Edexcel GCSE Higher June 2022 Paper 3 (calculator)
22 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (2 marks)
Here is a right-angled triangle.
Diagram: A right-angled triangle. The vertical side is 4 cm, the horizontal side is x cm and the sloping side (the hypotenuse) is 8.5 cm.
Work out the value of x.
(2 marks)
Question 2 (4 marks)
T = 4m² – 11
(a)
Work out the value of T when m = -3
(2 marks)
(b)
Make p the subject of the formula d = 3p + 4
(2 marks)
Question 3 (5 marks)
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.
(5 marks)
Question 4 (4 marks)
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.
Chic Decor 3 rolls for £36 Style Papers Pack of 5 rolls normal price £70 12% off the normal price 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.(4 marks)
Question 5 (2 marks)
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.
Diagram: A frequency polygon titled Lengths of pieces of string. The frequency axis is labelled 0, 10, 20, 30, 50, 60, evenly spaced. The points plotted are (5, 15), (15, 20), (25, 50), (35, 25), (50, 5), joined with straight lines.
Write down two mistakes that Amos has made.
(2 marks)
Question 6 (4 marks)
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.(4 marks)
Question 7 (3 marks)
The diagram shows rectangle STUV.
TQU and SRV are straight lines.
All measurements are in cm.Diagram: Rectangle STUV with T top left, U top right, V bottom right and S bottom left. Q is on TU and R is on SV, and the trapezium QUVR is shaded. TQ = 2x, ST = 4x, SR = 3x and RV = 5.
The area of trapezium QUVR is A cm²
Show that A = 2x² + 20x
(3 marks)
Question 8 (3 marks)
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.
Diagram: A graph of cost in pounds (0 to 20 up) against number of units used (0 to 140 across). A straight line goes from (0, 0) up to the right edge at about (140, 19.6).
(a)
Work out the gradient of the straight line.
(2 marks)
(b)
What does the gradient of this line represent?
(1 mark)
Question 9 (4 marks)
(a)
Express sqrtdfrac10³⁶⁰10¹⁵⁰ × 10⁹⁰ as a power of 10
(3 marks)
(b)
Liam was asked to express (12⁵⁰)² as a power of 12
Liam wrote (12⁵⁰)² = 12^(50²) = 12²⁵⁰⁰
Liam’s method is wrong.Explain why.
(1 mark)
Question 10 (3 marks)
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 £17010
Work out the value of the car when Jane bought it three years ago.
(3 marks)
Question 11 (2 marks)
Rayheem has
16 shirts
5 pairs of jeans
3 jacketsRayheem 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.
(2 marks)
Question 12 (3 marks)
ABC and ACD are right-angled triangles.
Diagram: Triangle ABD with C on DB and AC drawn straight up from C, at right angles to DB. DC = 8 cm, angle ADC = 45° and angle ABC = 20°.
DC = 8 cm
Angle ADC = 45°
Angle ABC = 20°Work out the length of AB.
Give your answer correct to 3 significant figures.(3 marks)
Question 13 (3 marks)
mathbfa and mathbfb are vectors such that
mathbfa = ( 2 , -3 ) and 3mathbfa – 2mathbfb = ( 8 , -17 )
Find mathbfb as a column vector.
(3 marks)
Question 14 (5 marks)
(a)
Factorise fully 4p² – 36
(2 marks)
(b)
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.(3 marks)
Question 15 (3 marks)
P, Q, R and S are four points on a circle.
Diagram: A circle with four points on it: P at the top left, Q at the top right, R on the right and S at the bottom left. The chords PQ, PR, SQ and SR are drawn; PR and SQ cross at X, inside the circle near Q and R.
PXR and SXQ are straight lines.
Prove that triangle PQX and triangle SRX are similar.
(3 marks)
Question 16 (3 marks)
p = √(2e/f)
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.(3 marks)
Question 17 (5 marks)
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 (a)
On the grid, draw a histogram for this information.
Diagram: A blank grid: distance (d miles) from 0 to 6 across, frequency density up with no scale.
(3 marks)
(b)
The histogram below shows information about the distances, in miles, that some Year 11 students live from school.
Diagram: A histogram with no scale on the frequency density axis. Bars: 0 to 0.5 miles, 7.5 small squares tall; 0.5 to 1, 5.2 small squares; 1 to 2, 3 small squares; 2 to 3, 1.4 small squares; 3 to 5, 0.6 of a small square.
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.
(2 marks)
Question 18 (5 marks)
Here is a prism ABCDSPQR.
Diagram: A prism standing on a square base ABCD, with A at the front left, B at the front right, C at the back right and D at the back left. P, Q, R and S are above A, B, C and D; PA is shorter than QB, so the top PQRS slopes up to the right. AB = 14 cm and CR = 12 cm. T is on BC, and the hidden lines DA, DC, DS and ST are dashed.
The base ABCD of the prism is a square of side 14 cm
T is the point on BC such that BT : TC = 4 : 3The cross section of the prism is in the shape of a trapezium of area 147 cm²
CR = 12 cmFind the size of the angle between the line ST and the base ABCD.
Give your answer correct to 1 decimal place.(5 marks)
Question 19 (4 marks)
Show that 3x/(x + 2) – (2x + 1)/(x – 2) – 1
can be written in the form (ax + b)/(x² – 4)
where a and b are integers.(4 marks)
Question 20 (4 marks)
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
P_n + 1 = aP_n + 800 where a is a constant.
The table shows the profit made by the shop in 2018 and in 2019
Year 2018 2019 Profit £24000 £29600 Work out the profit predicted to be made by the shop in 2021
(4 marks)
Question 21 (4 marks)
Ray has nine cards numbered 1 to 9
Diagram: Nine cards in a row, numbered 1, 2, 3, 4, 5, 6, 7, 8 and 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.
(4 marks)
Question 22 (5 marks)
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.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.