Edexcel GCSE Maths Paper 3: Calculator Higher June 2022 question paper 1MA1/3H

Here is a right-angled triangle.

Work out the value of x.

T = 4m² − 11

Work out the value of T when m = − 3

Make p the subject of the formula d = 3p + 4

Rick, Selma and Tony are playing a game with counters. Rick has some counters. Selma has twice as many counters as Rick. Tony has 6 counters less than Selma. In total they have 54 counters. the number of counters Rick has: the number of counters Tony has = 1: p Work out the value of p.

Jo is going to buy 15 rolls of wallpaper. Here is some information about the cost of rolls of wallpaper from each of two shops.

Jo wants to buy the 15 rolls of wallpaper as cheaply as possible. Should Jo buy the wallpaper from Chic Decor or from Style Papers? You must show how you get your answer.

The table gives information about the lengths, in cm, of some pieces of string.

Length (t cm)	Frequency
0 t 10	15
10 t 20	20
20 t 30	50
30 t 40	25
40 t 50	5

Amos draws a frequency polygon for the information in the table.

Write down two mistakes that Amos has made.

Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour.

The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.

The area of trapezium QUVR is Acm² Show that A = 2x² + 20x

An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.

Work out the gradient of the straight line.

What does the gradient of this line represent?

Liam was asked to express (12⁵⁰)² as a power of 12

Liam’s method is wrong.

Explain why.

Jane bought a new car three years ago. At the end of the first year the value of the car had decreased by 12.5% The value of the car then decreased by 10% each year for the next two years. At the end of the three years, the value of the car was £17 010 Work out the value of the car when Jane bought it three years ago.

Rayheem has 16 shirts 5 pairs of jeans 3 jackets Rayheem chooses an outfit to wear. An outfit is 1 shirt, 1 pair of jeans and 1 jacket. Work out how many different outfits Rayheem can choose.

ABC and ACD are right-angled triangles.

DC = 8 cm Angle ADC = 45° Angle ABC = 20° Work out the length of AB. Give your answer correct to 3 significant figures.

a and b are vectors such that

Find b as a column vector.

Factorise fully 4p² − 36

Show that (m + 4)(2m − 5)(3m + 1) can be written in the form am³ + bm² + cm + d where a, b, c and d are integers.

P, Q, R and S are four points on a circle.

PXR and SXQ are straight lines. Prove that triangle PQX and triangle SRX are similar.

e = 6.8 correct to 1 decimal place. f = 0.05 correct to 1 significant figure. Work out the upper bound for the value of p. Give your answer correct to 3 significant figures. You must show all your working.

The table gives information about the distances, in miles, that some Year 10 students live from school.

Distance (d miles)	Frequency
0 d 1.0	90
1.0 d 1.5	48
1.5 d 2.0	22
2.0 d 3.0	8
3.0 d 5.0	12

On the grid, draw a histogram for this information.

The histogram below shows information about the distances, in miles, that some Year 11 students live from school.

The number of Year 11 students who live between 1 and 2 miles from school is n.

Find an expression, in terms of n, for the number of Year 11 students who live between 3 and 5 miles from school.

Here is a prism ABCDSPQR.

The base ABCD of the prism is a square of side 14 cm T is the point on BC such that BT: TC = 4: 3 The cross section of the prism is in the shape of a trapezium of area 147 cm² CR = 12 cm Find the size of the angle between the line ST and the base ABCD. Give your answer correct to 1 decimal place.

19Show that 1 can be written in the form where a and b are integers.

The profit made by a shop increases each year. The profit made by the shop in year n is £P_n Given that the profit made by the shop in the next year is £P_{n+ 1} then

The table shows the profit made by the shop in 2018 and in 2019

Work out the profit predicted to be made by the shop in 2021

Ray has nine cards numbered 1 to 9

Ray takes at random three of these cards. He works out the sum of the numbers on the three cards and records the result. Work out the probability that the result is an even number.

L is the straight line with equation y = 2x − 5 C is a graph with equation y² = 6x² − 25x − 8 Using algebra, find the coordinates of the points of intersection of L and C. You must show all your working.