OCR GCSE Maths Paper 3: Calculator Foundation November 2021 question paper J560/03

In a survey, some students chose their favourite type of film from a list of five. The bar chart shows the results.

(a)(i)........

How many Year 11 students chose Action films?

What type of film was chosen by the most Year 10 students?

How many Year 10 students took part in the survey?

45 students took part in the survey.

Write the ratio

number of Year 10 students taking part: number of Year 11 students taking part

in its simplest form.

Use your calculator to work out.

4⁵

There are 150 coins in a jar. 20% of the coins are 10p coins. of the coins are 20p coins. The rest of the coins are 50p coins.

Work out the total value, in £, of the 150 coins. You must show your working.

A sports team played the same number of matches in 2019 and 2020. The two pie charts summarise their results.

What fraction of the matches did the team win in 2019?

Did the team’s results improve in 2020? Explain how you know.

Increase 600 by 17%.

The diagram shows how a rhombus is made by joining two equilateral triangles.

Find the size of each interior angle of the rhombus.

(a)........ °,........ °,........ °,........ °

The same rhombus can be made by joining two copies of an isosceles triangle.

Find the size of each angle of the isosceles triangle.

Rowan’s bath has a hot tap and a cold tap. When turned on full, each tap on its own will fill the bath in 6 minutes.

Rowan turns both taps on full.

How long will it take to fill the bath?

Simplify.

5 t - 3 u - t + 5 u

The elements 1 and 2 have been entered on this Venn diagram.

Complete the Venn diagram to show all of the elements.

Three Venn diagrams, numbered 1 to 3, are shown below.

Which diagram best shows the relationship between Set L and Set M? Give a reason for your choice.

Venn diagram 1:

Venn diagram 2:

Venn diagram 3:

Venn diagram........ because........

A student has some cubes that are all the same size. Each cube is 3 cm by 3 cm by 3 cm.

They put 4 of these cubes together to make this shape.

Calculate the surface area of the shape.

Here are some algebraic statements.

v = u + at a + 2 b 3(x + 2) = 3 x + 6 2 y < x 2 x = 5

From the list above, write down an example of each of the following.

An expression.

An inequality.

An equation.

Rearrange this formula to make w the subject.

P = 2 w + 2 h

Ellis has 28 m of ribbon. They cut the ribbon into lengths of 60 cm.

What is the least length of ribbon, in cm, that can be left over? You must show your working.

This table shows the names and areas of five lakes.

Write the area of Lake Mweru as an ordinary number.

Write the lakes in the order of their area, starting with the smallest.

smallest largest

Calculate the difference between the areas of Lake Ladoga and Lake Tana. Give your answer in standard form, correct to 2 significant figures.

Azmi, Beth and Callum share a flat.

The monthly rent is £760. They share the rent in the ratio 2: 3: 3.

How much does Beth pay for rent each month?

Azmi, Beth and Callum also share the fuel bill in the ratio 2: 3: 3. Callum pays £36 for fuel each month.

How much does Azmi pay for fuel each month?

Triangle A and triangle B are drawn on the coordinate grid.

Reflect triangle A in the line x = 0.

Describe fully the single transformation that maps triangle A onto triangle B.

Ling throws a six-sided dice 300 times. The table shows the frequencies of their results.

Complete the table to show the relative frequencies.

Ling thinks that the dice may be biased.

Explain why evidence from the table could support their opinion.

Explain why the dice may, in fact, not be biased.

A carpenter measures the length, k metres, of a piece of wood.

They write

3.35 ⩽ k < 3.45.

Put rings around all possible values of k in the list below.

3.349 3.39 3.44 3.45 3.55

The carpenter says

3.35 ⩽ k < 3.45 means that the length of the piece of wood is 3.4 metres correct to the nearest centimetre.

Explain how you know that she is incorrect.

Complete the interval for 3.4 m, correct to the nearest centimetre.

Amit says

My normal typing speed is 40 words per minute. Therefore, I estimate that my normal typing speed is about 210 characters per minute.

Each letter, space and piece of punctuation counts as a character.

How many letters per word is Amit most likely to have used in making the estimate? Show how you decide.

Amit starts some homework at their normal typing speed. Amit types 52 words in 1 minute 12 seconds.

What may be true about the length of the words that Amit has just typed? Show how you decide.

The diagram shows rectangle ABCD.

DB = 13 cm and BC = 5 cm.

Calculate the area of the rectangle. You must show your working.

A straight line has the equation y = 2 x - 1.

Write down the gradient of the line.

Here are the equations of four straight lines.

Which of the four straight lines is parallel to y = 2 x - 1 ?

A student says

y = x + 4 is the steepest of the four straight lines because it has the largest number added.

Explain why the student is wrong.

Here is part of the graph of y = 2 x - 1.

The line continues to the right.

Will the line pass above, below or through the point (45, 90)? Show how you decide.

The line y = 2 x - 1 will pass........ the point (45, 90) because........

In this question, all measurements are in centimetres.

The square and the rectangle have the same area.

Show that x² - 8x - 20 = 0.

Solve x² - 8x - 20 = 0.

Explain why one of the answers in part (b) is not possible in the context of the question.

Write down the following.

The area of the square.

The length of the rectangle.

A bag of sweets contains jellies, mints and toffees.

The ratio of jellies to mints is n: 2. The ratio of mints to toffees is 5: 3 n.

Work out the ratio of jellies to toffees. Give your answer in its simplest form.