(2 marks)Question 1
Sally estimates the value of 42.8 x 63.7 to be 8.
285
(a) Write down three numbers Sally could use to get her estimate.
(2 marks)
(b) Without finding the exact value of 42.8 63.7 , explain why it must
be more than 8. 285 (2 marks)
[4]
Question 2
Malika's father won £128.
He shared the £128 between his three children in the ratio 6:3:1.
Malika was given the biggest share.
(a) Work out how much money Malika received.
Malika saved 
of her share.
(b) Work out how much Malika saved.
[6]
Question 3
Mr. Singh shared £20 between his two children in the ratio of their ages.
Narinder is 7 years old and her brother is 3 years old.
Work out how much money Narinder received from her father.
[3]
Question 4
y is directly proportional to the cube of x.
When x = 2, y = 64.
(a) Find an expression for y in terms of x. (3 marks)
Hence or otherwise,
(3 marks)
[6]
Question 5
(a) Write down an expression in terms of x for the length of the rectangle.
The perimeter of the rectangle is P cm.
(b) Write down a formula for P in terms of x.
(c) Complete the table for x = 2, 4 and 8.
(d) On the grid below draw the graph of P against x for values of x from 2 to 8.
[6]
Question 6
Solve the equations
a) 3y + 7 = 28
b) 2(3p + 2) = 19
[4]
Question 7
The line with equation 3y = - 2x + 6 has been drawn on the grid.
(a) Draw the graph of y = 2x - 2 on the same grid. (2 marks)
(b) Use the graphs to find the solution of the simultaneous equations
3y = - 2x + 6
y = 2x - 2 (2 marks)
A line is drawn parallel to 3y = - 2x + 6 through the point (2, 1).
(c) Find the equation of this line. (2 marks)
[6]
Question 8
(a) Complete the table of values for the graphs of
y = x3 - 2 and
y = 3x2 + 3x -6.
(b) i) Use the graph paper on the following page to draw the graphs of
y = x3 - 2 and y = 3x2 + 3x - 6.
ii) Use your graph to solve the equation x3 - 3x2 - 3x + 4 = 0.
Question 9
i) Solve the inequality 3n > -8.
ii) Write down the smallest integer which satisfies the inequality 3n > -8.
(2 marks)
[2]
Question 10
Ten men took part in a long jump competition.
The table shows the heights of the ten men and the best jumps they made.
This information is shown in the scatter graph below.
(a) Draw a line of best fit (2 marks)
(b) Use your line of best fit to estimate
i) the height of a man who could make a best jump of 5.2 m.
ii) the best jump of a man of height 1.73 m. (2 marks)
[4]
Question 11
Here are the numbers of people living in the different houses in a short road.
4, 2, 3, 4, 5, 1, 3, 2
(a) Work out the mean number of people per house.
(b) Work out the range of the number of people living in a house.
One of the houses is to be chosen at random.
(c) On the probability line below, mark with a letter X the probability that the
house chosen will be the one with 5 people.
[6]
Alan throws a fair coin 600 times.
(a) How many times would you expect him to get Heads? (1 mark)
Here is a 5-sided spinner.
Its sides are labelled 1, 2, 3, 4, 5.
Alan spins the spinner and throws a coin.
One possible outcome is (3, Heads).
(b) List all the possible outcomes. (2 marks)
The spinner is biased.
The probability that the spinner will land on each of the numbers 1 to 4 is given in the table.
Alan spins the spinner once.
(c) i) Work out the probability that the spinner will land on 5. (2 marks)
ii) Write down the probability that the spinner will land on 6. (1 mark)
iii) Write down the number that the spinner is most likely to
land on. (1 mark)
[7]
Question 13
The diagram represents the frame for part of a building.
BD and CD are equal in length.
BD and AE are horizontal.
(a) Write down the special mathematical name for the triangle BCD. (1 mark)
(b) Work out the area of triangle BCD. (2 marks)
(c) Calculate the length BC.
Give your answer correct to 3 significant figures. (3 marks)
(d) Calculate the size of the angle marked x .
Give your answer correct to 1 decimal place. (3 marks)
[9]
Question 14
The scale diagram shows the position of a radio mast, M.
1 cm on the diagram represents 20 km.
M
Signals from the radio mast can be received up to a distance of 100 km.
(a) Shade the region on the scale diagram in which signals from the radio mast
can be received.
The distance of a helicopter from the radio mast is 70 km correct to the nearest kilometre.
(b) Write down
i) the maximum distance the helicopter could be from the radio mast,
ii) the minimum distance the helicopter could be from the radio mast.
[4]
Total = 73