Edexcel GCSE Maths Paper 2: Calculator Higher June 2022 question paper 1MA1/2H

Simplify (x³)⁵

Expand and simplify 4(x + 3) + 7(4 − 2x)

Factorise fully 15x³ + 3x²y

Describe fully the single transformation that maps shape S onto shape T.

The length of a football pitch is 90 metres, correct to the nearest metre. Complete the error interval for the length of the football pitch.

_........ m ≤ length <_........

Festival A will be in a rectangular field with an area of 80 000 m² The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700 m by 2000 m. The greatest number of people allowed to attend Festival B is 6750 The area per person allowed for Festival B is greater than the area per person allowed for Festival A.

How much greater? Give your answer correct to the nearest whole number.

Callum says, “300 cm² is the same as 3 m² because there are 100 cm in 1 m so you divide by 100” Callum’s method is wrong.

Explain why.

The points L, M and N are such that LMN is a straight line. The coordinates of L are (−3, 1) The coordinates of M are (4, 9) Given that LM: MN = 2: 3, find the coordinates of N.

A new phone cost £679 The value of the phone decreases at a rate of 4% per year. Work out the value of the phone at the end of 3 years.

In Spain, Sam pays 27 euros for 18 litres of petrol. In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol. 1 euro = £0.85 4.5 litres = 1 gallon Sam thinks that petrol is cheaper in Spain than in Wales. Is Sam correct? You must show how you get your answer.

Use your calculator to work out

Give your answer correct to 3 significant figures.

The face in contact with the floor is a rectangle of length 1.2 metres and width x metres. Work out the value of x.

The box plot shows information about the sales, in thousands of pounds (£000s), of an online store each month.

Andrew says, “Three quarters of the given data lies between 160 000 and 350 000 because these are the values of the lower quartile and the upper quartile.” Andrew is wrong.

Explain why.

The table shows information about the sales, in £000s, in a shop each month.

On the grid below, draw a box plot for this information.

Compare the distribution of the sales of the online store with the distribution of the sales in the shop.

Kieron has 13 workers he can use for a job. He knows that 6 workers would take 14 days to complete this job. Show that Kieron has enough workers to finish this job in less than 7 days.

12The equation of the line L₁ is y = 2x + 3 The equation of the line L₂ is 5y − 10x + 4 = 0 Show that these two lines are parallel.

Enlarge the shaded shape by scale factor −2 with centre of enlargement (0, 0)

Saffron wants to work out an estimate for the total number of fish in a lake. On Friday, Saffron catches 180 fish from the lake. She puts a tag on each of these fish and puts them back into the lake. On Saturday, Saffron catches 305 fish from the same lake. She finds that 45 of the 305 fish are tagged. Work out an estimate for the total number of fish in the lake.

The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6: 5 Both Marta and Khalid get an increase of £1.50 in their hourly pay. The ratio of Marta’s hourly pay to Khalid’s hourly pay after this increase is 13: 11 Work out the hourly pay before the increase for Marta and for Khalid.

A shop manager wants to advertise special offers on social media platforms. The manager asks 100 customers which of type A, type B or type C they use. Of these customers, 4 use all three types 16 do not use any of type A, type B or type C 8 use both type A and type B, but not type C 14 use both type B and type C 62 in total use type A all 20 who use type C also use at least one of type A and type B.

Complete the Venn diagram for this information.

One of the customers is chosen at random. Given that this customer uses type A,

find the probability that this customer also uses type B.

A solid cone is joined to a solid hemisphere to make the solid T shown below.

The diameter of the base of the cone is 7 cm. The diameter of the hemisphere is 7 cm. The total volume of T is 120πcm³ The total height of T is ycm.

Calculate the value of y. Give your answer correct to 3 significant figures.

The diameter of the base of the cone and the diameter of the hemisphere are both increased by the same amount. Assuming the total volume of T does not change,

explain the effect this would have on your answer to part (a).

PQR and QRS are triangles.

Calculate the length of QS. Give your answer correct to 3 significant figures. You must show all your working.

The functions g and h are such that

Find g(16)

Find hg⁻¹(x) Give your answer in terms of x in its simplest form.

hg⁻¹(x) =_........

A, B, C and D are points on the circumference of a circle, centre O. ADE and BCE are straight lines.

Work out the size of angle CDE. Give a reason for each stage of your working.

The graph of y = f (x) is shown on the grid below.

On the grid above, sketch the graph of y = f (−x) Here is a sketch of the graph of y = tanx°

The graph of y = tanx° is translated to give the graph of y = g(x) Following the translation the point Q, shown on the graph above, moves to point R. Point R has coordinates (90, −5)

Find an expression for g(x) in terms of x.

Find algebraically the set of values of x for which