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Ben takes 1 hour 5 minutes to do his homework.
Alisa takes 20 minutes less.
Work out how long Alisa takes.
Give your answer as a fraction of an hour.
..................................................hour
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521
Write down the mathematical name of each of these shapes. The first shape has been named for you.
[Image_1: Rectangle and other geometric shapes]
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538
Write down the value of
(a) \( \sqrt{81} \), ................................................................. [1]
(b) \( \sqrt[3]{8} \). ................................................................. [1]
545
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569
(a) Write 30\% as a fraction. .................................................... [1]
(b) Write \(\frac{18}{20}\) as a percentage. ........................................ \% [1]
(c) Work out 15\% of 340 metres. ................................................. m [2]
600
542
546
(a) Find the value of $x$.
$x = \text{.................................}$ [2]
(b) Find the value of $y$.
$y = \text{.................................}$ [2]
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536
Work out.
$$\frac{3}{5} \times \frac{2}{7}$$ ................................................
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568
(a) Write 2.96 correct to 1 significant figure.
........................................................... [1]
(b) Find the approximate value of
$$ \frac{9.1}{2.96} + \frac{30.5}{5.95}. $$
........................................................... [2]
(c) Is your answer to part (b) higher or lower than the actual answer?
Give a reason for your answer.
...................................... because ...........................................
............................................................................................ [1]
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531
A fair 6-sided die is numbered 1, 2, 3, 4, 5 and 6. The die is rolled once. Find the probability that the number on the top face is
(a) 2, ............................................... [1]
(b) not 2. ............................................ [1]
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(a) Factorise completely.
$x - 5x^2$ ..................................................... [1]
(b) $r = \frac{2a - 3b}{c}$
Find the value of $r$ when $a = 5$, $b = 2$ and $c = -5$.
$r =$ ....................................................... [3]
592
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584
Solve the following simultaneous equations.
$2x + 5y = 15$
$2x - 3y = 7$
$x = \text{.................................}$
$y = \text{.................................}$
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539
List the integer values of $n$ for which $3 \leq 3n < 15$.
546
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554
(a) Find the vector $\overrightarrow{AB}$. [2]
(b) $\overrightarrow{BC} = \begin{pmatrix} -2 \\ -1 \end{pmatrix}$.
On the grid above, plot and label the point $C$. [1]
554
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512
The diagram shows the graph of $y = f(x)$.
Write down the equations of the two asymptotes of the graph.
............... and .......................
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525
The diagram shows a cumulative frequency curve for the marks of 200 students in a test.
Estimate
(a) the median mark,
.................................................. [1]
(b) the interquartile range.
.................................................. [2]
573
526
553
