# GCSE Maths Paper 05 (Higher) Practice Paper in the Style of OCR - Non Calculator

In this assessment, students will be able to complete a timed GCSE Mathematics Paper 05 (Non-Calculator) in the style of OCR

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   OCR

Curriculum topic:   Higher Practice Papers

Curriculum subtopic:   Non-Calculator Practice Papers

Difficulty level:

### QUESTION 1 of 10

In this assessment, you will complete a timed GCSE Mathematics Paper 05 (Non-Calculator) in the style of OCR

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 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 OCR GCSE authors.

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

a) Work out                      [2]

b) Work out                      [2]

In a bag, the number of squares and circles are in the ratio 3:7.

The number of circles and triangles are given in the ratio 14:9.

If there are 36 squares in the bag, how many triangles are in the bag?

[3]

Calculate 36.2 x 4.9

[3]

a) A Formula One car travels at 182.9 miles per hour. Find an estimate of the number of miles travelled in 1 minute.                     [3]

Six apples and 5 bananas cost £3.80

Four apples and 6 bananas cost £3.60

Find the cost of 3 apples and 4 bananas.

[3]

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

The length of the side FG is 10 cm

The area of the rectangle DEFG is 50 cm2

Find the length of the side AB

[4]

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

b) Here is a right-angled triangle.

Cos 30 = 0.5

Find the value of x.

[2]

The heights of 60 boys 15 year-old boys are measured and plotted onto the following cumulative frequency graph.

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

(a) On the scale below, draw a box plot for the information about the heights of the boys.                     [3]

(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.                     [1]

(x + 3) (x - 1) (x + 2) can be written in the form ax3 + bx2 + cx + d.

Find the values of a, b, c and d.

[3]

The graph of f(x) is shown.

(a) What are the coordinates of the turning point of the graph?

(b) Write down estimates for the roots f(x) = 0

(c) Use the graph to find the value of f(-1).

[3]

(a) Give the value of                      [2]

(b) Give the value of                      [2]

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

[3]

A is directly proportional to B

A = 20 when B = 4

B is inversely proportional to C2

B = 4 when C = 2

Find an equation for A in terms of C.

[5]

The diagram shows a cone and a hemisphere. The two shapes have an equal volume.

The cone has a base diameter of 10 cm and a height of k cm.

The hemisphere has a radius of 8 cm.

Work out the value of k.                   [4]

In a bag, there are only red marbles, white marbles 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 graph for y = cos(x) for -180 ≤ x ≤ 180

On the grid, sketch the graph for y = 2cos(x) for -180 ≤ x ≤ 180

[2]

Simplify

[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]

A,B,C and D are points on the circumference of a circle.

RS is a tangent to the circle at D

Angle DBS = 69°.

a) Work out angle x. Give a reason for your answer.        [2]

b) Work out angle y. Give a reason for your answer.        [2]

Prove that the difference between the squares of any two consecutive integers is always equal to the sum of these integers        [4]

Last year, James earned £31 500.

He payed £7498 in tax and national insurance (NI).

James estimates that the ratio of his tax and NI to his pay is 1:4.

Is he correct?

(a) Write 2/9 as a recurring decimal.        [1]

(b) Johnny divided a two digit number by a single digit number. His answer was 2.77777777777.

What are the two numbers that he used?        [3]

Sketch the graph of y = x2 + 3x.

Show the coordinate of the solutions and of the turning point.                       [3]

• Question 1

a) Work out                      [2]

b) Work out                      [2]

EDDIE SAYS

• Question 2

In a bag, the number of squares and circles are in the ratio 3:7.

The number of circles and triangles are given in the ratio 14:9.

If there are 36 squares in the bag, how many triangles are in the bag?

[3]

EDDIE SAYS

• Question 3

Calculate 36.2 x 4.9

[3]

EDDIE SAYS

• Question 4

a) A Formula One car travels at 182.9 miles per hour. Find an estimate of the number of miles travelled in 1 minute.                     [3]

EDDIE SAYS

• Question 5

Six apples and 5 bananas cost £3.80

Four apples and 6 bananas cost £3.60

Find the cost of 3 apples and 4 bananas.

[3]

EDDIE SAYS

• Question 6

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

The length of the side FG is 10 cm

The area of the rectangle DEFG is 50 cm2

Find the length of the side AB

[4]

EDDIE SAYS

• Question 7

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

b) Here is a right-angled triangle.

Cos 30 = 0.5

Find the value of x.

[2]

EDDIE SAYS

• Question 8

The heights of 60 boys 15 year-old boys are measured and plotted onto the following cumulative frequency graph.

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

(a) On the scale below, draw a box plot for the information about the heights of the boys.                     [3]

(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.                     [1]

EDDIE SAYS

• Question 9

(x + 3) (x - 1) (x + 2) can be written in the form ax3 + bx2 + cx + d.

Find the values of a, b, c and d.

[3]

EDDIE SAYS

• Question 10

The graph of f(x) is shown.

(a) What are the coordinates of the turning point of the graph?

(b) Write down estimates for the roots f(x) = 0

(c) Use the graph to find the value of f(-1).

[3]

EDDIE SAYS

• Question 11

(a) Give the value of                      [2]

(b) Give the value of                      [2]

EDDIE SAYS

• Question 12

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

[3]

EDDIE SAYS

• Question 13

A is directly proportional to B

A = 20 when B = 4

B is inversely proportional to C2

B = 4 when C = 2

Find an equation for A in terms of C.

[5]

EDDIE SAYS

• Question 14

The diagram shows a cone and a hemisphere. The two shapes have an equal volume.

The cone has a base diameter of 10 cm and a height of k cm.

The hemisphere has a radius of 8 cm.

Work out the value of k.                   [4]

EDDIE SAYS

• Question 15

In a bag, there are only red marbles, white marbles 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 16

Given that x2:(3 – 4x) = 4:3

Find all the possible values of x.

[4]

EDDIE SAYS

• Question 17

Here is the graph for y = cos(x) for -180 ≤ x ≤ 180

On the grid, sketch the graph for y = 2cos(x) for -180 ≤ x ≤ 180

[2]

EDDIE SAYS

• Question 18

Simplify

[3]

EDDIE SAYS

• Question 19

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 20

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 21

A,B,C and D are points on the circumference of a circle.

RS is a tangent to the circle at D

Angle DBS = 69°.

a) Work out angle x. Give a reason for your answer.        [2]

b) Work out angle y. Give a reason for your answer.        [2]

EDDIE SAYS

• Question 22

Prove that the difference between the squares of any two consecutive integers is always equal to the sum of these integers        [4]

EDDIE SAYS

• Question 23

Last year, James earned £31 500.

He payed £7498 in tax and national insurance (NI).

James estimates that the ratio of his tax and NI to his pay is 1:4.

Is he correct?

EDDIE SAYS

• Question 24

(a) Write 2/9 as a recurring decimal.        [1]

(b) Johnny divided a two digit number by a single digit number. His answer was 2.77777777777.

What are the two numbers that he used?        [3]

EDDIE SAYS

• Question 25

Sketch the graph of y = x2 + 3x.

Show the coordinate of the solutions and of the turning point.                       [3]

EDDIE SAYS