No questions found
(a) Write down the equation of line $L$.
.......................................................[1]
(b) Write down the co-ordinates of the point of intersection of line $L$ and line $M$.
( ................ , ................. ) [1]
(c) Find the gradient of line $M$.
.................................................................[2]
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$v = \frac{uf}{u-f}$
Find $v$ when $u = 30$ and $f = 10$.
$v = \text{.................................}$ [2]
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531
(a) Find a fraction, $n$, that satisfies this inequality.
$$\frac{5}{7} < n < \frac{6}{7}$$
$$n= \text{...........................} \quad [1]$$
(b) Write down an irrational number, $m$, that satisfies this inequality.
$$4 < m < 7$$
$$m= \text{...........................} \quad [1]$$
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Q is the point (3, 7) and \( \overrightarrow{PQ} = \begin{pmatrix} -6 \\ 3 \end{pmatrix} \).
(a) Find the co-ordinates of \( P \).
( .............. , .....................) [2]
(b) Find \( |\overrightarrow{PQ}| \). Give your answer in its simplest surd form.
...................................................... [3]
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503
Work out $ (5.6 \times 10^{-7}) - (7.8 \times 10^{-8}) $.
Give your answer in standard form.
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590
Kim has a piece of rope 18 metres long. He cuts the rope into two pieces. The lengths of the pieces are in the ratio 1 : 5. Calculate the length of each piece.
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Jamil has a biased 6-sided die.
He rolls it 350 times.
The results are shown in the table.
[Table_1]
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{Number on die} & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
\text{Frequency} & 20 & 50 & 72 & 68 & 56 & 84 \\
\hline
\end{array}
\]
(a) Find the relative frequency of getting a 2 with Jamil’s die.
.............................................................. [1]
(b) Explain why your answer to part (a) is a good estimate of the probability of getting a 2.
....................................................................................................................[1]
(c) Estimate the number of times Jamil will get a 2 if he rolls the die 1400 times.
.............................................................. [1]
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(a) On the grid, sketch the graph of $y=\sin x^\circ$ for $0 \le x \le 360$.
(b) The point $(a, 0.5)$ is on the graph of $y=\sin x^\circ$.
Find the two possible values of $a$.
\( a = \text{................} \text{ or } a = \text{................} \) [2]
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568
The masses, $m\,\text{kg}$, of some watermelons are measured. The results are shown in the table.
[Table_1]
Part of the histogram to show this information is shown below.
(a) Complete the histogram. [2]
(b) Find the value of $p$.
$p = \text{.....................................................}$ [1]
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Rearrange this formula to make $x$ the subject.
$$y = \frac{ax}{bx + c}$$
$$x = \text{.....................}$$ [3]
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526
(a) Solve $3\log 2 - 2\log 5 = \log x$.
x = \text{...............................} [3]
(b) Solve $\log_y 4 = \frac{1}{3}$.
y = \text{...............................} [1]
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563
