# GCSE Maths Paper Three (Higher) Practice Paper in the Style of Edexcel - Calculator

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

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel

Curriculum topic:   Higher 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 EdExcel.

This is a extended answer style assessment.

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

At EdPlace, while you will write your answers online, we would recommend that you have paper to write your workings out on as you progress through.

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 Pearson Edexcel and these questions represent our own unique content developed by EdPlace GCSE authors.

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

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 from the universal set ξ

(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) On the grid, draw the graph of y = x2 + 2x – 1      [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.

Another regular polygon, X, is placed in the diagram.

Show that polygon X is a square.

[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                                 [3]

A metal cube has a total surface area of 54 cm2.

It is melted down and used to make spheres with a radius of 9 mm.

What is the maximum number of spheres that could be made?

[5]

m = 3.2 x 105

p = 4.3 x 104

(a) Find the value of n.

Give your answer in standard form correct to 3 significant figures    [2]

m is decreased by 5%

p is decreased by 15%

John says ‘n must be smaller because both m and p are smaller’

(b) Is John correct?

Three toy cars go around a track.

Car A completes a circuit every 40 seconds

Car B completes a circuit every 65 seconds

Car C completes a circuit every 70 seconds.

All three cars start at the same time from the start line.

Will all three cars cross the start line together within one hour?

[3]

Here is a pyramid with a square base ABCD.

AB = 6 cm

The vertex T is 8 cm above the midpoint of BD.

Calculate the size of angle ATC.

[4]

Here are two similar tins of paint:

The volume of tin A: the volume of tin B = 4:3

The surface area of the label on tin B is 100 cm2

Work out the surface area of the label on tin A.

[3]

Simplify the following fraction…

[3]

Make x the subject of the equation…

[3]

The graph shows the speed of a coach, in metres per second during the first 20 seconds of a journey.

(a) Work out an estimate of the distance travelled in the first 20 seconds. Use 5 strips of equal width.     [3]

(b) Is your answer to part (a) an underestimate or an overestimate of the actual distance travelled by the coach in the first 20 seconds?     [1]

The area of this triangle is (10√3) m2

Calculate the value of X, giving your answer to 3 standard figures.

[5]

Solve 2x2 – 3x – 9 < 0

[3]

(a) Show that the equation x3 + 2x = 2 has a solution between 0 and 1.      [2]

(b) Show that the equation x3 + 2x = 2 can be rearranged to give          [1]

(c) Starting with x0 = 0.5,

Use the iteration formula  three times to find an estimate for the solution of x3 + 2x = 2        [1]

Solve algebraically the simultaneous equations.

x2 + 3y2 = 10

2x + 3y = 7

[5]

Here are the first five terms of a quadratic sequence

10    21    38   61    90

Find an expression, in terms of n, for the nth term of this sequence

[3]

• Question 1

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 from the universal set ξ

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

EDDIE SAYS

• Question 2

Solve the simultaneous equations

3x + 2y = 9

4x – 3y = 3.5

[3]

EDDIE SAYS

• Question 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) On the grid, draw the graph of y = x2 + 2x – 1      [2]

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

EDDIE SAYS

• Question 4

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 5

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

Another regular polygon, X, is placed in the diagram.

Show that polygon X is a square.

[4]

EDDIE SAYS

• Question 6

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 7

Solve                                 [3]

EDDIE SAYS

• Question 8

A metal cube has a total surface area of 54 cm2.

It is melted down and used to make spheres with a radius of 9 mm.

What is the maximum number of spheres that could be made?

[5]

EDDIE SAYS

• Question 9

m = 3.2 x 105

p = 4.3 x 104

(a) Find the value of n.

Give your answer in standard form correct to 3 significant figures    [2]

m is decreased by 5%

p is decreased by 15%

John says ‘n must be smaller because both m and p are smaller’

(b) Is John correct?

EDDIE SAYS

• Question 10

Three toy cars go around a track.

Car A completes a circuit every 40 seconds

Car B completes a circuit every 65 seconds

Car C completes a circuit every 70 seconds.

All three cars start at the same time from the start line.

Will all three cars cross the start line together within one hour?

[3]

EDDIE SAYS

• Question 11

Here is a pyramid with a square base ABCD.

AB = 6 cm

The vertex T is 8 cm above the midpoint of BD.

Calculate the size of angle ATC.

[4]

EDDIE SAYS

• Question 12

Here are two similar tins of paint:

The volume of tin A: the volume of tin B = 4:3

The surface area of the label on tin B is 100 cm2

Work out the surface area of the label on tin A.

[3]

EDDIE SAYS

• Question 13

Simplify the following fraction…

[3]

EDDIE SAYS

• Question 14

Make x the subject of the equation…

[3]

EDDIE SAYS

• Question 15

The graph shows the speed of a coach, in metres per second during the first 20 seconds of a journey.

(a) Work out an estimate of the distance travelled in the first 20 seconds. Use 5 strips of equal width.     [3]

(b) Is your answer to part (a) an underestimate or an overestimate of the actual distance travelled by the coach in the first 20 seconds?     [1]

EDDIE SAYS

• Question 16

The area of this triangle is (10√3) m2

Calculate the value of X, giving your answer to 3 standard figures.

[5]

EDDIE SAYS

• Question 17

Solve 2x2 – 3x – 9 < 0

[3]

EDDIE SAYS

• Question 18

(a) Show that the equation x3 + 2x = 2 has a solution between 0 and 1.      [2]

(b) Show that the equation x3 + 2x = 2 can be rearranged to give          [1]

(c) Starting with x0 = 0.5,

Use the iteration formula  three times to find an estimate for the solution of x3 + 2x = 2        [1]

EDDIE SAYS

• Question 19

Solve algebraically the simultaneous equations.

x2 + 3y2 = 10

2x + 3y = 7

[5]

EDDIE SAYS

• Question 20

Here are the first five terms of a quadratic sequence

10    21    38   61    90

Find an expression, in terms of n, for the nth term of this sequence

[3]

EDDIE SAYS