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Increase 1h 30 min by 10%.
......................... h .......................... min [2]
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In the diagram, $DC$ is parallel to $AB$ and $AC = AB$.
Work out angle $ACB$.
Angle $ACB = \text{..........................}$
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Given: $t = \frac{1}{p^2}$
Rearrange the formula to write $p$ in terms of $t$.
$p =$ ext{................................................} [2]
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A biased die, that has six faces, is numbered 1 to 6. The table shows the results when the die is rolled 60 times.
[Table_1]
(a) Jose rolls the die.
Find the probability that the number shown is even.
............................................................. [1]
(b) Jose rolls the die 1200 times.
Find the expected number of times that the number shown on the die is even.
............................................................. [1]
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Solve the simultaneous equations.
$$3x - 2y = 7$$
$$5x + 2y = 1$$
$$x = ext{.....................}$$
$$y = ext{.....................}$$
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Work out \( \frac{8 \times 10^7}{5 \times 10^{-12}} \).
Give your answer in standard form.
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(a) \( x^3 \div x^p = x^5 \)
Find the value of \( p \).
\( p = \text{................................................} \) [1]
(b) Work out.
(i) \( (\sqrt{2})^6 \)
\text{................................................} [1]
(ii) \( \frac{1}{8^{-\frac{1}{3}}} \)
\text{................................................} [2]
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The line $2x + 3y = 36$ intersects the x-axis at $P$ and the y-axis at $Q$. $M$ is the midpoint of $PQ$.
Find the column vector $\overrightarrow{OM}$ where $O$ is the origin.
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Rationalise the denominator.
$$\frac{5}{\sqrt{2} + 1}$$
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The area of a semicircle is $32\pi \text{cm}^2$.
Work out the perimeter of the semicircle.
Give your answer in terms of $\pi$.
............................................................ cm [3]
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Complete the frequency table using the information in the histogram.
[Image_1: Histogram]
[Table_1: \begin{tabular}{|c|c|} \hline Class interval & Frequency \\ \hline 0 < x \leq 20 & \\ \hline 20 < x \leq 30 & \\ \hline \end{tabular}]
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y \propto \frac{1}{\sqrt{x}}
When \(x = 4, y = 3\).
Find \(y\) in terms of \(x\).
\(y = \text{.................................} [2]\)
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log y = 2 \log 3 + 3 \log 2 - \log 6
Find the value of y.
y = .................................................... [3]
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Describe fully the \textit{single} transformation that maps the graph of $y = \cos x$ onto the graph of $y = 3 \cos x$.
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