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GCSE Maths Paper 4 (Component 2 - Higher - Calculator) Practice Paper in the Style of Eduqas - Calculator

In this assessment, students will be able to complete a timed GCSE Mathematics Paper 4 (Component 2 - Higher - Calculator) in the style of Eduqas

'GCSE Maths Paper 4 (Component 2 - Higher - Calculator) Practice Paper in the Style of Eduqas - Calculator' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Eduqas

Curriculum topic:   Higher Practice Papers

Curriculum subtopic:   Calculator Practice Papers

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this assessment, you will complete a timed GCSE Mathematics Paper 4 (Component 2 - Non-Calculator) in the style of Eduqas

 

In the GCSE examinations, you will write your answers on the paper, however, at EdPlace you will input your answers on the computer.

 

We recommend that you have some paper handy as you work in which to write down rough workings.

 

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

 

You should aim for approximately 1 minute per mark.

 

The timer is set for 135 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 Eduqas and these questions represent our own unique content developed by Eduqas GCSE authors.

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

A is (4,7) and B is (2,2).

Select the midpoint of AB.

 

[1]

(3,3)

(3,4.5)

(2,3)

(2,4.5)

The Bearing of A from B is 80°

 

What is the bearing of B from A?

 

[1]

80°

100°

180°

260°

What does AUB represent in the following probability statement P(AUB)?

 

[1]

A or B or both

A but not B

not A or B

A and B

Which of the following is a quadratic sequence? 

 

[1]

2 5 10 17 26

3 5 7 9 11

1 1 2 3 5

2 4 8 16 32

This triangle is isosceles.

 

 

David says the length of this shape is greater than 1 metre?

 

Show that David is wrong.


[5]

BEG is a triangle

 

Work out the size of angle x

Give reasons for each stage of your working.

 

[4]

There are only red, black and blue marbles in a bag.

 

There are three times as many black marbles as red marbles and twice as many blue marbles as black.

 

Kim takes a marble from the bag at random.

Find the probability it is a black marble.

 

[3]

The diagram shows the side view of a step ladder.

The strut (BC) is one quarter of the way up the ladder

The symmetrical cross section  shows two similar isosceles triangles.

 

 

AD = 180 cm

BC = 60 cm

 

Work out the vertical height of the ladder.

 

[5]

 

The volume of a brass instrument is 360cm2

The instrument is made from copper and zinc.

 

The amount of copper and zinc is in the ratio 2:1

The density of copper is 8.96 g/cm3

The density of zinc is 7.13 g/cm3

 

Work out the mass of the instrument.

 

[4]

100 members of a triathlon club were asked if their favourite sport was cycling, swimming or running.

 

52 of the people asked were male

12 of the 41 who said cycling were female

19 men said running

17 people said swimming.

 

One of the female tri-athletes is picked at random, what is the probability she said swimming was her favourite sport?

 

[4]

 

David invests £11000 in the bank in an account that pays compound interest for 3 years.

 

For the first two years, the interest paid on the investment is X% per annum.

After two years, the investment is worth £11669.90

 

As a reward for leaving his money untouched for two years, the interest for the third year is doubled.

 

How much will David’s investment be worth at the end of the three years?

 

[4]

The vectors a and b are shown on the grid.

 

 

(a) On the grid, draw the vector -2b     [1]

 

(b) Work out the column vector b – 2a.     [2]

At the cinema, you can buy the following snacks… 

 

Two types of popcorn

5 different drinks

9 types of sweet

 

Andy is going to have one of the following to eat while watching his film.

   A drink and popcorn

   A drink and a pack of sweets

   A drink, some popcorn and some sweets.

 

How many different combinations of snack could Andy choose from?

 

 [3]

The diagram below shows a playing piece for a game.

The piece is a sector of a circle with centre O and a radius of 5.2cm

 

 

The area of the piece is 9.9 cm2

 

Calculate the perimeter of the piece.

 

[3]

Show that  simplifies to  where a, b, c and d are integers to be found.

 

[4]                      

On the grid, shade the region that satisfied all these inequalities.                           

x < 6      x + y > 8    y < x + 3

 

 

[3]

James has to get a bus to work on Monday and Tuesday.

The probability he is late and misses the bus on Monday is 0.32.

 

If he misses the bus on Monday, the probability he will miss it on Tuesday is 0.22

If he catches the bus on Monday, the probability he will miss it on Tuesday is 0.04.

 

(a) Complete the probability tree diagram.      [2]

 

 

(b) Find the probability he will catch the bus exactly once over the two days.          [3]

ABC and ACD are triangles.

 

 

Work out the area of ABCD.

Give your answer to 3 significant figures.

 

[6]

The histogram shows information about the heights of some plants.

 

 

(a) Complete the frequency table for this information.            [2]

 

Height (h cm)

Frequency

24 ≤ h < 26

50

26 ≤ h < 27

 

27 ≤ h < 28

 

28 ≤ h < 30

 

30 ≤ h < 37

 

 

(b) Which group contains the median height of the plants?       [2]

The straight line AB passes through the points (2,-1) and (5,-7)       

The straight line CD has a gradient of 4 and passes through the origin.

 

By finding the equations of the two lines in the form y = mx + c, find the point where they intersect.

 

[4]

Sarah is trying to find the density of a triangular prism made of metal.

 

She works out that…

the length of the shape is 15.1cm, correct to the nearest mm

the cross-sectional area of the shape is 3.2cm2, correct to the nearest mm.

 

She weighs the object and works out the mass as 16g, correct to the nearest gram.

 

By considering the bounds, work out the density of the metal to a suitable degree of accuracy.

 

Show all your working and give a reason for your final answer.

 

[5]

Avneet tries to solve this question    

 

Rationalise the denominator of

 

Her working is shown below

 

She has made two mistakes.

 

Find these two mistakes.

 

  [2]

The first 3 terms of a geometric sequence are given by

 

 

(a) Find the value of x.      [3]

 

(b) Show that the 5th term is          [2]

(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]

A motorbike track consists of:

Two straight sections of length 1.8 km and 3 km

Two semicircles

 

 

The length of a motorbike race must be at least 110 km in length.

 

How many full laps must the race be held over at this circuit?

You must show your working                          

 

[4]

 

 

m = 3.2 x 105

p = 4.3 x 104

 

(a) Find the value of n. 

Give your answer in standard form.

 

 [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?    

Explain your reasoning

 

[2]

The diagram below shows a pyramid with a square base.

 

The length AB is 6cm

The angle TĈA = 41°

Find the volume of the pyramid

Give your answer to 1 decimal place.

 

[5]

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]

Solve 2x2 – 3x – 9 < 0 

 

[3]

The diagram shows a non – right angled triangle

 

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

 

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

 

[5]

The circle x2 + 3y2 = 10 and the straight line 2x + 3y = 7 intersect at the points A and B.

 

Find the coordinates of A and B

 

[5]

  • Question 1

A is (4,7) and B is (2,2).

Select the midpoint of AB.

 

[1]

CORRECT ANSWER
(3,4.5)
EDDIE SAYS
When you are finding the midpoint, the easiest way to do it is to add the x corrdinates together and half this. If you do the same with the y coordinates, you'll find the midpoint.
  • Question 2

The Bearing of A from B is 80°

 

What is the bearing of B from A?

 

[1]

CORRECT ANSWER
260°
EDDIE SAYS
The neat little trick to remember here is that reverse bearings always add to 360°.
  • Question 3

What does AUB represent in the following probability statement P(AUB)?

 

[1]

CORRECT ANSWER
A or B or both
EDDIE SAYS
Think of the Venn diagram, AUB means A OR B so it covers all the ones in both the circles.
  • Question 4

Which of the following is a quadratic sequence? 

 

[1]

CORRECT ANSWER
2 5 10 17 26
EDDIE SAYS
Think what the word quadratic implies. It means there will be a square in there somewhere. The numbers in 2 5 10 17 26 are just one more than the square numbers, meaning this must be a quadratic sequence.
  • Question 5

This triangle is isosceles.

 

 

David says the length of this shape is greater than 1 metre?

 

Show that David is wrong.


[5]

CORRECT ANSWER
EDDIE SAYS

  • Question 6

BEG is a triangle

 

Work out the size of angle x

Give reasons for each stage of your working.

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 7

There are only red, black and blue marbles in a bag.

 

There are three times as many black marbles as red marbles and twice as many blue marbles as black.

 

Kim takes a marble from the bag at random.

Find the probability it is a black marble.

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 8

The diagram shows the side view of a step ladder.

The strut (BC) is one quarter of the way up the ladder

The symmetrical cross section  shows two similar isosceles triangles.

 

 

AD = 180 cm

BC = 60 cm

 

Work out the vertical height of the ladder.

 

[5]

 

CORRECT ANSWER
EDDIE SAYS

  • Question 9

The volume of a brass instrument is 360cm2

The instrument is made from copper and zinc.

 

The amount of copper and zinc is in the ratio 2:1

The density of copper is 8.96 g/cm3

The density of zinc is 7.13 g/cm3

 

Work out the mass of the instrument.

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 10

100 members of a triathlon club were asked if their favourite sport was cycling, swimming or running.

 

52 of the people asked were male

12 of the 41 who said cycling were female

19 men said running

17 people said swimming.

 

One of the female tri-athletes is picked at random, what is the probability she said swimming was her favourite sport?

 

[4]

 

CORRECT ANSWER
EDDIE SAYS

  • Question 11

David invests £11000 in the bank in an account that pays compound interest for 3 years.

 

For the first two years, the interest paid on the investment is X% per annum.

After two years, the investment is worth £11669.90

 

As a reward for leaving his money untouched for two years, the interest for the third year is doubled.

 

How much will David’s investment be worth at the end of the three years?

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 12

The vectors a and b are shown on the grid.

 

 

(a) On the grid, draw the vector -2b     [1]

 

(b) Work out the column vector b – 2a.     [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 13

At the cinema, you can buy the following snacks… 

 

Two types of popcorn

5 different drinks

9 types of sweet

 

Andy is going to have one of the following to eat while watching his film.

   A drink and popcorn

   A drink and a pack of sweets

   A drink, some popcorn and some sweets.

 

How many different combinations of snack could Andy choose from?

 

 [3]

CORRECT ANSWER
EDDIE SAYS

  • Question 14

The diagram below shows a playing piece for a game.

The piece is a sector of a circle with centre O and a radius of 5.2cm

 

 

The area of the piece is 9.9 cm2

 

Calculate the perimeter of the piece.

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 15

Show that  simplifies to  where a, b, c and d are integers to be found.

 

[4]                      

CORRECT ANSWER
EDDIE SAYS

  • Question 16

On the grid, shade the region that satisfied all these inequalities.                           

x < 6      x + y > 8    y < x + 3

 

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 17

James has to get a bus to work on Monday and Tuesday.

The probability he is late and misses the bus on Monday is 0.32.

 

If he misses the bus on Monday, the probability he will miss it on Tuesday is 0.22

If he catches the bus on Monday, the probability he will miss it on Tuesday is 0.04.

 

(a) Complete the probability tree diagram.      [2]

 

 

(b) Find the probability he will catch the bus exactly once over the two days.          [3]

CORRECT ANSWER
EDDIE SAYS

  • Question 18

ABC and ACD are triangles.

 

 

Work out the area of ABCD.

Give your answer to 3 significant figures.

 

[6]

CORRECT ANSWER
EDDIE SAYS

  • Question 19

The histogram shows information about the heights of some plants.

 

 

(a) Complete the frequency table for this information.            [2]

 

Height (h cm)

Frequency

24 ≤ h < 26

50

26 ≤ h < 27

 

27 ≤ h < 28

 

28 ≤ h < 30

 

30 ≤ h < 37

 

 

(b) Which group contains the median height of the plants?       [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 20

The straight line AB passes through the points (2,-1) and (5,-7)       

The straight line CD has a gradient of 4 and passes through the origin.

 

By finding the equations of the two lines in the form y = mx + c, find the point where they intersect.

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 21

Sarah is trying to find the density of a triangular prism made of metal.

 

She works out that…

the length of the shape is 15.1cm, correct to the nearest mm

the cross-sectional area of the shape is 3.2cm2, correct to the nearest mm.

 

She weighs the object and works out the mass as 16g, correct to the nearest gram.

 

By considering the bounds, work out the density of the metal to a suitable degree of accuracy.

 

Show all your working and give a reason for your final answer.

 

[5]

CORRECT ANSWER
EDDIE SAYS

  • Question 22

Avneet tries to solve this question    

 

Rationalise the denominator of

 

Her working is shown below

 

She has made two mistakes.

 

Find these two mistakes.

 

  [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 23

The first 3 terms of a geometric sequence are given by

 

 

(a) Find the value of x.      [3]

 

(b) Show that the 5th term is          [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 24

(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]

CORRECT ANSWER
EDDIE SAYS

  • Question 25

A motorbike track consists of:

Two straight sections of length 1.8 km and 3 km

Two semicircles

 

 

The length of a motorbike race must be at least 110 km in length.

 

How many full laps must the race be held over at this circuit?

You must show your working                          

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 26

 

 

m = 3.2 x 105

p = 4.3 x 104

 

(a) Find the value of n. 

Give your answer in standard form.

 

 [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?    

Explain your reasoning

 

[2]

CORRECT ANSWER
EDDIE SAYS

  • Question 27

The diagram below shows a pyramid with a square base.

 

The length AB is 6cm

The angle TĈA = 41°

Find the volume of the pyramid

Give your answer to 1 decimal place.

 

[5]

CORRECT ANSWER
EDDIE SAYS

  • Question 28

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]

CORRECT ANSWER
EDDIE SAYS

  • Question 29

Solve 2x2 – 3x – 9 < 0 

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 30

The diagram shows a non – right angled triangle

 

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

 

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

 

[5]

CORRECT ANSWER
EDDIE SAYS

  • Question 31

The circle x2 + 3y2 = 10 and the straight line 2x + 3y = 7 intersect at the points A and B.

 

Find the coordinates of A and B

 

[5]

CORRECT ANSWER
EDDIE SAYS

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