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The diagram shows two parallel lines with two straight lines crossing. Find the value of $w$.
$$w = \text{...............................}$$
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The volume of a cube is $27 ext{ cm}^3$.
Find the total surface area.
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Find the highest common factor (HCF) of 30, 48 and 66.
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f(x)=2x-3
Find the range of f(x) for the domain \{0,1,2\}. \{.............................................\} [1]
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Work out the length of $AB$.
[Image_1: A triangle with vertices labeled A, B, and C. The length AC is $10\text{ cm}$, BC is $\sqrt{91}\text{ cm}$, and there is a right angle at B.]
$AB=\text{................................. cm}$
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Given: $y = 2x^2 - 1$
Rearrange the formula to write $x$ in terms of $y$.
$x =$ ..........................
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(a) Change 20 m/s into km/h.
............................................................ km/h [2]
(b) A train travels at 20 m/s for 45 minutes.
Work out the distance travelled.
Give your answer in kilometres.
............................................................ km [2]
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Work out \((3.2 \times 10^{20}) + (2.3 \times 10^{21})\), giving your answer in standard form.
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ABCD is a cyclic quadrilateral. DC is extended to E. Angle $BCE = 130^{\circ}$, angle $ABC = 6x^{\circ}$ and angle $ADC = 9x^{\circ}$. Find the value of
(a) angle $BAD$,
$\text{Angle } BAD = \text{.................................................................} \; [1]$
(b) angle $ABC$.
$\text{Angle } ABC = \text{.................................................................} \; [2]$
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Simplify.
(a) \( \frac{12x^{12}}{4x^4} \) ............................................................... [2]
(b) \( (16x^{16})^{\frac{1}{4}} \) ............................................................... [2]
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y is proportional to $\frac{1}{\sqrt{x}}$.
When $x = 4$, $y = 2$.
Find $y$ when $x = 64$.
y = \text{..........................} [3]
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(a) Simplify $\sqrt{18} + \sqrt{72}$.
[2]
(b) Rationalise the denominator. $\frac{1}{\sqrt{5} + 2}$
[2]
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(a) $\log k = 2 \log 3 - 5 \log 2$
Find the value of $k$.
$k = \text{............................................}$ [2]
(b) $\log_2 p = -1$
Find the value of $p$.
$p = \text{...................................}$ [1]
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θ is an acute angle and \( \tan \theta = \sqrt{3} \).
Write down the value of \( \theta \).
\( \theta = \text{...............................} \) [1]
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