# GCSE Maths Paper 04 (Higher, Calculator) Practice Paper in the Style of OCR

In this assessment, students will be able to complete a timed GCSE Mathematics Paper 04 (Calculator) in the style of OCR

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   OCR

Curriculum topic:   Higher Practice Papers

Curriculum subtopic:   Calculator Practice Papers

Difficulty level:

### QUESTION 1 of 10

In this assessment, you will complete a timed GCSE Mathematics Paper 04 (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.

The table shows the relative frequency that a biased dice will land on 1, on 2, on 3, on 4 and on 6.

 Number 1 2 3 4 5 6 Probability 0.3 0.05 0.12 0.13 0.21

(a) Complete the table.      [1]

(b) Gemma rolls the dice 150 times. Estimate the total number of times the dice will land on a prime number.         [2]

Some adults and children went to see a rugby match.

The ratio of children to adults was 2:7

Each person either had a seated or a standing ticket.

4/5 of the children had seated tickets

The stadium has a capacity of 9500.

Work out what percentage of the stadium was full.

[5]

BEG is a triangle

ABC and DEF are parallel lines.

Work out the size of angle x giving 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.

John takes a marble from the bag at random.

Find the probability it is a black marble.

[3]

ABD and ACE are straight lines

BC is parallel to DB

AB = 4.2 cm

DE = 9 cm

(a) Work out the length of BC         [2]

AE = 7.74 cm

(b) Work out the length of CE          [2]

A force of 80 newtons acts on an area of 15 cm2.

The force is increased by 5 newtons

The area is decreased by 2 cm2

Gregg says;

“The pressure decreases by less than 10%”

Is Gregg correct?

[3]

(a) Write the number 0.005648 in standard form.  [1]

(b) Work out             [2]

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 females is picked at random, what is the probability that she said swimming was her favourite sport?

[4]

David puts £11000 in a bank account that pays compound interest for 3 years.

For the first two years, the bank pays R% interest.

After two years, he has £11669.90 in the bank.

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

How much money will David have at the end of the three years?

[4]

The vectors a and b are shown on the grid.

(a) Draw the vector -2b on the grid.  [1]

(b) Work out b – 2a, giving your answer as a column vector.  [2]

At the cinema, you can buy the following snacks…

2 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.

Show that there are 145 possible different combinations.

[3]

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

The area of the sector is 9.9 cm2

Calculate the perimeter of the sector, giving your final answer to 3 significant figures.

[3]

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

[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]

(a) On the graph provided, draw the graph of x2 + y2 = 9      [2]

(b) Hence, or otherwise, find the solutions of the simultaneous equations.

x2 + y2 = 9

x + y = 1

[3]

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.

Find the point where these two lines intersect.

[4]

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

She works out:

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

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

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

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

[5]

James tries to solve this question

Rationalise the denominator of

His working is shown below

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) i) Write 150 as a product of its prime factors.          [3]

ii) The lowest common multiple (LCM) of y and 150 is 600.

Find the smallest possible value of y.       [2]

(b) Two numbers, A and B, are written as a product of prime factors.

A = 23 x 32 x 53                 B = 22 x 34 x 5

Find the Highest Common Factor (HCF) of A and B.    [2]

(a) Solve x2 – 4x -7 = 1 – 6x                  [4]

(b) Expand and simplify.                       [4]

(2x + 1)(x – 5)(5x + 2)

.[6]

• Question 1

The table shows the relative frequency that a biased dice will land on 1, on 2, on 3, on 4 and on 6.

 Number 1 2 3 4 5 6 Probability 0.3 0.05 0.12 0.13 0.21

(a) Complete the table.      [1]

(b) Gemma rolls the dice 150 times. Estimate the total number of times the dice will land on a prime number.         [2]

EDDIE SAYS

• Question 2

Some adults and children went to see a rugby match.

The ratio of children to adults was 2:7

Each person either had a seated or a standing ticket.

4/5 of the children had seated tickets

The stadium has a capacity of 9500.

Work out what percentage of the stadium was full.

[5]

EDDIE SAYS

• Question 3

BEG is a triangle

ABC and DEF are parallel lines.

Work out the size of angle x giving reasons for each stage of your working.

[4]

EDDIE SAYS

• Question 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.

John takes a marble from the bag at random.

Find the probability it is a black marble.

[3]

EDDIE SAYS

• Question 5

ABD and ACE are straight lines

BC is parallel to DB

AB = 4.2 cm

DE = 9 cm

(a) Work out the length of BC         [2]

AE = 7.74 cm

(b) Work out the length of CE          [2]

EDDIE SAYS

• Question 6

A force of 80 newtons acts on an area of 15 cm2.

The force is increased by 5 newtons

The area is decreased by 2 cm2

Gregg says;

“The pressure decreases by less than 10%”

Is Gregg correct?

[3]

EDDIE SAYS

• Question 7

(a) Write the number 0.005648 in standard form.  [1]

(b) Work out             [2]

EDDIE SAYS

• Question 8

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 females is picked at random, what is the probability that she said swimming was her favourite sport?

[4]

EDDIE SAYS

• Question 9

David puts £11000 in a bank account that pays compound interest for 3 years.

For the first two years, the bank pays R% interest.

After two years, he has £11669.90 in the bank.

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

How much money will David have at the end of the three years?

[4]

EDDIE SAYS

• Question 10

The vectors a and b are shown on the grid.

(a) Draw the vector -2b on the grid.  [1]

(b) Work out b – 2a, giving your answer as a column vector.  [2]

EDDIE SAYS

• Question 11

At the cinema, you can buy the following snacks…

2 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.

Show that there are 145 possible different combinations.

[3]

EDDIE SAYS

• Question 12

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

The area of the sector is 9.9 cm2

Calculate the perimeter of the sector, giving your final answer to 3 significant figures.

[3]

EDDIE SAYS

• Question 13

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

[4]

EDDIE SAYS

• Question 14

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

x < 6      x + y > 8    y < x + 3

[3]

EDDIE SAYS

• Question 15

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]

EDDIE SAYS

• Question 16

(a) On the graph provided, draw the graph of x2 + y2 = 9      [2]

(b) Hence, or otherwise, find the solutions of the simultaneous equations.

x2 + y2 = 9

x + y = 1

[3]

EDDIE SAYS

• Question 17

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]

EDDIE SAYS

• Question 18

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.

Find the point where these two lines intersect.

[4]

EDDIE SAYS

• Question 19

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

She works out:

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

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

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

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

[5]

EDDIE SAYS

• Question 20

James tries to solve this question

Rationalise the denominator of

His working is shown below

Find these two mistakes.

[2]

EDDIE SAYS

• Question 21

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]

EDDIE SAYS

• Question 22

(a) i) Write 150 as a product of its prime factors.          [3]

ii) The lowest common multiple (LCM) of y and 150 is 600.

Find the smallest possible value of y.       [2]

(b) Two numbers, A and B, are written as a product of prime factors.

A = 23 x 32 x 53                 B = 22 x 34 x 5

Find the Highest Common Factor (HCF) of A and B.    [2]

EDDIE SAYS

• Question 23

(a) Solve x2 – 4x -7 = 1 – 6x                  [4]

(b) Expand and simplify.                       [4]

(2x + 1)(x – 5)(5x + 2)

EDDIE SAYS

• Question 24

.[6]

EDDIE SAYS