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Complete the statement.
The common factors of 24 and 45 are 1 and ..............................................................
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Alex invests $200 at a rate of 2\% per year simple interest.
Work out the total interest earned at the end of 4 years.
$ .................................... [2]
509
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Didi buys 2 books at $b each and $p$ magazines at $m$ each.
Find an expression, in terms of $b$, $p$ and $m$, for the total amount Didi pays.
$\text{........................................................................................}$
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(a) Rodrigo runs at an average speed of 10 km/h.
Work out the number of minutes he takes to run 5 km. ..................................... min [1]
(b) Roberta takes 1 hour 30 minutes to run 12 km.
Work out Roberta’s average speed. ..................................... km/h [1]
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Each of 100 students records the time taken to walk one kilometre. The cumulative frequency curve shows the results.
Find
(a) the median ............................... min [1]
(b) the lower quartile ........................... min [1]
(c) the number of students who took more than 20 minutes to walk one kilometre. .......................................... [2]
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Work out $\frac{3}{11} \div \frac{1}{2}$. \text{.....................} [2]
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570
The interior angle of a regular polygon is 160°.
Work out the number of sides for this polygon.
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The mean of five numbers is 7.
The five numbers are 3, 5, 10, 11 and $x$.
Find the value of $x$.
$x = \text{........................................}$
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Simplify $\left( 64x^{18} \right)^{\frac{2}{3}}$.
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A, B \text{ and } C \text{ lie on the circle centre } O.
(a) \text{ Work out the value of } x.
x = \text{...........................................} \ [2]
(b) \ Y \text{ is a point on the minor arc } BYC.
\text{Work out angle } BYC.
\text{Angle } BYC = \text{.......................................} \ [1]
\text{}
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Simplify fully.
$$\sqrt{20} + \sqrt{45} + \sqrt{80}$$
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The triangles $ABC$ and $PQR$ are similar.
The area of triangle $ABC$ is $24 \text{ cm}^2$.
$$\frac{PQ}{AB} = \frac{1}{2}$$
Work out the area of triangle $PQR$.
........................................... $\text{cm}^2$ [2]
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$x^2 + 18x + 2 = (x + p)^2 + t$
Find the value of $p$ and the value of $t$.
$p = \text{...............................}$
$t = \text{...............................}$
504
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542
y varies inversely as $\sqrt{x}$.
When $x = 4$, $y = 8$.
Find $y$ in terms of $x$.
$y =$ ext{...............................} [2]
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cos x = -\frac{\sqrt{3}}{2} \text{ and } 0^\circ \leq x < 360^\circ.
Find the values of x.
x = \text{......................} \text{ or } x = \text{......................} [2]
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log 4 + 2 log x = 2
Find the value of x.
x = ................................... [3]
501
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509
