OCR GCSE Maths Paper 4: Calculator Higher November 2020 question paper J560/04

Write these numbers in standard form.

6500

0.0584

Work out (4.2 × 10⁵) × (1.8 × 10^-2), giving your answer in standard form.

James is taking three examination papers in Spanish. Here are his first two results.

Paper 3 is out of 95. The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

In a survey, 60 students were asked whether they have a bank account (B) and whether they have a part-time job (J).

The number of students who had neither a bank account nor a part-time job was x. The Venn diagram shows the results in terms of x.

One of the 60 students is chosen at random.

Find the probability that they have a bank account. Show your working.

ABCD is a quadrilateral.

Construct the bisector of angle ABC.

Show all your construction lines.

Construct the perpendicular bisector of BC.

Show all your construction lines.

Shade the region which is

• nearer to BC than to AB

and

• nearer to B than to C.

A cuboid measures 6 cm by 8 cm by 15 cm. A cube has the same volume as the cuboid.

Find the surface area of the cube, giving your answer correct to 3 significant figures.

This graph shows part of a straight line.

Show that the gradient of the line is 2.5.

Write down the equation of the line.

Lily buys and sells microwaves.

She buys each one for £32 and sells it for £60. She also pays £7 for the delivery of each microwave she sells.

If she sells a microwave that is faulty then Lily must pay for its repair and redelivery. This costs her another £25 for each faulty microwave.

Last month, 6 out of the 80 microwaves Lily sold were faulty.

This month she has orders for 133 microwaves.

Calculate her expected percentage profit on this month’s order. Showing your working in the boxes below may help you present your work.

The graph shows the number of umbrellas sold in Ling’s shop for each quarter from quarter 1 of 2017 to quarter 3 of 2019.

The shop sold 32 umbrellas in quarter 4 of 2019.

Complete the graph.

Make one comment about the seasonal variation shown in this graph.

Make one comment about the annual variation shown in this graph.

Ling predicts that she will sell 50 umbrellas in quarter 1 of 2020.

What assumption has she made?

The diagram shows Jane’s lawn. It is in the shape of a square of side 36 m and three semi-circles.

She is going to spread fertiliser on the lawn at a rate of 30 g per square metre. The fertiliser is only sold in 10 kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn. You must show all your working.

The length, d, of Jamal’s car is 4.72 m, correct to 2 decimal places.

Complete the error interval for the length, d.

Jamal travels 430 km, correct to the nearest 10 km. His average speed is 57.3 km / h, correct to 1 decimal place.

Calculate the shortest possible time for Jamal’s journey. Give your answer correct to the nearest minute.

(b)........ hours........ minutes

Triangle T is drawn on a coordinate grid.

Translate triangle T by vector .

Describe fully the single transformation that is equivalent to:

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

• a reflection in the x-axis.

You may use the grid above to help you.

Ali and Beth take it in turns to play a computer game. On each turn, the player achieves a score out of 50. Ali and Beth play the computer game many times and record their scores.

Ali’s scores are summarised below.

• median = 31

• highest score = 38

• range = 23

• lower quartile = 24

• interquartile range = 11

Draw a box plot to show the distribution of Ali’s scores.

This box plot shows the distribution of Beth’s scores.

Find the interquartile range of Beth’s scores.

Kareem says

Beth was more consistent than Ali because Beth had a lower median score.

Is his statement correct? Explain your reasoning.

The diagram shows triangle ABC.

AC = 15 cm, BC = 18 cm and angle BAC = 72°.

Calculate length AB, giving your answer correct to 3 significant figures. Show your working.

Here are two pieces of work.

For each one, describe the error made and give the complete correct solution.

Correct solution:

Correct solution:

y is inversely proportional to the square of x. y = 2 when x = 5.

Find a formula linking x and y.

Expand and simplify.

(x + 1)(x - 1)(x + 2)

Here is a sketch of the circle x² + y² = 45.

Find the equation of the tangent at the point (-3, 6).

The graph shows the speed of a vehicle during the first 40 seconds of motion.

Calculate the distance travelled by the vehicle during the 40 seconds.

The graph shows the distance travelled by a particle over 6 seconds.

Work out the average speed of the particle between 2 and 4 seconds.

Estimate the speed of the particle at 4 seconds.

Solve.

x² + y² = 34 y = x + 2

Show your working.