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(a) Write 49059300 correct to 3 significant figures. .................................................. [1]
(b) Write your answer to part (a) in standard form. .................................................. [1]
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Shade two small squares so that the shape has exactly one line of symmetry.
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p = \(\begin{pmatrix} -3 \\ 5 \end{pmatrix}\)
(a) Find the column vector 3p. \(\begin{pmatrix} \quad \end{pmatrix}\) [1]
(b) Find \(|\mathbf{p}|\), giving your answer in surd form. [2]
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f(x) = |2x - 7| for all real x.
(a) Find f(2). [1]
(b) Write down the range of f(x). [1]
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The line with equation $2x + 3y = 6$ is drawn on the grid.
On the grid, show clearly the \textbf{single} region defined by these three inequalities.
$2x + 3y \leq 6 \quad x \geq -3 \quad y \leq -1$
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Factorise.
(a) $64x^2 - 1$ ................................. [1]
(b) $2y^2 - y - 6$ ................................. [2]
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(a) $2^3 \div 2^7 = 2^p$
Find the value of $p$. ......................................... [1]
(b) $\sqrt{2^5} = 2^q$
Find the value of $q$. ......................................... [1]
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An archer shoots 150 arrows at a target with sections coloured gold, red, blue, black and white. The table shows her results.
[Table_1]
Complete the compound bar chart to show these results as percentages.
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The diagram shows nine sketch graphs.
Write the letter of the graph which shows each of these functions.
f(x) = 2x - 3 Graph ...............
f(x) = x^2 - 3 Graph ...............
f(x) = 3 - x^3 Graph ...............
f(x) = (x - 3)^2 Graph ............... [4]
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A, B, C and D are points on the circle centre O.
PQ is a tangent to the circle at C.
Find these angles.
(a) Angle DAC
Angle DAC = ..................................................... [2]
(b) Angle ABC
Angle ABC = ..................................................... [1]
(c) Angle ACQ
Angle ACQ = ..................................................... [2]
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(a) Find the value of $n$ when $\log 5 + \log 3 - \log 2 = \log n$. [1]
(b) Find $\log_3(3^{1.4})$. [1]
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f(x) = 3 \sin 2x^{\circ}
(a) Write down the amplitude of the graph of f(x). ................................................... [1]
(b) The graph of $y = f(x)$ goes through the points $(75, 1.5)$ and $(a, 1.5)$.
Find a possible value of $a$, greater than 75. ................................................... [1]
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