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On the number line, show the inequality $-2 \leq x < 3$.
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Work out \( 4 \times \binom{6}{-2} \).
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593
From the list of numbers, write down
(a) the prime number,
\text{.............................} [1]
(b) the cube number.
\text{.............................} [1]
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596
(a) Write 7.29784 correct to 3 significant figures. ......................................... [1]
(b) Write 0.00000306 in standard form. ......................................... [1]
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Solve.
(a) $4x = 28$
$x = \text{.........................................}$ [1]
(b) $3(a - 6) = 24$
$a = \text{.........................................}$ [2]
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514
Karen has 3 blue hats, 5 red hats and 2 white hats.
She also has 4 blue scarves, 3 red scarves and 1 white scarf.
(a) Karen takes a hat at random and replaces it.
Find the probability that it is white.
.......................................................... [1]
(b) Karen takes a hat and a scarf at random.
Find the probability that both the hat and the scarf are blue.
.......................................................... [2]
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541
Find the magnitude of the vector \( \begin{pmatrix} 2 \\ 6 \end{pmatrix} \).
Give your answer in simplest surd form.
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(a) Shade $P \cup Q$.
(b) Describe the shaded area using set notation.
(c) The Venn diagram shows the number of elements in each subset.
Find $n((B' \cap C) \cap A)$.
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(a)
A, B, C, and D are points on a circle.
Angle $DAC = 32^{\circ}$.
$BC = DC$.
Find angle $BCD$.
Angle $BCD = \text{.........................................................}$ [2]
(b)
A, B and C are points on the circle centre O.
$ECD$ is a tangent to the circle at C.
Angle $ACE = 42^{\circ}$.
Find angle $AOC$.
Angle $AOC = \text{.........................................................}$ [2]
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(a) Simplify fully.
\( \sqrt{75} - \sqrt{48} + \sqrt{12} \) ................................................ [2]
(b) Rationalise the denominator, giving your answer in its simplest form.
\( \frac{1}{\sqrt{3} + 5} \) ................................................ [2]
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$x^2 - 14x + c = (x + d)^2$
Find the value of $c$ and the value of $d$.
\(c = \text{.................................}\)
\(d = \text{.......................................}\) [3]
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586
(a) Factorise fully.
$$6x^2 - 7x - 3$$ ............................................................................... [2]
(b) Solve.
$$6x^2 - 7x - 3 < 0$$ ............................................................................... [3]
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Solve.
$$2 \log 3 - \log 2 = \log p$$
$$p = \text{..............................................}$$ [2]
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534
