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(a) Write a mathematical word in each box to describe the three lines and the shaded area.
(b) Measure angle $x$.
$x$ = \text{.....................................................} [1]
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Complete the table for the three sequences.
[Table_1]
\begin{tabular}{|c|c|}\hline Rule & Sequence \\ \hline -4 & 27, 23, \text{........}, \text{..........}, \text{..........} \\ \hline \text{.........................} & 64, 32, 16, 8, 4 \\ \hline \times 3 \text{ then } +1 & 2, 7, \text{........}, \text{..........}, \text{..........} \\ \hline \end{tabular}
595
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(a) Here are some scores in a mathematics test.
15 7 10 12 20 19 16 11 9 14
(i) Work out the range of these scores.
.................................................. [1]
(ii) Work out the mean score.
.................................................. [1]
(b) A group of students were asked if they preferred lessons in mathematics or science.
Complete the table.
[Table_1]
[Total Marks: 3]
(c) The results for 30 students in an English exam are shown in the table.
[Table_2]
Complete the pie chart to show this information.
You must show all your working.
[Total Marks: 5]
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(a) Write in figures the number seven thousand and sixty one.
(b) Write down
(i) a multiple of 9,
(ii) an even number between 21 and 29.
(c) Find the value of
(i) $\sqrt{625}$,
(ii) $11^3$,
(iii) $5^2 - \sqrt[3]{729}$.
(d) Insert one pair of brackets to make this calculation correct.
$$3 \times 6 + 5 - 4 = 29$$
(e) Work out.
$$\frac{25.2}{6.1 + 3.8}$$
Write your answer correct to two decimal places.
(f) Write 0.031 626
(i) correct to three significant figures,
(ii) in standard form.
589
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(a) A train takes 1 hour 30 minutes to travel from Cambridge to London.
(i) The train leaves Cambridge at 07 25.
Find the time that this train arrives in London.
................................................... [1]
(ii) The distance from Cambridge to London is 105 km.
Work out the average speed of this train.
............................................. km/h [2]
(b) There are 104 trains travelling from Cambridge to London each day.
(i) 3\% of these trains arrive late in London.
Work out how many of the trains arrive late in London.
................................................... [2]
(ii) Trains from Cambridge are either express trains or local trains.
The ratio express trains : local trains = 5 : 3.
How many of the 104 trains are local trains?
................................................... [2]
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The number 7 is drawn on a rectangular piece of paper. \(\)
(a) Work out the area of the rectangular piece of paper. .............................................. cm$^2$ [2]
(b) Work out the total area of the shaded number 7. .............................................. cm$^2$ [4]
(c) What fraction of the area of the rectangular piece of paper is the area of the shaded number 7? Give your answer as a fraction in its simplest form. .............................................. [2]
(d) Write down the mathematical name for each of the two quadrilaterals that make up the shaded number 7. .............................................. and .............................................. [2]
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Solve these equations to find the value of $x$, the value of $y$ and the value of $z$.
$$x + x + x = 42$$
$$x + y + y = 32$$
$$x + y + z = 22$$
$x = \text{..................................................}$
$y = \text{..................................................}$
$z = \text{....................................... [4]}$
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(a) (i) Work out the perimeter of the triangle.
.................................................. cm [1]
(ii) Write your answer to part (a)(i) in metres.
.................................................. m [1]
(b) Work out the size of angle $x$.
$x = \text{..................................................}$ [1]
(c) The triangle is enlarged by scale factor 3.
Find the lengths of the sides and the sizes of the angles in the enlarged triangle.
Sides .............................. cm .............................. cm .............................. cm .............................. cm
Angles .............................. ° .............................. ° .............................. ° [3]
(d) Complete this statement with a mathematical word.
The enlarged triangle is ........................................... to the original triangle. [1]
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In a class of students, 11 like classical music $(C)$, 15 like pop music $(P)$, 8 like both and 6 like neither.
(a) Complete the Venn diagram to show this information.
[2]
(b) Find the total number of students in the class.
..............................................................[1]
(c) One student is chosen at random.
Find the probability that this student likes both classical music and pop music.
..............................................................[1]
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A cycle track has two straight sections, each 78 m long. Each of the two semi-circular ends has diameter 30 m. Work out the perimeter of the cycle track.
501
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(a) Factorise.
$5x - 15$
.................................................. [1]
(b) Solve.
$4(3x - 2) = 28$
.................................................. [3]
(c) Simplify.
$\frac{4a}{b} \times \frac{3b^2}{2a^2}$
.................................................. [2]
(d) On the number line, show the inequality $x \leq 3$.
[Image of number line]
.................................................. [1]
(e) Solve.
$7x > 3x + 6$
.................................................. [2]
(f) Solve these simultaneous equations.
$\begin{align*} x + y &= 5 \\ x - y &= 7 \end{align*}$
$x = \text{...........................................}$
$y = \text{...........................................}$ [2]
522
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549
Find the highest common factor (HCF) and the lowest common multiple (LCM) of 54 and 72.
Highest common factor ..............................................................
Lowest common multiple ...................................................... [4]
572
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Sandy is playing a game with a fair dice numbered 1 to 6. To win the game she needs a 6 on each of the next two throws.
(a) Complete the tree diagram.
(b) Work out the probability that Sandy does not win the game.
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The line AB is drawn on a 1 cm$^2$ grid.
(a) Write down the co-ordinates of the midpoint of $AB$.
$\text{(.................... , ....................)}$ [1]
(b) Use Pythagoras' Theorem to work out the length of $AB$.
$AB = \text{........................................ cm}$ [2]
(c) Work out the gradient of $AB$.
$\text{.................................................}$ [2]
(d) Write down the equation of $AB$ in the form $y = mx + c$.
$y = \text{..............................................}$ [2]
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(a) On the diagram, sketch the graph of $y = 8x^2 - 18x - 5$ for $-1 \leq x \leq 3$. [2]
(b) Solve the equation $8x^2 - 18x - 5 = 0$.
$x = \text{..................}$ or $x = \text{..................}$ [2]
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