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(a) Work out $(0.3)^2$.
Answer(a) ..................................................... [1]
(b) Find $n$ when $\frac{5}{6} = \frac{n}{24}$.
Answer(b) $n$ = ................................................. [1]
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(a) Find the value of
(i) $25^0$,
Answer(a)(i) ............................................................. [1]
(ii) $100^{\frac{3}{2}}$.
Answer(a)(ii) ............................................................. [1]
(b) Write as a single power of 5.
$$\frac{5^{12}}{5^3 \times 5^2}$$
Answer(b) ............................................................. [1]
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Find the magnitude of \( \begin{pmatrix} -6 \\ 4 \end{pmatrix} \).
Write your answer in surd form as simply as possible.
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Anneke, Babar, Céline, and Dieter each throw the same biased die.
They want to find the probability of throwing a six with this die.
They each throw the die a different number of times.
These are their results.
[Table_1]
(a) Complete the table below to show the relative frequencies of their results.
Write your answers as decimals.
[Table_2]
(b) Whose result gives the best estimate of the probability of throwing a six with the biased die?
Give a reason for your answer.
$\text{Answer(b)}$ ................................................ because ..............................................................................
............................................................................................................................. [1]
(c) The probability of throwing a six with a different biased die is 0.41.
Find the expected number of sixes when this die is thrown 600 times.
$\text{Answer(c)}$ ...................................................................................... [1]
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A is the point (2, 8) and B is the point (6, 0).
(a) Find the co-ordinates of the midpoint of AB.
Answer(a) $(........................, ........................)$ [1]
(b) Find the gradient of AB.
Answer(b) .................................................... [2]
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Solve.
$2x + 3 \leq 4(x - 2)$
Answer ....................................................... [3]
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The diagram shows a shape made from a cylinder and a cone. The cylinder and cone have a common radius of 6 m. The height of the cylinder is 10 m and the height of the cone is 3 m.
Calculate the total volume of the shape.
Leave your answer as a multiple of \( \pi \).
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Solve these simultaneous equations.
$$5x + 2y = 11$$
$$4x - 3y = 18$$
Answer \( x= \) ..................................................
\( y= \) ................................................. [4]
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Solve the following equations.
(a) $\log x + \log 3 = \log 12$
$\text{Answer(a) } x = \text{....................................} \quad [1]$
(b) $\log x = 3$
$\text{Answer(b) } x = \text{....................................} \quad [1]$
(c) $2\log x - \log 5 = \log 20$
$\text{Answer(c) } x = \text{....................................} \quad [3]$
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A, B, C and D are points on the circle, centre O.
P Q is a tangent to the circle at the point C.
Angle PCD = 55^∘ and angle ADO = 40^∘.
Find
(a) angle COD,
Answer(a) ................................................... [2]
(b) angle DAC,
Answer(b) ................................................... [1]
(c) angle ABC.
Answer(c) ................................................... [1]
[Image of the described circle: A, B, C, D on the circle, with tangent P Q]
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These are sketches of the graphs of six functions.
In the table below are four functions. Write the correct letter in the table to match each function with its graph.
[Table_1]
\( \begin{array}{|c|c|} \hline \text{Function} & \text{Graph} \\ \hline f(x) = 2x - 3 & \text{..................} \\ f(x) = (x - 2)^2 & \text{..................} \\ f(x) = 4x - x^3 & \text{..................} \\ f(x) = 5 - 2x & \text{..................} \\ \hline \end{array} \)
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