Q1.
Use ruler and compasses only to construct the perpendicular bisector of line AB.
You must show all your construction lines.
(Total for question = 2 marks)
Q2.
Reeta has a biased dice.
Each time Reeta rolls the dice, the probability that she will get a six is 0.1
(a) Write down the probability that she will not get a six.
...........................................................
(1)
Reeta rolls the dice 50 times.
(b) Work out an estimate for the number of times that she will get a six.
...........................................................
(2)
(Total for Question is 3 marks)
Q3.
A is the point with coordinates (−5, 12)
B is the point with coordinates (19, −48)
Find an equation of the straight line that passes through the points A and B
...........................................................
(Total for question = 3 marks)
Q4.
(a) Describe fully the single transformation that maps shape P onto shape Q.
.............................................................................................................................................
.............................................................................................................................................
(2)
(b) On the grid above, enlarge shape P with scale factor 3 and centre O.
(2)
(c) On the grid above, rotate shape R 90° anticlockwise with centre (0, 1)
(2)
(Total for question = 6 marks)
Q5.
Jack, Kate and Lila share some money in the ratios 5 : 9 : 6
In total, Jack and Kate receive £56
Work out the amount of money Lila receives.
£...........................................................
(Total for question = 3 marks)
Q6.
The diagram shows the graph of y = f(x)
The point P has x coordinate –2
Use the graph to find an estimate for the gradient of the curve at P
...........................................................
(Total for question = 3 marks)
Q7.
Expand and simplify (2x + 3)(x − 5)(x + 4)
...........................................................
(Total for question = 3 marks)
Q8.
(a) On the grid, draw the straight line with equation
(i) x = 3 (ii) y = 1 (iii) x + y = 7
Label each line with its equation.
(3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x≥3 y≥1 x+y≤7
Label the region R
(1)
(Total for question = 4 marks)
Q9.
The first four terms of an arithmetic sequence are
5 9 13 17
(a) Write down an expression, in terms of n, for the nth term.
...........................................................
(2)
(b) Write down an expression, in terms of n, for the (n + 1)th term.
...........................................................
(1)
(Total for question = 3 marks)
Q10.
In a school, there is a total of 640 children.
The ratio of the number of girls to the number of boys is 7 : 9
How many boys are there in this school?
...........................................................
(Total for question = 2 marks)
Q11.
A cylinder has diameter 12 cm and length 30 cm.
Work out the curved surface area of the cylinder.
Give your answer correct to 3 significant figures.
........................................................... cm 2
(Total for Question is 3 marks)
Q12.
A, B, C and D are points on a circle.
ABP and DCP are straight lines.
AB = 16 cm, BP = 14 cm, CP = 12 cm
Work out the length of DC
........................................................... cm
(Total for question = 3 marks)
Q13.
A = 23 × 32 × 54
B = 35 × 5 × 7 3
Find the Highest Common Factor (HCF) of A and B.
...........................................................
(Total for question = 2 marks)
Q14.
Here are the heights, in millimetres, of 11 seedlings.
16 12 19 17 24 27 19 15 23 27 10
Work out the interquartile range of these heights.
........................................................... mm
(Total for question = 3 marks)
Q15.
The grouped frequency table gives information about the ages of 200 elephants.
(a) Complete the cumulative frequency table.
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
(2)
(c) Use the graph to find an estimate for the number of elephants with ages of more than
26 years.
...........................................................
(2)
(Total for question is 5 marks)
Q16.
Here are two vectors.
Calculate the magnitude of the vector
...........................................................
(Total for question = 3 marks)
Q17.
(a) Express 600 as a product of powers of its prime factors.
Show your working clearly.
...........................................................
(3)
(b) Simplify
Give your answer as a power of 5
...........................................................
(2)
(Total for question = 5 marks)
Q18.
Here is a rectangle.
Given that the area of the rectangle is less than 75 cm2
find the range of possible values of x
...........................................................
(Total for question = 5 marks)
Q19.
Ava writes down five whole numbers.
For these five numbers
the median is 7
the mode is 8
the range is 5
Find a possible value for each of the five numbers that Ava writes down.
...........................................................
(Total for question = 3 marks)
Q20.
Express in the form where a, b and c are integers to be found.
...........................................................
(Total for question = 2 marks)
Q21.
n is an integer.
(a) Write down all the values of n such that –2 ≤ n < 3
...........................................................
(2)
(b) On the number line, represent the inequality y ≤ 1
(1)
(Total for question = 3 marks)
Q22.
Solve the simultaneous equations
x + 2y = 15
4x – 6y = 4
Show clear algebraic working.
x = ...........................................................
y = ...........................................................
(Total for question = 3 marks)
Q23.
The diagram shows an isosceles triangle.
Work out the area of the triangle.
........................................................... cm 2
(Total for question = 4 marks)
Q24.
A solid metal sphere has radius 1.5 cm.
The mass of the sphere is 109.6 grams.
Work out the density of the sphere.
Give your answer correct to 3 significant figures.
........................................................... g / cm 2
(Total for question = 3 marks)
Q25.
The diagram shows a solid cube.
The cube is placed on a table so that the whole of one face of the cube is in contact with
the table.
The cube exerts a force of 56 newtons on the table.
The pressure on the table due to the cube is 0.14 newtons/cm2
Work out the volume of the cube.
........................................................... cm 3
(Total for question = 4 marks)
Q26.
A and B are two similar vases.
Vase A has height 10 cm.
Vase B has height 15 cm.
The difference between the volume of vase A and the volume of vase B is 1197 cm3
Calculate the volume of vase A
........................................................... cm 3
(Total for question = 4 marks)
Q27.
y = x3 – x2 – 54x + 10
(a) Find
...........................................................
(2)
The curve with equation y = x3 – x2 – 54x + 10 has two turning points.
(b) Find the x coordinate of each of these two points.
...........................................................
(3)
(Total for question = 5 marks)
Q28.
A particle moves along a straight line.
The fixed point O lies on this line.
The displacement of the particle from O at time t seconds is s metres, where
s = t3 − 6t + 3
(a) Find an expression for the velocity, v m/s, of the particle at time t seconds.
v = ...........................................................
(2)
(b) Find the acceleration of the particle at time 5 seconds.
........................................................... m/s 2
(2)
(Total for Question is 4 marks)
Q29.
The diagram shows a cuboid ABCDEFGH.
EH = 9 cm, HG = 5 cm and GB = 6 cm.
Work out the size of the angle between AH and the plane EFGH.
Give your answer correct to 3 significant figures.
........................................................... °
(Total for question = 4 marks)
