OCR GCSE Maths Paper 5: Non-calculator Higher June 2023 question paper J560/05

Work out.

Give your answer as a fraction in its simplest form.

The diagram shows two straight lines crossing a pair of parallel lines.

Write down the value of a. Give a reason for your answer.

Work out the value of b.

Work out.

3.8 ÷ 0.02

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.

Taylor has a full bottle of medicine. The bottle holds 20 doses of medicine.

Each day Taylor takes one dose of medicine out of the bottle. After 8 days, there are 180 millilitres of medicine left in the bottle.

Work out how many millilitres of medicine the bottle holds when full.

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 block made of iron is in the shape of a cuboid. The block is 3.1 cm by 4.9 cm by 2.2 cm. The density of iron is 7.87 g / cm³. Sam thinks that the mass of the block is about 2.4 kg.

Use estimation to decide if Sam’s answer is reasonable. Show how you decide.

Sam’s answer is........ because........

A zoo counts its animals. The ratio of antelope to zebra is 3: 2. The ratio of meerkats to zebra is 7: 3.

Write the number of antelope as a percentage of the number of zebra.

There are 15 more meerkats than antelope.

Work out the number of zebra in the zoo.

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

y is directly proportional to the square of x.

Find the percentage decrease in y when x is decreased by 30%.

Here are the first four terms of a sequence.

2 5 8 11 5 10 17 26

Find the next term.

Find the n th term.

The diagram shows a triangle, ABC, with perpendicular height BD.

BC = 12 cm, angle BCD = 30° and angle BAD = 45°.

Work out the length of BD.

Work out the exact length of AB. Give your answer in its simplest form.

The graphs of x = - 3 and y = - x are drawn on the grid.

The region R satisfies the following inequalities.

By drawing one more line, find and label the region R.

Factorise.

9x² - 4

Solve by factorisation.

3x² - 2x - 8 = 0

Solve.

Work out.

where is a fraction in its lowest terms. Find the value of p and the value of q.

A rhombus is drawn on a coordinate grid. One diagonal of the rhombus has equation y = + 3. The other diagonal passes through the point (1, 7).

Find the equation of the other diagonal of the rhombus. Give your answer in the form y = mx + c.

Show that the value of x is

A box contains 25 discs. The discs are either blue or yellow in the ratio 4: 1. Two discs are chosen at random from the box without replacement.

Find the probability that the two discs are different colours. You must show your working.

OABC is a parallelogram.

Find the following vectors in terms of a and c. Give your answers in their simplest form.

Line CN is extended to reach point P, such that =

Show, using vectors, that OAP is a straight line.