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The diagram shows a straight line intersecting two parallel lines.
Find the value of $k$ and the value of $m$.
$k = \text{.....................}$
$m = \text{.....................}$
540
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571
Solve the equation.
$$2q - 7 = 2 - 7q$$
$$q = \text{.........................}$$ [2]
529
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551
1 $\text{m}^2 = 10^n\ \text{cm}^2$
Find the value of $n$.
$n = \text{...............................}$
593
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597
An unbiased six-sided die is numbered 1, 2, 3, 4, 5, 6. The die is rolled.
Find the probability that it shows
(a) 6, ............................................... [1]
(b) a number greater than 6. ............................................... [1]
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539
A cone has base radius 5 cm and height $\frac{5}{4}$ cm.
A hemisphere has radius $r$ cm.
The volume of the hemisphere is equal to the volume of the cone.
Find the value of $r$.
$r = \text{...............................}$
600
543
518
The diagram shows two triangles formed by two parallel lines and two intersecting lines.
(a) Use one of these words to complete the statement.
alternate congruent similar cyclic parallel
The triangles are ..................................................... [1]
(b) The area of the smaller triangle is 24 cm$^2$.
Calculate the area of the larger triangle.
...................................................... cm$^2$ [2]
526
592
576
Complete each statement.
(a) $(P \cup Q)' = \{.............................................................\}$ [1]
(b) $\{a, e\} = P\.......Q$ [1]
(c) $n(P' \cup Q) = .............$ [1]
U = \{a, b, c, d, e, f, g, h, i, j\}
547
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517
Rearrange the formula to write $x$ in terms of $a$ and $y$.
$$y = \sqrt{x^2 + 2a^2}$$
$x = \text{.......................................................}$
599
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524
A, B, C and D are four points on a circle.
AC and BD meet at E.
XAY is a tangent to the circle at A.
Find
(a) angle $CDB$,
Angle $CDB = \text{................................................}$ [1]
(b) angle $ACB$,
Angle $ACB = \text{................................................}$ [1]
(c) angle $DCE$,
Angle $DCE = \text{................................................}$ [1]
(d) angle $YAD$.
Angle $YAD = \text{................................................}$ [1]
511
534
527
Simplify \((3 \times 10^{85}) \times (7 \times 10^{15})\).
Give your answer in standard form.
597
510
586
Factorise.
(a) $49 - 16u^2$ ............................................... [1]
(b) $1 + 4xy - 2x - 2y$ ............................................... [2]
535
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550
Rationalise the denominator.
\(\frac{5}{\sqrt{3} - \sqrt{2}}\)
558
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517
log y = log h + log p - log x
Find y in terms of h, p and x.
y = ...................................... [1]
509
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545
$8^{\frac{4}{3}}=32^x$
Find the value of $x$.
$x=\text{..................................}$ [2]
523
502
578
Simplify.
$$2 - \frac{4 - 3x}{x - 2}$$
Write your answer as a single fraction in its simplest form.
536
530
599
