \text{and } V$ lie on a circle, centre $O$. $PQ$ is a tangent to the circle at $T$. $TU$ is a diameter. Find the value of $x$ and the value of $y$.
$x = \text{.....................},$
$y = \text{.....................} \text{ } [2]$
(b) $ABCD$ is a cyclic quadrilateral. Find the value of $p$ and the value of $q$.
$p = \text{.....................},$
$q = \text{.....................} \text{ } [2]$
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sin \( \theta = -\frac{1}{\sqrt{2}} \) and \( 0^\circ \leq \theta \leq 360^\circ \). Find the two values of \( \theta \).
\( \theta = \text{.....................} \) or \( \theta = \text{..................} \) [2]
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Find the equation of the straight line perpendicular to the line $y = 2x + 1$ that passes through the point (2, 5).
Give your answer in the form $y = mx + c$.
$y = \text{..................................}$
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The two solids are mathematically similar. The larger solid has a volume of 64 cm³. The smaller solid has a volume of 8 cm³ and a height of 5 cm.
Work out the height of the larger solid.
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Write as a single fraction in its simplest form.
\( \frac{7}{x-1} - \frac{5}{2x+3} \)
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