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(a) Write 4347849 correct to the nearest ten thousand.
(b) Write 0.0040243 correct to 2 significant figures.
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From this list, write down
(a) a prime number, .......................................... [1]
(b) a common multiple of 4 and 6. .......................................... [1]
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Draw all the lines of symmetry on each of these shapes.
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The table shows the percentage of students in each of three classes who study physics, chemistry and biology.
[Table_1]
Physics (P) | Chemistry (C) | Biology (B)
Class H: 34 | 28 | 38
Class J: 24 | 18 | 58
Class K: 46 | 32 | 22
Complete the compound bar chart to show this information.
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Solve.
$$2(4x - 1) = 3(2x + 1)$$
x = \text{...............................} \quad [3]
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(a) Write 0.0000586 in standard form. .................................. [1]
(b) $(2 \times 10^{a}) \div (8 \times 10^{b}) = k \times 10^{n}$ where $1 \leq k \lt 10$.
(i) Find the value of $k$.
$k = ..................................$ [1]
(ii) Write an expression for $n$ in terms of $a$ and $b$.
$n = ..................................$ [1]
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Mia carries out a survey in a school to find out what students will do when they leave school. These are her results.
[Table_1]
(a) Find the relative frequency of university.
...................................................... [1]
(b) There are 1600 students in this school.
(i) Explain why the result in part (a) is a reasonable estimate of the probability that a student from this school will go to university.
.............................................................................................................................. [1]
(ii) Calculate an estimate for the number of students in this school who will go travelling.
...................................................... [2]
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Solve the simultaneous equations.
$$3x - 2y = 12$$
$$5x + y = 7$$
\( x = \text{..........................} \)
\( y = \text{..........................} \)
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y varies inversely as the square of (x + 2). When $x = 4$, $y = 0.5$.
Find $y$ in terms of $x$.
$y =$ ext{.............................} [2]
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The diagram shows a sector of a circle with radius 6 cm and sector angle 30°. The area of the shaded segment is $(a\pi - b)\text{ cm}^2$.
Find the value of $a$ and the value of $b$.
a = .............................................
b = .............................................
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In this question all lengths are in centimetres.
Find the value of $x^2$.
Give your answer in the form $a + b\sqrt{3}$ where $a$ and $b$ are integers.
$x^2 =$ .....................................................
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The diagram shows the lines $y = \frac{1}{2}x + 1$, $y = 3x$ and $3x + 4y = 12$.
These lines divide the space into 7 regions, $A, B, C, D, E, F,$ and $G$.
Write down the letter of the region which is defined by
(a) $y \leq \frac{1}{2}x + 1$, $y \leq 3x$ and $3x + 4y \leq 12$,
Region ....................................................... [1]
(b) $y \geq \frac{1}{2}x + 1$, $y \geq 3x$ and $3x + 4y \leq 12$.
Region ....................................................... [1]
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The equation of the curve is $y = ax^2 + bx - 12$.
Find the value of $a$ and the value of $b$.
[Image_1: Graph of a parabola showing its x-intercepts at -2 and 3, and vertex at (0, -12)]
$a = \text{.................................}$
$b = \text{.........................................} \ [3]$
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Solve.
(a) $\log_{3}x = 4$
$x = \text{.....................................} \; [1]$
(b) $2 \log x - 3 \log 2 = \log 50$
$x = \text{.....................................} \; [3]$
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