OCR GCSE Maths Paper 2: Non-calculator Foundation June 2023 question paper J560/02

Write down the percentage of this circle that is shaded.

Work out.

20 - 16 ÷ 2

Insert one pair of brackets to make this calculation correct.

2 + 7 - 3 × 8 = 34

A store carries out a satisfaction survey on a sample of its customers. The bar chart shows the results.

Work out how many customers were in the sample.

The store manager decides to display the results in a pictogram.

Complete the final row of the pictogram and the key.

Complete this statement by writing the missing value in the box.

Work out.

Work out, giving your answer as a fraction in its simplest form. 2 15 5^× 16

Solve.

2 x = - 14

Alex is 1.34 metres tall. Gabi is 95 centimetres tall.

Find, in centimetres, how much taller Alex is than Gabi.

Azmi invests £700 at a rate of 2% per year simple interest.

Work out the interest Azmi receives after one year.

Work out the value of Azmi’s investment after 3 years.

Increase 200 by 15%.

The scale drawing shows the positions of two towns, A and B.

Scale: 1 cm represents 10 km

Find the actual distance between town A and town B.

Town C is 55 km from town B on a bearing of 330°.

On the scale drawing, mark and label the position of town C with a cross.

Hiro and Ling work in a restaurant. Hiro is paid £9 per hour and Ling is paid £10 per hour.

One week, Hiro works a total of 30 hours. Ling earns £50 more than Hiro that week.

Work out the number of hours that Ling works.

Work out.

Sasha is trying to remember a 4-digit pin number. Sasha knows it has the following digits and that the first digit is 9.

Write down all of the possible orders for Sasha’s 4-digit pin number.

Sasha tries one of these orders at random.

Write down the probability that the last digit of the pin number that Sasha tries is 2.

Ryan started with 80 counters.

Ryan says

I still have enough counters to make Pattern 5 and Pattern 6.

Is Ryan correct? Show how you decide.

Complete the table below for the addition of counters in consecutive patterns.

The number of counters in Pattern k + Pattern (k + 1) is 144.

Find the value of k.

A student is buying some gifts for their friends. The gifts are shown below with the prices.

Key ring
Badge
Wallet £3.50 £2.99 £7.50

The student has £50 to spend. They first buy 6 key rings and 2 wallets. They then buy badges with the remainder of the money.

Work out the maximum number of badges that the student can buy. You must show your working.

(a) Number of badges........

Work out the amount of money they have left over.

(b) Amount left over £........

Taylor performs in a show. Taylor spends of the show singing, of the show dancing and the remaining 55 minutes backstage.

Work out how long the show lasted. Give your answer in hours and minutes. You must show your working.

Complete this identity by writing in the missing numbers.

4 (........ x + 1) = 14 x - 6 (x - 2) -........

Vector a = and vector b = .

On the grid, draw vector a.

On the grid, draw vector a + b.

In the diagram, line AB is parallel to line ED. The points A, C and D lie on a straight line. The points B, C and E lie on a straight line.

Angle BCA = 45°, angle ABC = x ° and angle CDE = y °. The ratio x: y is 3: 2.

Work out the value of x.

A sphere has a radius of 3 cm.

Calculate the volume of the sphere. Give your answer in terms of π in its simplest form. [The volume V of a sphere with radius r is V = r³.]

The diagram shows a prism of length 10 cm.

The cross-section of the prism is a right-angled triangle. The base, b cm, is 2 cm longer than the height, h cm. The volume of the prism is 240 cm³.

A student is explaining how they worked out the value of b.

They say

b is 6 because that means h is 4 and 6 × 4 × 10 = 240.

Describe the student’s error and find the correct value of b.

The table shows the ages and heights of 12 children.

The points for the first eight children (shaded in the table above) are plotted on the scatter diagram.

Plot the points for the remaining four children.

Describe the type of correlation shown in the completed scatter diagram.

One of these children is taller than expected for their age.

On the scatter diagram, circle the point representing this child.

Kai is 8 years old. By drawing a line of best fit, estimate Kai’s height.

Describe an assumption you have made in giving your answer to part (d)(i).

Explain why using this data to estimate the height of a child that is 17 years old may be unreliable.

The diagram shows a right-angled triangle.

Work out the value of a.

Factorise x² + 10x + 24.

Write down the solutions to x² + 10x + 24 = 0.

A volunteer packs boxes for a charity. They can pack 5 boxes in 45 seconds.

Use this information to show that they can pack 55 boxes in less than 9 minutes.

What assumption did you make in part (a) ?

A student draws two different regular polygons. The exterior angle of one polygon is p °. The exterior angle of the other polygon is q °.

The sum of p and q is 112°. The difference between p and q is 32°.

Find the number of sides of each polygon. You must show your working.

........ sides and........ sides