# GCSE Maths Paper 03 (Foundation) Practice Paper in the Style of OCR - Calculator

In this assessment, students will be able to complete a timed GCSE Mathematics Paper 3 (Calculator) in the style of OCR

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   OCR

Curriculum topic:   Foundation Practice Papers

Curriculum subtopic:   Calculator Practice Papers

Difficulty level:

### QUESTION 1 of 10

In this assessment, students will be able to complete a timed GCSE Mathematics Paper 3 (Calculator) in the style of OCR.

This is a mixture of single number and extended answer style assessment.

In the GCSE Examinations, you will have space given in the paper to write your answer.

At EdPlace, you will input your answers online, however, we recommend that you also have paper to use for any workings out or diagrams that you may need to draw.  Marks are allocated for this information.  For this paper, you will need graph paper to work on.

For each question, the marks awarded for each section are written next to the questions and look like this [4].

You should aim for 1 minute per mark

The timer is set for 90 minutes for this practice paper, although you can keep working after the timer has run out.

If you are struggling to answer a question do not waste time on it, but move onto the next question.

Disclaimer:

We have no affiliation to OCR and these questions represent our own unique content developed by EdPlace GCSE authors.

None of the content displayed here has been supplied by OCR or any other third party suppliers.

Write 3786 to the nearest 100.

[1]

Give a multiple of 7 that is between 52 and 64

[1]

Change 1.2 m into mm

[1]

Here is a list of numbers, select down all the numbers that are square numbers.

1      3     8     15     25     37

[1]

1

3

8

15

25

37

Write 36% as a decimal

[1]

A fair spinner has six sides.

They are labelled 1,2,3,4,5,6

(a) On the probability scale shown below, mark with a cross (x) the probability the spinner lands on a prime number.

(b) Write down the probability that the dice lands on a number less than 3.

[2]

There are four types of counter in a bag.

The table shows the number of each type of counter in the bag.

 Type Blue Spheres Red Spheres Red Cubes Blue cubes Number 28 14 31 12

There are more cubes than spheres. How many more?

[2]

Work out.

(a) √(4.84 x 2.25)      [1]

(b) (4.35 – 1.14)2 + 1.213        [2]

Simplify 2a – 5b + 3a + 2b

[2]

AB is a straight line

Angle X and angle Y are in the ratio 1 : 4

Find the size of angle y

[3]

In a school year group, there are a combination of boys and girls.

There are 84 boys in the year group

72% of the year group are girls

How many students are in the year group?

[3]

Andy, Bill and Charlie share some sweets in the ratio 1:3:2

What fraction of the sweets does Charlie get?

[2]

In a triangle, the biggest angle is six times the smallest angle. The other angle is 28 degrees smaller than the largest angle.

Work out the size of all the angles.

[5]

Here is a four-sided spinner.

The probability of each outcome from the spinner are shown in the table.

 Number 1 2 3 4 Probability 0.3 0.1 0.4

The spinner is spun once.

(a) What is the probability the spinner lands on 3?     [1]

(b) Which number is the spinner most likely to land on?       [1]

If I spin the spinner 200 times.

(c) how many times would I expect to get the number 2?      [2]

The rule to work out the total hire charge (C), in pounds (£) for hiring a car for a given number of days (D) is given by…

C = 60D+ 100

Zach wants to hire a car for 5 days.

(a) Work out the total hire charge.    [2]

Simon hires a car. The total charge is £700

(b) How many days did Simon hire the car for?        [2]

Fred has hired a storage container to store his belongings while he moves house.

He will use boxes of the following size to store his belongings.

The storage container is 3m wide, 4.5 m deep and 3m tall.

Fred wants to fill the container.

He can put six boxes a minute into the container.

Assuming the container is in the shape of a cuboid,

(a) Work out how long it will take Fred (in minutes) to fill the container.     [4]

(b) The container may not be in the shape of a perfect cuboid. How will this affect the time it takes to fill the storage container.      [1]

Work out.

[2]

Rearrange this formula to make b the subject

a = 3b + 4

[2]

(a) On a number line, show the inequality x ≥ -2     [2]

– 1 ≤ y < 5

(b)Write down all the possible values of y.      [2]

(c) Solve 5x + 3 ≤ 3x + 7       [3]

ξ = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A = {Multiples of 3}

B = {Factors of 18}

(a) Complete the Venn diagram to represent this information     [4]

A number is chosen at random.

(b) What is the probability the number is in the set AUB?    [2]

Solve the simultaneous equations

3x + 2y = 9

4x – 3y = 3.5

[3]

(a) Complete this table of values for y = x2 + 2x – 1        [2]

 x -4 -3 -2 -1 0 1 2 y 7 -1 2

(b) Draw the graph of y = x2 + 2x – 1 for -4 ≤ x ≤ 2      [2]

(c) Use the graph to estimate a solution to x2 +2x – 1 = 0         [1]

ABC is a right-angled triangle

(a) Work out the size of angle CAB.

The length of side BC is increased by 2 cm

The length of AB stays the same

Triangle ABC is still right-angled.

(b) Will the value of tan CAB increase or decrease? Give a reason for your answer.       [1]

In the diagram A,B and C are three regular polygons.

David thinks that a square will fit into the space for polygon X.

Is he correct?

[4]

Doris wants to paint a gas tank sat in her garden.

The gas tank is in the shape of a cylinder and she wants to paint all the sides including the top and bottom.

The gas tank has a diameter of 2.2 metres and a height of 1.3 metres.

Doris has 6 tins of paint that each cover 3.2 m2.

Does she have enough paint to cover the tank?

[5]

Solve the simultaneous equations.

2x + 3y = 26

3x – y = 6

[3]

Jenny has a bag that contains a blue counter, a red counter and a green counter.

Without looking, she picks out one, then another and then the final one.

(a) List all the different order in which she can pull out the counters.         [2]

One possible order is already shown in the table

You will need to use all the rows in the table

 First Second Third B R G

(b) Find the probability that the red counter is removed before the blue counter.         [1]

2 people take 7 hours to cut a hedge.

Assume that all the people cut the hedge at the same rate.

(a) How long would it take one person to cut the hedge?       [1]

(b) How long would it take 5 people to cut the same hedge?    [4]

Here is a right-angled triangle.

Work out the value of x.

[3]

(a) Show that p7 ÷ (p2)3 can be written as p       [2]

(b) Write (1/216) x 364 as a power of 6.           [3]

ABCD is a square

F is the midpoint of AB and E if the midpoint of AD

Find the percentage of the square ABCD that is not shaded. Give your answer in its simplest form,

[4]

• Question 1

Write 3786 to the nearest 100.

[1]

3800
3,800
EDDIE SAYS
The easiest way to do this is to count up and down until you get to a number with at least two zeros at the end. Counting up gets to 3800 Counting down gets to 3700 Which one is 3786 closest to?
• Question 2

Give a multiple of 7 that is between 52 and 64

[1]

56
63
EDDIE SAYS
Multiple just means 'times table' The times table for 7 is 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 All you are looking for is one of the numbers to be between 52 and 64
• Question 3

Change 1.2 m into mm

[1]

1200
1200mm
1200 mm
EDDIE SAYS
We need to look at conversion factors here m --> cm = x 100 cm --> mm = x 10 So to change m into mm, we have to...
• Question 4

Here is a list of numbers, select down all the numbers that are square numbers.

1      3     8     15     25     37

[1]

1
25
EDDIE SAYS
We need to think about what a square number is here. It's a number that is the answer to a number multiplied by itself. Can you times the same number together to get 37? Can you times the same number together to get 25?
• Question 5

Write 36% as a decimal

[1]

0.36
EDDIE SAYS
What does the word percent mean? Out of, or divide by, 100.
• Question 6

A fair spinner has six sides.

They are labelled 1,2,3,4,5,6

(a) On the probability scale shown below, mark with a cross (x) the probability the spinner lands on a prime number.

(b) Write down the probability that the dice lands on a number less than 3.

[2]

EDDIE SAYS

• Question 7

There are four types of counter in a bag.

The table shows the number of each type of counter in the bag.

 Type Blue Spheres Red Spheres Red Cubes Blue cubes Number 28 14 31 12

There are more cubes than spheres. How many more?

[2]

EDDIE SAYS

• Question 8

Work out.

(a) √(4.84 x 2.25)      [1]

(b) (4.35 – 1.14)2 + 1.213        [2]

EDDIE SAYS

• Question 9

Simplify 2a – 5b + 3a + 2b

[2]

EDDIE SAYS

• Question 10

AB is a straight line

Angle X and angle Y are in the ratio 1 : 4

Find the size of angle y

[3]

EDDIE SAYS

• Question 11

In a school year group, there are a combination of boys and girls.

There are 84 boys in the year group

72% of the year group are girls

How many students are in the year group?

[3]

EDDIE SAYS

• Question 12

Andy, Bill and Charlie share some sweets in the ratio 1:3:2

What fraction of the sweets does Charlie get?

[2]

EDDIE SAYS

• Question 13

In a triangle, the biggest angle is six times the smallest angle. The other angle is 28 degrees smaller than the largest angle.

Work out the size of all the angles.

[5]

EDDIE SAYS

• Question 14

Here is a four-sided spinner.

The probability of each outcome from the spinner are shown in the table.

 Number 1 2 3 4 Probability 0.3 0.1 0.4

The spinner is spun once.

(a) What is the probability the spinner lands on 3?     [1]

(b) Which number is the spinner most likely to land on?       [1]

If I spin the spinner 200 times.

(c) how many times would I expect to get the number 2?      [2]

EDDIE SAYS

• Question 15

The rule to work out the total hire charge (C), in pounds (£) for hiring a car for a given number of days (D) is given by…

C = 60D+ 100

Zach wants to hire a car for 5 days.

(a) Work out the total hire charge.    [2]

Simon hires a car. The total charge is £700

(b) How many days did Simon hire the car for?        [2]

EDDIE SAYS

• Question 16

Fred has hired a storage container to store his belongings while he moves house.

He will use boxes of the following size to store his belongings.

The storage container is 3m wide, 4.5 m deep and 3m tall.

Fred wants to fill the container.

He can put six boxes a minute into the container.

Assuming the container is in the shape of a cuboid,

(a) Work out how long it will take Fred (in minutes) to fill the container.     [4]

(b) The container may not be in the shape of a perfect cuboid. How will this affect the time it takes to fill the storage container.      [1]

EDDIE SAYS

• Question 17

Work out.

[2]

EDDIE SAYS

• Question 18

Rearrange this formula to make b the subject

a = 3b + 4

[2]

EDDIE SAYS

• Question 19

(a) On a number line, show the inequality x ≥ -2     [2]

– 1 ≤ y < 5

(b)Write down all the possible values of y.      [2]

(c) Solve 5x + 3 ≤ 3x + 7       [3]

EDDIE SAYS

• Question 20

ξ = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A = {Multiples of 3}

B = {Factors of 18}

(a) Complete the Venn diagram to represent this information     [4]

A number is chosen at random.

(b) What is the probability the number is in the set AUB?    [2]

EDDIE SAYS

• Question 21

Solve the simultaneous equations

3x + 2y = 9

4x – 3y = 3.5

[3]

EDDIE SAYS

• Question 22

(a) Complete this table of values for y = x2 + 2x – 1        [2]

 x -4 -3 -2 -1 0 1 2 y 7 -1 2

(b) Draw the graph of y = x2 + 2x – 1 for -4 ≤ x ≤ 2      [2]

(c) Use the graph to estimate a solution to x2 +2x – 1 = 0         [1]

EDDIE SAYS

• Question 23

ABC is a right-angled triangle

(a) Work out the size of angle CAB.

The length of side BC is increased by 2 cm

The length of AB stays the same

Triangle ABC is still right-angled.

(b) Will the value of tan CAB increase or decrease? Give a reason for your answer.       [1]

EDDIE SAYS

• Question 24

In the diagram A,B and C are three regular polygons.

David thinks that a square will fit into the space for polygon X.

Is he correct?

[4]

EDDIE SAYS

• Question 25

Doris wants to paint a gas tank sat in her garden.

The gas tank is in the shape of a cylinder and she wants to paint all the sides including the top and bottom.

The gas tank has a diameter of 2.2 metres and a height of 1.3 metres.

Doris has 6 tins of paint that each cover 3.2 m2.

Does she have enough paint to cover the tank?

[5]

EDDIE SAYS

• Question 26

Solve the simultaneous equations.

2x + 3y = 26

3x – y = 6

[3]

EDDIE SAYS

• Question 27

Jenny has a bag that contains a blue counter, a red counter and a green counter.

Without looking, she picks out one, then another and then the final one.

(a) List all the different order in which she can pull out the counters.         [2]

One possible order is already shown in the table

You will need to use all the rows in the table

 First Second Third B R G

(b) Find the probability that the red counter is removed before the blue counter.         [1]

EDDIE SAYS

• Question 28

2 people take 7 hours to cut a hedge.

Assume that all the people cut the hedge at the same rate.

(a) How long would it take one person to cut the hedge?       [1]

(b) How long would it take 5 people to cut the same hedge?    [4]

EDDIE SAYS

• Question 29

Here is a right-angled triangle.

Work out the value of x.

[3]

EDDIE SAYS

• Question 30

(a) Show that p7 ÷ (p2)3 can be written as p       [2]

(b) Write (1/216) x 364 as a power of 6.           [3]

EDDIE SAYS

• Question 31

ABCD is a square

F is the midpoint of AB and E if the midpoint of AD

Find the percentage of the square ABCD that is not shaded. Give your answer in its simplest form,

[4]

EDDIE SAYS