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A quadrilateral has all sides equal and exactly two lines of symmetry. Write down the mathematical name of this quadrilateral.
............................... [1]
550
570
504
Find the value of $x$.
[Image_1: Diagram showing angles $x^\circ$, $60^\circ$, $50^\circ$, and a right angle.]
$x = \text{..........................................}$ [1]
588
524
538
Find the size of one interior angle of a regular polygon with 20 sides.
600
545
584
A van has length 9 m.
It takes 1 second for the van to completely pass a gate of length 1 m.
Find the speed of the van.
Give your answer in km/h.
566
591
508
The faces of a die are numbered 1, 1, 2, 3, 3 and 4. When it is rolled it is equally likely to show any face. The die is rolled twice. Find the probability that it shows an odd number both times.
533
526
575
Here are the first five terms of a sequence.
$$\frac{1}{4} \quad 1 \quad 4 \quad 16 \quad 64$$
(a) Find the next term. .............................................................. [1]
(b) Find the $n^{th}$ term. .............................................................. [2]
536
556
513
The diagram shows two similar triangles, $ABC$ and $PQR$.
(a) Find the length of $PR$.
$PR = \text{.............................}$ cm [2]
(b) The triangles are the cross-sections of mathematically similar prisms.
The volume of the larger prism is $500 \text{ cm}^3$.
Find the volume of the smaller prism.
$\text{.............................}$ cm$^3$ [2]
534
550
512
$A = P(1+x)^3$
Rearrange the formula to write $x$ in terms of $A$ and $P$.
$x = ext{............................................}$
592
559
592
Points $Q, R, S$ and $T$ lie on the circle.
$AB$ is a tangent to the circle at $T$.
Angle $RTB = 70^{\circ}$.
Find angle $RQT$.
Angle $RQT = \text{..................................................} \; [2]$
589
503
579
p varies inversely as the square root of q.
When $q = 9, p = 12$.
Find p when $q = 16$.
$p = \text{.................................}$ [3]
568
555
504
Simplify by rationalising the denominator. $\frac{3}{2 \sqrt{2} - 1}$
503
593
594
The diagram shows the graph of $y = |ax + b|$, where $a > 0$.
Find the value of $a$ and the value of $b$.
a = ext{.........................................}
b = ext{.........................................}
594
587
547
Write as a single fraction in its simplest form.
\( \frac{3}{x - 2} - 2 \) ........................................................................................ [2]
503
587
577
2\log p = 3\log x - \log y
Find $p$ in terms of $x$ and $y$.
\( p = \text{......................} \) [3]
531
539
579
