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GCSE Maths Paper 3 (Component 1 - Higher - Non-Calculator) Practice Paper in the Style of Eduqas

In this assessment, students will be able to complete a timed GCSE Mathematics Paper 3(Component 1 - Non-Calculator) in the style of Eduqas

'GCSE Maths Paper 3 (Component 1 - Higher - Non-Calculator) Practice Paper in the Style of Eduqas' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Eduqas

Curriculum topic:   Higher Practice Papers

Curriculum subtopic:   Non-Calculator Practice Papers

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this assessment, you will complete a timed GCSE Mathematics Paper 03 (Component 1 - Non-Calculator) in the style of Eduqas

 

This is an extended answer style assessment.

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.

 

 

 

 

 

Simplify (33)2

 

[1]

55

56

255

256

What is the volume of a cone with a radius of 3 cm and height 6 cm?

 

[1]

50π

60π

150π

300π

Which of these is the exact value of cos 45?

 

[1]

√3

√3/3

√2/2

√2

What is the sector area, in centimetres, of a quarter circle with a radius of 6 cm?

 

[1]

1.25π


18π

36π

Work out                     

Give your answer as a mixed number in its simplest form.

 

 [4]

In a bag, there are blue discs, red discs and black discs.

There are three times as many blue discs as red discs.

The number of blue discs: the number of black discs is 2:3.

One disc is selected at random.

 

Work out the probability the disc is either blue or black

 

[3]

Work out 36.2 x 4.9

 

[3]

 

A Formula One car travels at 182.9 miles per hour.

What is the best estimate for the of the number of miles travelled in 1 minute.

 

[3]

 

Solve the simultaneous equations

 

6x + 5y = 38

4x + 6y = 36

 

[3]

The diagram shows a rectangle and a triangle that have the same perimeter.

 

 

The side FG  has a length of 10 cm

The area of the rectangle DEFG is 50 cm2

 

Work out the value of the length AB.

 

[4]

a) Write down the exact value of sin 60    [1]                 

 

b) Here is a right-angled triangle. 

 

 

Cos 30 = 0.5

 

Calculate the size of the side marked x.      [2]

 

The cumulative frequency graph shows information about the heights of 60 Year 10 boys.

 

 

The smallest boy was 131 cm tall and the tallest was 206 cm tall.

 

(a) Use the graph to draw a box plot on the scale below showing information about the heights of the boys.     [2]

 

 

(b) At the same time, 60 15-year-old girls had their heights measured. The box plot below shows the heights of the girls.     [2]

 

 

Compare the distributions of the heights of the boys with the heights of the girls.

 

(c) Jimmy says that there must be some girls who are between 140 and 150 cm.

Is Jimmy right? You must give a reason for your answer.       [2]

(x + 3) (x - 1) (x + 2) = ax3 + bx2 + cx + d.

Work out the values of the integers a, b, c and d.

 

[3]

Find the value of each of the following.

(a)               [2]

 

(b)           [2]

Simplify

 

[3]

B is inversely proportional to C2

B = 4 when C = 2

 

(a) Work out an equation connecting B and C       [3]

 

 

 

 

(b) Work out the value of B when C is 1.5        [2]

The diagram shows two shapes with the same volume.

 

The cone has a diameter of 10 cm.

The hemisphere has a radius of 8 cm.

 

Work out the perpendicular height of the cone.

[4]

In a bag, there are only red, white and blue marbles.

The red marbles and the blue marbles are in the ratio 4:5.

The probability you will pull out a white marble is 0.19

Find the probability you would pull out a blue marble.

 

[3]

Given that x2:(3 – 4x) = 4:3

 

Find all the possible values of x.

 

[4]

Here is the sketch of y = cos (x) for values of x from -180 to 180

 

 

On the grid, sketch the graph for y = 2cos (x)

 

[2]

 

Show that  can be written in the form  where a,b and c are integers.

 

Give your answer in its simplest form.

 

[3]

The functions f(x) and g(x) are defined, for x ≥ 0, by

 

f(x) = 2x – 3   and    g(x) = 2x2 + 1

 

 

a) Find an expression for f-1(x)      [2]

 

Given that fg(x) = 3gf(x)

 

b) Show that 10x2 – 36x + 29 = 0       [5]

There are only red and black marbles in a bag.

There are 2 more black marbles than red marbles.

Jenny takes 3 marbles from the box at random.

The probability that the marbles are different colours is 168/325

Find the number of black marbles in the bag.

 

[6]

The diagram below shows a rectangle and a triangle.

AB = 40cm

BC = 15cm.

 

 

The lengths ED and DC are in the ratio 2:3

 

Work out the length of the line AD.

 

[4]

Prove that the difference between the squares of any two consecutive numbers is always an odd number.  

 

[4]

Solve

 

[3]

A hemisphere has a radius of 3x

 

A cone has a radius of 2x and a height of h

 

The sphere and the cone have the same volume

 

For the cone, work out the

 

                  height : radius

 

in the form a:b where a and b are integers.

[5]

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]

Simplify the following fraction…  

 

 

[3]

Rearrange

to make x the subject.

 

[3]

Here are the first five terms of a quadratic sequence 

    10    21    38   61    90

 

Find an expression for the nth term of this sequence

 

[3]

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

 

 

(a) Calculate an estimate of the distance the coach traveled from t = 0 to t = 20. You must use 5 regions, each of equal width, in your calculation..    [3]

 

(b) Work out the acceleration of the coach in the first 4 seconds.      [2]

  • Question 1

Simplify (33)2

 

[1]

CORRECT ANSWER
56
EDDIE SAYS
When raising one power to another, we MULTIPLY the powers and leave the base the same.
  • Question 2

What is the volume of a cone with a radius of 3 cm and height 6 cm?

 

[1]

CORRECT ANSWER
50π
EDDIE SAYS
Remember that the volume of a cone is given by 1/3 x π x r2. All you have to do is bang the numbers in, work it out and slap the Pi back on the end
  • Question 3

Which of these is the exact value of cos 45?

 

[1]

CORRECT ANSWER
√2/2
EDDIE SAYS
Think of an isosceles right angled triangle with sides of 1,1 and √2 This will have angles of 45° cos = A/H = 1/√2 All you have to do is rationalise it!
  • Question 4

What is the sector area, in centimetres, of a quarter circle with a radius of 6 cm?

 

[1]

CORRECT ANSWER
EDDIE SAYS
A quarter circle will be the area of a full circle divided by 4. If we had a full circle of radius 6, we would have an area of 36π Dividing this by 4 gives...
  • Question 5

Work out                     

Give your answer as a mixed number in its simplest form.

 

 [4]

CORRECT ANSWER
EDDIE SAYS

  • Question 6

In a bag, there are blue discs, red discs and black discs.

There are three times as many blue discs as red discs.

The number of blue discs: the number of black discs is 2:3.

One disc is selected at random.

 

Work out the probability the disc is either blue or black

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 7

Work out 36.2 x 4.9

 

[3]

 

CORRECT ANSWER
EDDIE SAYS

  • Question 8

A Formula One car travels at 182.9 miles per hour.

What is the best estimate for the of the number of miles travelled in 1 minute.

 

[3]

 

CORRECT ANSWER
EDDIE SAYS

  • Question 9

Solve the simultaneous equations

 

6x + 5y = 38

4x + 6y = 36

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 10

The diagram shows a rectangle and a triangle that have the same perimeter.

 

 

The side FG  has a length of 10 cm

The area of the rectangle DEFG is 50 cm2

 

Work out the value of the length AB.

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 11

a) Write down the exact value of sin 60    [1]                 

 

b) Here is a right-angled triangle. 

 

 

Cos 30 = 0.5

 

Calculate the size of the side marked x.      [2]

 

CORRECT ANSWER
EDDIE SAYS

  • Question 12

The cumulative frequency graph shows information about the heights of 60 Year 10 boys.

 

 

The smallest boy was 131 cm tall and the tallest was 206 cm tall.

 

(a) Use the graph to draw a box plot on the scale below showing information about the heights of the boys.     [2]

 

 

(b) At the same time, 60 15-year-old girls had their heights measured. The box plot below shows the heights of the girls.     [2]

 

 

Compare the distributions of the heights of the boys with the heights of the girls.

 

(c) Jimmy says that there must be some girls who are between 140 and 150 cm.

Is Jimmy right? You must give a reason for your answer.       [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 13

(x + 3) (x - 1) (x + 2) = ax3 + bx2 + cx + d.

Work out the values of the integers a, b, c and d.

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 14

Find the value of each of the following.

(a)               [2]

 

(b)           [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 15

Simplify

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 16

B is inversely proportional to C2

B = 4 when C = 2

 

(a) Work out an equation connecting B and C       [3]

 

 

 

 

(b) Work out the value of B when C is 1.5        [2]

CORRECT ANSWER
EDDIE SAYS

  • Question 17

The diagram shows two shapes with the same volume.

 

The cone has a diameter of 10 cm.

The hemisphere has a radius of 8 cm.

 

Work out the perpendicular height of the cone.

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 18

In a bag, there are only red, white and blue marbles.

The red marbles and the blue marbles are in the ratio 4:5.

The probability you will pull out a white marble is 0.19

Find the probability you would pull out a blue marble.

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 19

Given that x2:(3 – 4x) = 4:3

 

Find all the possible values of x.

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 20

Here is the sketch of y = cos (x) for values of x from -180 to 180

 

 

On the grid, sketch the graph for y = 2cos (x)

 

[2]

 

CORRECT ANSWER
EDDIE SAYS

  • Question 21

Show that  can be written in the form  where a,b and c are integers.

 

Give your answer in its simplest form.

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 22

The functions f(x) and g(x) are defined, for x ≥ 0, by

 

f(x) = 2x – 3   and    g(x) = 2x2 + 1

 

 

a) Find an expression for f-1(x)      [2]

 

Given that fg(x) = 3gf(x)

 

b) Show that 10x2 – 36x + 29 = 0       [5]

CORRECT ANSWER
EDDIE SAYS

  • Question 23

There are only red and black marbles in a bag.

There are 2 more black marbles than red marbles.

Jenny takes 3 marbles from the box at random.

The probability that the marbles are different colours is 168/325

Find the number of black marbles in the bag.

 

[6]

CORRECT ANSWER
EDDIE SAYS

  • Question 24

The diagram below shows a rectangle and a triangle.

AB = 40cm

BC = 15cm.

 

 

The lengths ED and DC are in the ratio 2:3

 

Work out the length of the line AD.

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 25

Prove that the difference between the squares of any two consecutive numbers is always an odd number.  

 

[4]

CORRECT ANSWER
EDDIE SAYS

  • Question 26

Solve

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 27

A hemisphere has a radius of 3x

 

A cone has a radius of 2x and a height of h

 

The sphere and the cone have the same volume

 

For the cone, work out the

 

                  height : radius

 

in the form a:b where a and b are integers.

[5]

CORRECT ANSWER
EDDIE SAYS

  • Question 28

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]

CORRECT ANSWER
EDDIE SAYS

  • Question 29

Simplify the following fraction…  

 

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 30

Rearrange

to make x the subject.

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 31

Here are the first five terms of a quadratic sequence 

    10    21    38   61    90

 

Find an expression for the nth term of this sequence

 

[3]

CORRECT ANSWER
EDDIE SAYS

  • Question 32

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

 

 

(a) Calculate an estimate of the distance the coach traveled from t = 0 to t = 20. You must use 5 regions, each of equal width, in your calculation..    [3]

 

(b) Work out the acceleration of the coach in the first 4 seconds.      [2]

CORRECT ANSWER
EDDIE SAYS

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