# GCSE Maths Paper One (Higher, Non-Calculator) Practice Paper in the Style of AQA

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

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA

Curriculum topic:   Higher Practice Papers

Curriculum subtopic:   Non-Calculator Practice Papers

Difficulty level:

### QUESTION 1 of 10

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

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 complete your answers online but we would recommend that you have some paper to write show your workings out and diagrams on.  There will be marks allocated to this part of the paper.

You will need graph paper to complete some of the questions in this paper.

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

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

Work out

[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.

Use approximations to estimate the of the number of miles travelled in 1 minute.

[3]

Solve the simultaneous equations

6x + 5y = 38

4x + 6y = 36

[3]

Here are two shapes, a rectangle and a triangle that have the same perimeter.

FG = 10 cm

Area of DEFG = 50 cm2

Find the value of AB

[4]

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

b) Here is a right-angled triangle.    [2]

Cos 30 = 0.5

Find the value of x

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]

(a) Find the value of       [2]

(b) Find the value of       [2]

Show that can be written in the form  where a is an integer.

[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:

Diameter = 10 cm

Height = k cm.

The hemisphere:

Work out the 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.

[3]

The functions f(x) and g(x) are defined such that

f(x) = 2x – 3   and    g(x) = 2x2 + 1

a) Find 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]

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

• Question 1

Work out

[4]

EDDIE SAYS

• Question 2

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]

EDDIE SAYS

• Question 3

Work out 36.2 x 4.9

[3]

EDDIE SAYS

• Question 4

A Formula One car travels at 182.9 miles per hour.

Use approximations to estimate the of the number of miles travelled in 1 minute.

[3]

EDDIE SAYS

• Question 5

Solve the simultaneous equations

6x + 5y = 38

4x + 6y = 36

[3]

EDDIE SAYS

• Question 6

Here are two shapes, a rectangle and a triangle that have the same perimeter.

FG = 10 cm

Area of DEFG = 50 cm2

Find the value of AB

[4]

EDDIE SAYS

• Question 7

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

b) Here is a right-angled triangle.    [2]

Cos 30 = 0.5

Find the value of x

EDDIE SAYS

• Question 8

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]

EDDIE SAYS

• Question 9

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

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

[3]

EDDIE SAYS

• Question 10

(a) Find the value of       [2]

(b) Find the value of       [2]

EDDIE SAYS

• Question 11

Show that can be written in the form  where a is an integer.

[3]

EDDIE SAYS

• Question 12

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]

EDDIE SAYS

• Question 13

The diagram shows two shapes with the same volume.

The cone:

Diameter = 10 cm

Height = k cm.

The hemisphere:

Work out the height of the cone..

[4]

EDDIE SAYS

• Question 14

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]

EDDIE SAYS

• Question 15

Given that x2:(3 – 4x) = 4:3

Find all the possible values of x.

[4]

EDDIE SAYS

• Question 16

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]

EDDIE SAYS

• Question 17

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

[3]

EDDIE SAYS

• Question 18

The functions f(x) and g(x) are defined such that

f(x) = 2x – 3   and    g(x) = 2x2 + 1

a) Find f-1(x)      [2]

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

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

EDDIE SAYS

• Question 19

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]

EDDIE SAYS

• Question 20

Simplify (33)2

[1]

56
EDDIE SAYS
When raising one power to another, we MULTIPLY the powers and leave the base the same.
• Question 21

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

[1]

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 22

Which of these is the exact value of cos 45?

[1]

√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 23

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

[1]

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...