OCR GCSE Maths Paper 4: Calculator Higher June 2019 question paper J560/04

Calculate.

Give your answer correct to 3 significant figures.

The ratio 50 grams to 1 kilogram can be written in the form 1: n.

Find the value of n.

Delia, Edwin and Freya share some money in the ratio 5: 7: 8. Freya’s share is £1600.

How much money did they share?

A bus timetable shows the following information.

• A bus following route T leaves for the train station every 20 minutes.

• A bus following route A leaves for the airport every 18 minutes.

• A bus following route T and a bus following route A both leave at 8.37 am.

When is the next time one of each bus is timetabled to leave at the same time?

Write down one assumption that was necessary to solve this problem.

Bennie is 7 years older than Ayesha. Chloe is twice as old as Bennie. The sum of their three ages is 57.

Work out the ages of Ayesha, Bennie and Chloe.

120 students in Year 10 and Year 11 sit a test.

• 61 of the students are in Year 10.

• 83 of the students are right-handed.

• 20 of the students in Year 11 are left-handed.

One of the students in Year 10 and one of the students in Year 11 are chosen at random.

Which one is more likely to be left-handed? Show your working. You may use the table if you wish.

The diagram shows a shape ABCDE. The shape is made from a rectangle, a right-angled triangle and a quarter of a circle.

F is the mid-point of BD. AE = 18 m and the perpendicular distance from C to AE is 41 m.

Work out the perimeter of the shape ABCDE.

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

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

Describe fully the single transformation that is equivalent to:

• a reflection in the line x = 3, followed by

• a translation by .

You may use the grid above to help you.

The diagram shows triangle ABC. CD is parallel to AB. A, C and E lie in a straight line. Angles of size a °, b ° and c ° are shown.

Insert a °, b ° or c ° to make this statement true. Give a reason for your answer.

Angle DCE =........ because........

Use the diagram and the answer to part (a) to show that the angles of a triangle add up to 180°.

Give a reason for each statement you make.

Claudia invests £25 000 at a rate of 2% per year compound interest.

Calculate the total amount of interest she will have earned after 5 years. Give your answer correct to the nearest penny.

The area of a rectangle is 56 m², correct to the nearest m². The length of the rectangle is 9.2 m, correct to the nearest 0.1 m.

Calculate the smallest possible width of the rectangle.

Here are the first four terms of a sequence.

- 1 4 9 14

Write an expression for the n th term of this sequence.

The n th term of another sequence is given by

The third term is 9 and the sixth term is 126.

Find the value of a and the value of b.

The cumulative frequency graph shows the distribution of the heights of members of a rowing

Find the median.

Find the interquartile range.

Calculate the percentage of the members who are at least 180 cm tall.

The histogram summarises the heights of the 153 members of a swimming club.

Which club has the greater median height? You must show all your working.

The graph shows the speed of a train during the first 60 seconds of motion.

What is the speed of the train after 9 seconds?

What does the straight line suggest about the speed of the train over the first 15 seconds?

Work out the average speed of the train, in m / s, during the 60 seconds.

The diagram shows triangle OAB and points C and D.

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

The table shows values of x and y.

a is inversely proportional to b² and a = 3.75 when b = 4.

Find a formula linking a and b.

Region R satisfies these inequalities.

y > 3 y ⩾ x x + y ⩽ 9

By drawing three straight lines on the grid, find and label the region R.

Solve this equation algebraically. Give your solutions correct to 2 decimal places.