Non-Calculator Practice Questions
May/June 2017
GCSE Mathematics (OCR style)
Foundation Tier
Paper 2
Name
………………………………………………………………
Class
………………………………………………………………
INSTRUCTIONS TO CANDIDATES




Answer all the questions.
Read each question carefully. Make sure you know what you have to do before
starting your answer.
You are NOT permitted to use a calculator in this paper.
Do all rough work in this book.
INFORMATION FOR CANDIDATES


The number of marks is given in brackets at the end of each question or part
question on the Question Paper.
You are reminded of the need for clear presentation in your answers.
© The PiXL Club Limited 2017
This resource is strictly for the use of member schools for as long as they remain members of The PiXL Club. It may not
be copied, sold nor transferred to a third party or used by the school after membership ceases. Until such time it may be
freely used within the member school. All opinions and contributions are those of the authors. The contents of this
resource are not connected with nor endorsed by any other company, organisation or institution.
Page 1 of 40
Number Operations and Integers
1
Calculate the following
(a) 22 x 15
................................................. [1]
(b) 306 ÷ 9
................................................. [1]
(c) 5 x -2
................................................. [1]
(d)
−30
−6
................................................. [1]
2
(a) Complete the table with suitable values. Do not use the same value more than once.
Square
number
Cube number
Prime number
Factor of 60
Even number
Multiple of 5
[3]
(b) Explain why a prime number can never also be a square number.
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
[1]
Page 2 of 40
3
Rose is 8 years old and her brother Zach is 5 years old. They are going to the fair with both their parents.
The costs of entry are given below.
Adult ticket
£6.70
Child ticket (under 15 years old)
£5.50
Family ticket (2 adults and 2 children)
£22
Rosie finds a voucher on the internet for 10% off the full price adult and child tickets, it doesn’t apply to
the family ticket. What is the cheapest way for them to get into the fair? Show how you decide.
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
[3]
4
(a) Write the number 420 as a product of its prime factors
................................................. [2]
(b) The number 600 can be written in the form 2𝑥 × 3𝑦 × 5 𝑧 . Find the values 𝑥, 𝑦 and 𝑧.
................................................. [1]
(c) Find the highest common factor of 420 and 600.
................................................. [2]
Page 3 of 40
5
(a) Calculate
4 + 5 x 22
(i)
................................................. [2]
√25+32
2
(ii)
................................................. [2]
(b) Theo thinks of a number greater than zero, doubles it, adds three and then squares it. He gets 64.
What was the number he first thought of?
................................................. [2]
Fractions, Decimals & Percentages
6
(a) Simplify these fractions:
(i)
3
15
................................................. [1]
(ii)
4
24
................................................. [1]
(b) Which fraction has the greatest value
3
15
or
4
24
?
................................................. [1]
(c) For each pair of numbers decide which is greater.
(i)
1
9
or
0.09
................................................. [1]
(ii) 25% or
0.3
................................................. [1]
(iii) 15% or
1
5
................................................. [1]
Page 4 of 40
7
Maria is getting a new carpet fitted in her living room. The room is 2
3
1
4
2
3
m wide and 3
1
4
m long.
m
2
2
3
m
(a) Calculate the total area of the carpet Maria needs to buy.
Give your answer as a mixed number.
………………………………….... m2 [4]
(b) She is also going to buy a skirting board which will go around the full perimeter of the living room.
Calculate the length of skirting board that Maria needs.
Give your answer as a mixed number.
................................................. m [3]
Page 5 of 40
8
Marlowe does a survey of his class, he asks all of them whether they are left handed or right handed.
There are 30 people in his class.
3
(a) He says that 4 of the class are right handed. Explain why he could not be correct.
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
[1]
(b) 25 students were right handed. What fraction of the class were right handed, give your answer in
its simplest terms.
.........................[2]
9
Becky was doing the calculation 0.24 ÷ 6 and she got the answer 4. Is she right? Explain how you know.
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
………………………………………………………………………………………………………………[1]
Indices & Surds
10
Write each of these as a single power of 2.
(a) 2 x 2 x 2 x 2 x 2
................................................. [1]
(b) 24 x 26
................................................. [1]
(c)
26
23
................................................. [1]
(d) (24)3
................................................. [1]
(e)
1
8
................................................. [2]
Page 6 of 40
11
(a) The distance to the sun is approximately 150 million km away. Write this number in standard form.
................................................. [1]
(b) The thickness of a piece of paper is approximately 0.05 mm. Write this number is standard form.
................................................. [1]
(c) Using these values, calculate how many pieces of paper it would take to reach the sun.
Give your answer in standard form.
................................................. [3]
Approximation & Estimation
12
(a) Show that 100 is a good estimate for this calculation
10.1 × 31.4
5.9 − 3.1
................................................. [2]
(b) Will the accurate answer be greater or less than your estimate? Show your reasoning.
................................................. [1]
13
(a) Marco won a 60m sprint race.
Page 7 of 40
His time was measured as 7.1 seconds rounded to 1 decimal place.
Complete the error interval for Marco’s time, s.
(a) ………… ≤ 𝑠 < ………… [2]
(b) Justin came second in the same race.
His time was measured as 7.23 seconds truncated to 2 decimal places.
Complete the error interval for Justin’s time, t.
(b) ………… ≤ 𝑡 < ………… [2]
Ratio, Proportion & Rates of Change
14
Share the following into the given ratios.
(a) 50 kg into 2:5:3
................................................. [2]
(b) 1 hour 20 minutes into 3:2
................................................. [3]
15
Write 2 minutes to 45 seconds as a ratio in the form 1 : n.
……............. [2]
Page 8 of 40
16
(a) The length of an Airbus A300 aeroplane is 54 m.
The ratio of the length of this aeroplane to its wingspan is 6 : 5.
Work out the wingspan of the aeroplane.
................................................. [2]
17
Cameron, Dan and Eric share £274 between them.
Cameron receives £70 more than Dan.
The ratio of Cameron’s share to Dan share is 8 : 3.
Work out the ratio of Eric’s share to Dan’s share.
Give your answer in its simplest form.
................................................. [4]
18
Colin, Dave and Emma share some money.
Colin gets 30% of the money.
Emma and Dave share the rest of the money in the ratio 3 : 2
What is Dave's share of the money?
................................................. [4]
Page 9 of 40
19
Here are the ingredients needed to make 10 pancakes.
Matthew makes 30 pancakes.
(a) Work out how much flour he uses.
................................................. [1]
Tara makes some pancakes.
She uses 750 ml of milk.
(b) Work out how many pancakes she makes.
................................................. [3]
20
(a) y is directly proportional to the square of x.
x = 3 when y = 54.
Work out y when x = 2.
(a) y = …………………… [2]
(b) y is inversely proportional to x.
y = 6 when x = 10.
Find the value of x when y = 15.
(b) x = …………………… [2]
Page 10 of 40
Algebra
21
(a) Simplify 7x – 4y – 4x + 3y
………………………………… [2]
(b) Georgina, Samantha and Mason collect football stickers.
Georgina has x stickers in her collection.
Samantha has 7 stickers less than Georgina.
Mason has 4 times as many stickers as Georgina.
Write down an expression, in terms of x, for the total number of these stickers.
Give your answer in its simplest form.
………………………………… [4]
22
The diagram shows a triangle.
Write down an expression in terms of x and y, for the perimeter of this triangle.
Give your answer in its simplest form.
................................................. [3]
23
A garden in the shape of an isosceles triangle has two equal sides 8m longer than the other and the
perimeter is 40m.
Form an equation and find the length of the shorter side.
................................................. [3]
24
Solve:
(a) 7x – 5 = 3x + 9
Page 11 of 40
x = …………………………… [2]
Simplify:
(b) 3p2q3 x 2p3q5
…………………………… [2]
Expand:
(c) s(3s – 4)
…………………………… [1]
Factorise fully:
(d) 3ad – 6ac
…………………………… [2]
25
Work out the perimeter of the semi-circle with radius 8 cm.
Give your answer in terms of π.
………………………………… cm [3]
26
1
Given that s = ut + at2 , work out the value of s when u = 3, t = 4, a = –5.
2
s = ………………… [3]
27
James is 35 years old.
Three years ago, he was four times as old as his son was then.
Page 12 of 40
How old is his son now?
…………………………… [3]
28
Rearrange the formula y = 5x – 3 to make x the subject.
x = …………………………… [2]
29
A rectangle has a width of x cm. Its length is 5 cm longer than the width.
(a) Write down an expression for the area of the rectangle.
……………………………cm2 [1]
(b) Given that the area is 84 cm2, work out the length and width of the rectangle.
length = …………………………… cm
width = …………………………… cm
[4]
Page 13 of 40
30
Expand and simplify.
(a) 3(2x + 5y) – 2(4x + 3y)
………………………………… [2]
(b) (x – 4)(x + 7)
………………………………… [3]
31
3 rulers and 4 pens cost £1.02.
2 rulers and 5 pens cost 96 pence.
Calculate the cost of each ruler and each pen.
Ruler = …………………………………
Pen = …………………………………
[3]
32
Solve simultaneously.
5x + 3y = 14
2x – y = 10
x = ……., y = ……. [3]
33
(a) Solve the inequality.
2x + 5 ≥ 11
………………………………… [2]
(b) Show your solution on the number line.
[1]
Page 14 of 40
34
(a) Complete the table of values for the equation y = 3x – 2 from -3 ≤ x ≤ 3
x
-3
y
-11
-2
-1
0
-2
1
2
3
4
[2]
(b) Plot the graph on the axes below.
[2]
(c) Give the equation of a line parallel to the equation y = 3x – 2
………………………………… [2]
Page 15 of 40
35
(a) Complete the table of values for the equation y = x2 – 2x from -2 ≤ x ≤ 3
x
-2
y
8
-1
0
1
2
3
-1
[2]
(b) Plot the graph on the axes below.
[2]
(c) Use your graph to find out the solutions to the equation
x2 – 2x = 1.5
x = ………., x = ………. [2]
Page 16 of 40
36
Explain why for any value of x both function machines give the same value of y.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
[1]
37
Here is a linear sequence
8, 11, 14, 17, …, …
(a) Write down the next two terms.
………………… and ……………… [1]
(b) Find an expression for the nth term.
………………………………… [2]
(c) David says that 63 is in the sequence. Is he correct?
Give reasons for your answer.
………………………………… [2]
Page 17 of 40
38
Match the graphs with the corresponding equations.
Equation
y =x 2
y = -2x + 1
y = x3
y=
1
𝑥
Graph
[3]
Page 18 of 40
39
The conversion graph below can be used to convert between pounds (GBP) and Euros.
(a) Write down the exchange rate from pounds to Euros shown by the graph.
£1 = ………………. Euros [1]
(b) Using this exchange rate, convert £150 into Euros.
………………. Euros [2]
Page 19 of 40
Basic Geometry
40
(a) A shape is a quadrilateral with one pair of parallel sides. What’s the name of the shape?
………………………………… [1]
(b)
(i) Write down the name of this type of triangle.
………………………………… [1]
(ii) What type of angle is ABC?
………………………………… [1]
41
Complete the sentences below.
This 3D shape is called a …………………… .
The shape has ……… vertices.
The shape has ……… edges.
The shape has ……… faces.
[4]
Page 20 of 40
42
(a) Construct the perpendicular bisector of the line below.
[2]
(b) Construct the bisector of the angle shown.
[2]
Page 21 of 40
43
Sam is building a new house and needs to supply water to the house.
He can take a water pipe from the main water supply at any point. He wants to save money so wants it
to be the shortest distance.
Construct the shorted possible pipeline to his house.
[3]
Page 22 of 40
44
Jane wants to buy a new house.
She wants to live within 10km of Aldington and within 8km of Broughton.
She also wants to live closer to Crick than Aldington.
Shade the region that Jane should look to buy a house.
Scale: 2km=1cm.
[4]
Page 23 of 40
45
AB and DE are parallel. AE and BD are straight lines
(a) Explain why angle BDE is 46°.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………… [1]
(b) Calculate the size of angle ACB. Show your working and give reasons.
Angle ACB is …………° because ………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………… [2]
46
A regular polygon has an interior angle of 150°. Calculate how many sides the polygon has.
……………………………… [2]
Page 24 of 40
47
ABCDE is a regular pentagon. DEFGHI is a regular hexagon.
(a) Calculate the size of the angle DEF.
DEF = …………° [2]
(b) Hence, or otherwise, calculate the size of angle AEF
AEF = …………° [2]
Page 25 of 40
48
(a) Describe the single transformation that maps shape A onto shape B.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
[2]
(b) Describe the single transformation that maps shape B onto shape C.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
[3]
(c) Translate shape C [
5
]. Label this image D.
0
[2]
(d) Describe the single transformation that maps shape A onto shape D.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
[2]
Page 26 of 40
49
Enlarge the shape below by scale factor 3 using the origin as the centre of enlargement.
[2]
50
Point E is the midpoint of line AB and CD.
Prove that triangle ABE and CDE are congruent.
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
[2]
Page 27 of 40
51
State if the triangles below are similar.
Show how you decide.
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
[2]
52
A titanium bar measures 5cm by 10cm by 4cm. Titanium has a density of 4.506 g/cm³.
Calculate the mass of the titanium bar.
State the units of your answer
…………………… …………
[4]
Page 28 of 40
53
Calculate the area of the following sector, leaving your answer in terms of π.
…………………… m2 [2]
54
Triangle ABC is shown below.
State which type of triangle this is.
Show how you decide.
……………………………… triangle [3]
Page 29 of 40
55
Calculate the area of the following shapes.
(a)
…………………… cm2 [2]
(b)
…………………… cm2 [2]
56
(a) Write down the correct name of this 3D shape.
…..…………………… [1]
(b) Calculate the volume of this shape.
…………………… cm3 [2]
(c) Calculate the total surface area of this shape.
…………………… cm2 [3]
Page 30 of 40
57
A container is made in the shape of a cylinder joined to a hemisphere at both ends. The diameter of the
shape is 6 cm and the height of the cylinder is 10 cm.
Calculate the volume of the container in terms of 𝜋.
[The volume V of a sphere with radius r is 𝑉
4
= 𝜋𝑟 3 ]
3
................................................. [5]
58
The diagram shows triangle ABC.
The point D lies on BC such that CD = 12 cm.
AC = 13 cm, angle ABD = 60° and angle ADB = 90°.
Calculate the exact value of the length of AB in its simplest form.
................................................. [5]
Page 31 of 40
59
Complete this table of exact values.
[2]
Probability
60
At ‘The Turing Maths Academy’, a soda machine sells Cola (C), Pop (P) and Fizzy (F).
Steve buys 2 drinks at random.
(a) List all the possible pairs of drinks he could buy.
[2]
(b) Find the probability that both drinks are the same.
........................ [2]
Page 32 of 40
61
Jim, Hannah and Laura want to find out if a coin is biased.
They decide to toss the coin and count the number of times it lands on heads.
The table shows the number of trials each person completes and the number of times the coin lands on
heads.
(a) Complete the table to show the relative frequency for each experiment.
Give your answer as a decimal.
[3]
(b) Which person is likely to have the most accurate estimate of the probability of a head?
Explain your choice.
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
[2]
(c) Is the coin fair? Explain your answer.
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
[1]
Page 33 of 40
62
The button in the picture below has a pattern on one side and is plain on the other.
Chris, Jim and Gary each drop a number of these identical buttons and count how many times the
buttons land with the pattern side facing up. This table shows some of their results.
(a) Chris says:
1
“There are only two sides to the button, so the probability of a button landing ‘pattern up’ is .”
2
Criticise Chris’s statement.
……………………………………………………………………………………………………………………
……………………………………………………………………………………………………………… [1]
(b) Gary’s results give the best estimate of a button landing ‘pattern up’.
Explain why.
……………………………………………………………………………………………………………………
……………………………………………………………………………………………………………… [1]
(c) Gary drops three further buttons.
Estimate the probability that all three buttons land ‘pattern up’.
(c) ................................................. [2]
Page 34 of 40
63
Phil uses two fair spinners in a game.
5
3
4
7
9
6
4
8
4
Spinner 1
2
Spinner 2
He spins both spinners and adds the two results together.
(a) Phil works out the probability of getting a total of 11.
His workings are shown below.
Phil has made a number of mistakes.
Describe two of these.
(i) ………………………………………………………………………………………………………………
………………………………………………………………………………………………………… [1]
(i) ………………………………………………………………………………………………………………
………………………………………………………………………………………………………… [1]
(b) Zahra uses the same two spinners in a different game.
She finds the difference between the results when she spins the spinners.
Find the probability the difference will be 1.
[3]
Page 35 of 40
64
A class of 35 students are asked if they like cereal or fruit for breakfast.
21 students said they like fruit. 20 students said they like cereal. 4 students said they don’t like either.
(a) Complete the Venn diagram.
[3]
One student is chosen at random. What is the probability that this student:
(b) only likes fruit?
................................. [2]
Page 36 of 40
65
Samir sometimes gets a bus to football training.
When he doesn’t get a bus, he walks.
The probability that he gets a bus to training is 0.6.
The probability that he walks home from training is 0.2.
(a) Complete the tree diagram.
[2]
(b) Find the probability that Samir takes a bus to training and then walks home.
................................. [2]
(c) Find the probability that Samir doesn’t get a bus on a particular day.
................................. [2]
Page 37 of 40
Statistics
66
The table shows some information about the number of medals won by each of 5 countries in the Winter
Olympics.
(a) Complete the table for Germany and Norway.
[2]
(b) What was the total number of Bronze medals that were awarded?
................................. [2]
(c) For one country, the number of Silver medals was more than half its total number of medals.
Which country is this?
................................. [1]
Page 38 of 40
67
The frequency polygon below represents the sales on different days of a major ice cream manufacturer
in London and Paris.
(a) Draw two comparisons from the frequency polygon.
(i) …………………………………………………………………………………………………………
…………………………………………………………………………………………………………
(ii) …………………………………………………………………………………………………………
…………………………………………………………………………………………………………
[4]
(b) What conclusions can you draw about the temperature in London and Paris?
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
[2]
Page 39 of 40
68
The scatter diagram below shows the test data from a science test and maths test for a class of
students.
(c) One of the results is an outlier. Write down the scores this student achieved for maths and science.
Science ………… Maths …………[2]
(d) Another student sits the science test and scores 40 marks. Estimate the score they are likely to
achieve in maths.
................................. [2]
(e) One final student sits the maths test and scores 70. Estimate the score they are likely to achieve in
science.
................................. [1]
(f) Which of these two estimates is likely to be most accurate?
Explain your reasoning.
………………… because ………………………………………………………………………………………
…………………………………………….…………………………………………….………………………...
…………………………………………….…………………………………………….………………………...
[3]
(g) Which subject has the most consistent results? Explain your reasoning.
………………… because ………………………………………………………………………………………
…………………………………………….…………………………………………….………………………...
[2]
Page 40 of 40