OCR GCSE Maths Paper 4: Calculator Higher November 2023 question paper J560/04

The price of a phone increases from £240 to £262.80.

Calculate the percentage increase in the price of the phone.

A prime number is a whole number that has exactly two factors.

Explain why 1 is not a prime number.

a and b are prime numbers. Write down the 6 factors of a²b.

The table shows the results for a sports club’s ‘A’ team.

Complete a labelled pie chart to show these results.

Here are the results for the sports club’s ‘B’ team and ‘C’ team.

‘B’ team
‘C’ team

The ‘C’ team manager says

The pie charts show that the ‘C’ team won more games than the ‘B’ team.

Referring to the pie charts, explain why the ‘C’ team manager may not be correct.

The graph shows Taylor’s journey from home to an airport. During the journey Taylor stops for petrol.

For how long did Taylor stop for petrol?

Taylor drives the same route back home from the airport at an average speed of 45 km / h. Taylor leaves the airport at 22:00.

Work out the time when Taylor arrives home.

Write an expression for the weight, in grams, of an object weighing x kilograms.

Write an expression for the area, in m², of a garden of area ycm².

2 kg of carrots and 5 kg of potatoes cost £6.36. 3 kg of carrots and 2 kg of potatoes cost £5.25.

Find the cost of 1 kg of carrots and the cost of 1 kg of potatoes. You must show your working.

1 kg of carrots cost £........

1 kg of potatoes cost £........

Find all the possible integer values that satisfy the inequality - 10 < 3 x + 2 ⩽ 8.

Here are sketches of six graphs, labelled A to F.

Write the letter of the graph that represents the following relationships.

y is directly proportional to x.

y is inversely proportional to x.

Here are two pieces of work. Each shows a question and an incorrect solution.

For each part, describe the error made and write out a correct solution.

A correct solution is........

A correct solution is........

The diagram shows a pentagon ABCDE.

Find the area of the pentagon. You must show your working.

Riley and Sam are conducting surveys. They are both given the same list of 12 463 people from which to select their sample.

Riley selects every 56th person. Sam selects every 64th person. They both start counting from the first name in the list.

Work out how many people will be selected to be in both surveys. You must show your working.

In a computer game the player can either win or lose. A student thinks the ratio of the probability of winning to the probability of losing is 2: 3.

The student plays two games.

Use the information to complete the tree diagram.

Find the probability that the student wins at least one of the two games.

The student now thinks the ratio of the probability of winning to the probability of losing has changed to 2: 5.

Explain the effect this change will have on your answer to part (b).

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

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

Describe fully the single transformation that is equivalent to:

• a rotation of 90° clockwise about centre (0,0), followed by

• a reflection in the y-axis.

You may use the grid above to help you.

The histogram shows the heights of some plants out of a total of 80 plants.

Complete the histogram to show the plants with heights between 0 cm and 20 cm.

P, Q, T and V are points on the circumference of a circle. TV is a diameter of the circle. M is a point on PQ such that PM = MQ.

Complete these sentences to show that triangle TMP is congruent to triangle TMQ.

Side PM = side MQ because it is given to you.

Angle PMT = angle........ because........

Triangle TMP is congruent to triangle TMQ because........

A biologist assumes the population, P, of birds on an island can be predicted using the formula

P = 3800 × 1.042ⁿ

where n is the number of years after the start of 2020.

Write down the percentage increase per year that is used in the formula.

Calculate the predicted population at the start of 2024.

Show that the number of birds is predicted to exceed 7000 during 2034.

A researcher says that between 2022 and 2030 the percentage increase per year in the population will be 2.8%.

If the researcher is correct, explain how this new information will affect the answer in part (c)(i).

A sequence is defined by

Work out the value of u₂ and the value of u₃.

Here are the first four terms of a quadratic sequence.

- 2 7 22 43

The sequence has the formula x_n = an² + b.

Find the value of a and the value of b.

Solve this quadratic equation by factorisation.

2x² - 6x - 24 = 5x - 3

The diagram shows the positions of three towns A, B and C.

The bearing of town B from town A is 053°. The bearing of town C from town B is 108°. AB = 35 km and BC = 61 km.

Calculate AC. You must show your working.

The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2).

Write down the equation of the circle.

Show that the tangent to the circle at the point (4, 2) has gradient - 2.

Find the equation of the tangent to the circle at the point (4, 2).

Solve.

You are given this identity.

Find the value of a and the value of b. You must show each step in your working.