No questions found
The points $A$, $B$ and $C$ are plotted on a one centimetre square grid.
(a) Write down the coordinates of point $A$, point $B$ and point $C$.
$$A = ( \text{.........................} , \text{.........................} )$$
$$B = ( \text{.........................} , \text{.........................} )$$
$$C = ( \text{.........................} , \text{.........................} )$$ \quad [3]
(b) On the grid, plot and label point $D (6, -3)$.
[1]
(c) Complete the quadrilateral $ABCD$.
Write down the mathematical name of quadrilateral $ABCD$.
................................................
[1]
(d) On the grid, draw the line of symmetry of quadrilateral $ABCD$.
[1]
(e) Write down the coordinates of the mid-point of $CB$.
$$( \text{.........................} , \text{.........................} )$$ \quad [1]
(f) Work out the gradient of $CB$.
................................................
[2]
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505
This table shows the number of newspapers sold in a shop each day during one week.
[Table_1]
(a) Find the total number of newspapers sold that week.
.................................................. [1]
(b) Find how many more newspapers were sold on Saturday than on Tuesday.
.................................................. [1]
(c) Find the range.
.................................................. [1]
(d) Find the median number of newspapers sold.
.................................................. [2]
Complete the bar chart to show the information in the table.
[Graph_1] [2]
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505
(a) Work out $2.87^2$. Give your answer correct to 2 decimal places.
(b) Work out. $$\frac{29.7}{6.1 + 3.8}$$
(c) Work out $\sqrt[3]{64}$.
(d) Work out $5800 \times 250$. Give your answer in standard form.
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559
578
(a) Petrol costs $2.47 for each litre.
Dev buys a whole number of litres of petrol.
Work out the greatest number of litres he can buy with $50 and how much change he gets.
....................... litres with $ ....................... change [3]
(b) At the petrol station, it takes 3 seconds to pump each litre of petrol into a car.
Work out how long it would take to pump 28 litres of petrol into a car.
Give your answer in minutes and seconds.
....................... minutes ....................... seconds [2]
(c) Dev drives at an average speed of 20 km/h for 30 minutes and then at an average speed of 58 km/h for 2 hours.
Calculate the average speed for the whole journey.
...................................... km/h [4]
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532
571
In the diagram, $FED$ is a straight line.
$AB$ is parallel to $DC$ and $BD = BC$.
(a) Find the value of $x$, the value of $y$ and the value of $z$. Give a geometric reason for each answer.
$x = \text{................................. because ........................................................}$
..........................................................................................................................
$y = \text{................................. because ........................................................}$
..........................................................................................................................
$z = \text{................................. because ........................................................}$
.......................................................................................................................... [6]
(b) Find the value of $p$.
$p = \text{.................................}$ [2]
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539
(a) Factorise.
$5x + 10$
.................................................... [1]
(b) Multiply out the brackets.
$x(x^2 - 3x)$
.................................................... [2]
(c) In this question, all lengths are in centimetres.
(i) Find an expression, in terms of $x$, for the perimeter of this rectangle.
Give your answer in its simplest form.
.................................................... [2]
(ii) The perimeter of this rectangle is 36 cm.
Write down an equation in terms of $x$ and solve it to find the longest side of the rectangle.
.................................................... cm [4]
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This formula can be used to convert between a temperature in \(^\circ\)C, and a temperature in \(^\circ\)F.
$F = 1.8C + 32$
(a) Use the formula to convert 15\(^\circ\)C to \(^\circ\)F.
...................................................... \(^\circ\)F [2]
(b) Use the formula to convert 86\(^\circ\)F to \(^\circ\)C.
...................................................... \(^\circ\)C [2]
(c) Rearrange $F = 1.8C + 32$ to make $C$ the subject.
\(C = \text{......................................................}\) [2]
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Sam has a biased six-sided die. The table shows the probability of the die landing on each of the numbers 2 to 6.
[Table_1]
$$\begin{array}{|c|c|c|c|c|c|c|} \hline \text{Number} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text{Probability} & 0.16 & 0.18 & 0.18 & 0.16 & 0.11 \\ \hline \end{array}$$
(a) Work out the probability that the die will land on 1.
........................................................... [2]
(b) Sam throws the die once.
Work out the probability that the die lands on 5 or 6.
........................................................... [1]
(c) Sam throws the die 50 times.
Calculate an estimate of the number of times the die will land on 2.
........................................................... [1]
(d) Sam throws the die twice.
(i) Complete the tree diagram.
First throw
Second throw
........
6 6
0.11 ........
........
Not a 6
........
........ ........
Not a 6
Not a 6
........ ........
6
........ ........
Not a 6
........ ........
........
Not a 6
[2]
(ii) Find the probability that Sam does not throw a 6 on either throw.
........................................................... [2]
503
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(a)
The diagram shows the front of a washing machine. The front is a rectangle and the door is a circle.
Work out the shaded area.
.......................................... $\text{cm}^2$ [3]
(b) In a sale, the price of a washing machine is reduced from \$1250 to \$1175.
(i) Work out the percentage reduction.
.................................................. \% [3]
(ii) 3 years ago Tony invested \$1000 at a rate of 8\% per year simple interest.
Is the value of his investment enough to buy the washing machine in the sale? Show how you decide. [4]
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531
Kiara and Prisha are sisters.
At New Year 2023, Kiara was 10 years old and Prisha was 14 years old.
(a) At New Year 2023, their grandfather gives money to Kiara and Prisha.
The money is divided in the ratio of their ages.
Kiara receives $250.
Work out the total amount the grandfather gives the sisters.
$ \text{..................................................} \quad [3]
(b) At New Year 2023, Kiara and Prisha’s aunt gives them $180 also to be divided in the ratio of their ages.
Work out how much of the $180 each sister gets.
Kiara $ \text{..................................................}
Prisha $ \text{..................................................} \quad [2]
(c) Work out the ratio \text{ Kiara’s age : Prisha’s age } at New Year 2029.
Give your answer in its simplest form.
\text{........................} : \text{........................} \quad [2]
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551
The diagram shows the cross-section of a garden shed. The diagram has one line of symmetry.
(a) The shed is a prism with length 1.5 m. Work out the volume of the shed. Give the units of your answer. [5]
(b) Use Pythagoras’ Theorem to work out the value of $x$. [3]
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533
(a) (i) On the diagram, sketch the graph of $y = x^3 + 6x^2$ for $-6 \leq x \leq 2$. [2]
(ii) Find the coordinates of the local minimum.
( \text{..............................., ...............................} ) [1]
(iii) Find the coordinates of the local maximum.
( \text{..............................., ...............................} ) [1]
(b) On the diagram, sketch the graph of $y = 10 - 3x$ for $-6 \leq x \leq 2$. [2]
(c) Find the x-coordinate of each point of intersection of $y = x^3 + 6x^2$ and $y = 10 - 3x$.
$x = \text{.......................................... and } x = \text{..........................................} \text{ and } x = \text{..........................................}$ [3]
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