OCR GCSE Maths Paper 4: Calculator Higher June 2022 question paper J560/04

Write 6 050 000 in standard form.

Write 4.58 × 10^-3 as an ordinary number.

Calculate.

In January 2018, an art collector bought an antique painting. In January 2020, he sold it for £17 640.

Assume the value of the painting increased by 5% each year.

Calculate the art collector’s profit. You must show your working.

Three regular polygons meet at a point.

Two of the polygons are pentagons.

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

The scatter diagram shows the midday temperature at 13 different heights on a mountain.

The table has the information for 2 more heights.

Plot these on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

By drawing a line of best fit, estimate the temperature at 1000 m.

Circle the outlier on the scatter diagram.

Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.

Find the percentage of the 15 temperatures which are below 6 °C.

A machine can dig, on average, 2 cm of tunnel each minute. It operates 24 hours each day.

Work out how many days it should take to dig a tunnel of length 3.5 km. Give your answer to the nearest day.

The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.

How would this affect your answer to part (a) ?

The diagram shows a square-based pyramid and a sphere.

The pyramid has base length 12.3 cm and perpendicular height 15.7 cm. The sphere has radius r cm.

The pyramid and the sphere have the same volume.

Work out the radius of the sphere. You must show your working. [The volume of a pyramid is × area of base × perpendicular height. The volume V of a sphere with radius r is V = r³.]

Here is a table of values for y = x² + 2x - 2.

Draw the graph of y = x² + 2x - 2 for -4 ⩽ x ⩽ 2.

Write down the equation of the line of symmetry of the graph.

Use the graph to solve the equation x² + 2x - 2 = 0. Give your answers to 1 decimal place.

(c) x =........ or x =........

Points A, B and C lie on the circumference of a circle, centre O.

Angle ACB = 90°, AC = 6.4 m and BC = 3.7 m.

Work out the circumference of the circle. You must show your working.

A student is researching the difference in how much exercise adults and children do. To collect their data, the student interviews the first 25 people found in the High Street at 11 am on one Monday morning.

Make three different criticisms of the student’s method of collecting data.

Here is the data collection table that the student used.

Make one criticism of the student’s table.

Jamie buys fence panels that fit tightly together.

Each panel has a length of 1.8 m, correct to 1 decimal place. Jamie measures the length of a garden as 42 m, correct to the nearest metre.

Work out the minimum number of panels Jamie should buy in order to be certain that there are enough panels for the length of the garden. Show how you decide.

Points A, B and C lie on the circumference of a circle. EAF is a tangent to the circle.

Write down the value of angle BCA giving a reason for your answer.

Angle BCA = ……………….° because........

Points G, H and J lie on the circumference of a circle, centre O.

Angle GOJ = 52° and angle GJH = x °. Lines JO and GH are parallel.

Find the value of x. You must show your working.

Here is a restaurant’s menu.

A 3-course meal consists of one starter, one main and one dessert.

Work out how many different 3-course meals can be chosen from the menu.

Find the fraction of the 3-course meals which are completely vegetarian (V).

(x + 2)(3x + a)(bx + 3) = 6x³ + 11x² - 17x - 30

Find the value of a and the value of b.

Use algebra to prove that an odd number multiplied by a different odd number always gives an

answer that is an odd number.

Li bought a house at the start of 2016. Li assumes the value of the house, £ V, can be predicted using the formula

V = 185000 × 1.035ⁿ

where n is the number of years after the start of 2016.

Explain how you know that the value of the house is predicted to increase each year.

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

Write down the value of the house at the start of 2016.

Calculate the predicted value of the house at the start of 2020, giving your answer correct to 4 significant figures.

Compared with its value at the start of 2016, show that the formula predicts the house

will have doubled in value at some point during 2036.

Give one reason why this may not happen.

There are 15 sweets in a bag. 10 of the sweets are toffee and 5 are mint. Reece takes two of the sweets at random.

Work out the probability that Reece takes one of each type of sweet.

The diagram shows a circle, centre the origin.

Write down the equation of the circle.

Write as a single fraction in its simplest form.

Simplify.

Solve this inequality.

x² + 4x - 12 ⩽ 0

Give your answer using set notation. You must show your working.