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Solve the equation.
$$2x - 7 = -3$$
$x = \text{....................................} \quad [2]$
588
597
510
Work out $\frac{5}{6} \div \frac{15}{16}$.
Give your answer as a fraction in its lowest terms.
526
518
507
Find the integer values of $x$ when $-1 \leq x < 3$.
515
544
589
Solve the simultaneous equations.
$$2p - 3q = 7$$
$$p + 3q = 2$$
$$p = \text{......................................}$$
$$q = \text{......................................}$$
523
515
573
Find the area of the sector.
Give your answer, in terms of \( \pi \), in its simplest form.
586
559
556
Find, as a fraction, the value of $\sin y$.
$\sin y = \text{.................................................}$ [3]
513
544
521
Find the value of
(a) \( \left( \frac{1}{2} \right)^{-3} \), .......................................... [1]
(b) \( \log_5 125 \). .......................................... [1]
544
542
503
$J = m(k^2 + h^2)$
Rearrange the formula to make $h$ the subject.
$h = \text{.................................}$
570
558
514
Find the value of $x^2$ for the triangle given below:
[Image_1: A triangle with sides 8 cm, 10 cm, and x cm, and an angle of 60° between the 8 cm and 10 cm sides.]
530
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511
In the diagram, $A$, $B$ and $C$ are points on parallel lines. $AC = BC$.
Work out the value of $y$.
$y = \text{.................................}$
512
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564
(2\sqrt{3} - 3\sqrt{2})^2 = p + q\sqrt{6}
Find the value of $p$ and the value of $q$.
$p$ = ...................................
$q$ = ..................................... [3]
546
517
594
y varies inversely as $(x - 3)^2$. When $x = 1$, $y = 4$.
Find $y$ in terms of $x$.
y = \text{..........................................} \hspace{10pt} [2]
577
535
531
log x = 2 \log 3 - 5 \log 2
Find the value of x.
x = \text{.....................................................} [2]
517
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582
α is acute and tan α = x.
Find, in terms of x,
(a) tan(180−α),
tan(180−α) = .......................................... [1]
(b) tan(90−α).
tan(90−α) = .......................................... [1]
529
582
504
Simplify.
$$\frac{3x - 6y - ax + 2ay}{x^3 - 2x^2 y}$$
588
554
569
