Edexcel GCSE Higher June 2022 Paper 1 (non-calculator)
21 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)
Solve 7x – 27 < 8
(2 marks)
Question 2 (2 marks)
Write 124 as a product of its prime factors.
(2 marks)
Question 3 (5 marks)
A delivery company has a total of 160 cars and vans.
the number of cars : the number of vans = 3 : 7
Each car and each van uses electricity or diesel or petrol.
1/8 of the cars use electricity.
25% of the cars use diesel.
The rest of the cars use petrol.Work out the number of cars that use petrol.
You must show all your working.(5 marks)
Question 4 (4 marks)
(a)
Write 1.63 × 10⁻³ as an ordinary number.
(1 mark)
(b)
Write 438 000 in standard form.
(1 mark)
(c)
Work out (4 × 10³) × (6 × 10⁻⁵)
Give your answer in standard form.(2 marks)
Question 5 (3 marks)
Here is a regular hexagon and a regular pentagon.
Diagram: A regular hexagon and a regular pentagon joined along one side. At the bottom end of the shared side, the angle between the hexagon and the pentagon, outside both shapes, is marked x.
Work out the size of the angle marked x.
You must show all your working.(3 marks)
Question 6 (6 marks)
(a)
Complete the table of values for y = x² – 3x + 1
x –1 0 1 2 3 4 y 1 –1 (2 marks)
(b)
On the grid, draw the graph of y = x² – 3x + 1 for values of x from –1 to 4
Diagram: A graph.
(2 marks)
(c)
Using your graph, find estimates for the solutions of the equation x² – 3x + 1 = 0
(2 marks)
Question 7 (3 marks)
Here are two cubes, A and B.
Diagram: Two cubes: cube A with edges of 3 cm and cube B with edges of 4 cm.
Cube A has a mass of 81 g.
Cube B has a mass of 128 g.
Work out
the density of cube A : the density of cube B
Give your answer in the form a : b, where a and b are integers.
(3 marks)
Question 8 (3 marks)
The table shows the amount of snow, in cm, that fell each day for 30 days.
Amount of snow (s cm) Frequency 0 ≤ s < 10 8 10 ≤ s < 20 10 20 ≤ s < 30 7 30 ≤ s < 40 2 40 ≤ s < 50 3 Work out an estimate for the mean amount of snow per day.
(3 marks)
Question 9 (3 marks)
A cube is placed on top of a cuboid, as shown in the diagram, to form a solid.
Diagram: A cube with edges 4 cm placed on top of a 7 cm by 6 cm by 5 cm cuboid, against the back left corner of its top face.
The cube has edges of length 4 cm.
The cuboid has dimensions 7 cm by 6 cm by 5 cm.Work out the total surface area of the solid.
(3 marks)
Question 10 (6 marks)
The table shows some information about the profit made each day at a cricket club on 100 days.
Profit (£x) Frequency 0 ≤ x < 50 10 50 ≤ x < 100 15 100 ≤ x < 150 25 150 ≤ x < 200 30 200 ≤ x < 250 5 250 ≤ x < 300 15 (a)
Complete the cumulative frequency table.
Profit (£x) Cumulative frequency 0 ≤ x < 50 0 ≤ x < 100 0 ≤ x < 150 0 ≤ x < 200 0 ≤ x < 250 0 ≤ x < 300 (1 mark)
(b)
On the grid, draw a cumulative frequency graph for this information.
Diagram: A graph.
(2 marks)
(c)
Use your graph to find an estimate for the number of days on which the profit was less than £125
(1 mark)
(d)
Use your graph to find an estimate for the interquartile range.
(2 marks)
Question 11 (3 marks)
Cormac has some sweets in a bag.
The sweets are lime flavoured or strawberry flavoured or orange flavoured.In the bag
number of lime flavoured sweets : number of strawberry flavoured sweets : number of orange flavoured sweets = 9 : 4 : x
Cormac is going to take at random a sweet from the bag.
The probability that he takes a lime flavoured sweet is 3/7
Work out the value of x.
(3 marks)
Question 12 (3 marks)
Express 0.11̇7̇ as a fraction.
You must show all your working.(3 marks)
Question 13 (3 marks)
A right-angled triangle is formed by the diameters of three semicircular regions, A, B and C
as shown in the diagram.Diagram: A right-angled triangle with a semicircle on each side, drawn outwards: region A on the longest side, region B on the horizontal side and region C on the vertical side. The regions are shaded.
Show that
area of region A = area of region B + area of region C
(3 marks)
Question 14 (4 marks)
Here is a speed-time graph.
Diagram: A curve starting at (0, 0), rising to a highest speed of just over 4 m/s at about 4.5 seconds, then falling back to 0 at 9 seconds. At 2 seconds the speed is 2.8 m/s.
(a)
Work out an estimate of the gradient of the graph at t = 2
(3 marks)
(b)
What does the area under the graph represent?
(1 mark)
Question 15 (5 marks)
A, B and C are three points such that
overrightarrowAB = 3mathbfa + 4mathbfb
overrightarrowAC = 15mathbfa + 20mathbfb(a)
Prove that A, B and C lie on a straight line.
(2 marks)
(b)
D, E and F are three points on a straight line such that
overrightarrowDE = 3mathbfe + 6mathbff
overrightarrowEF = -10.5mathbfe – 21mathbffFind the ratio
length of DF : length of DE
(3 marks)
Question 16 (4 marks)
A first aid test has two parts, a theory test and a practical test.
The probability of passing the theory test is 0.75
The probability of passing only one of the two parts is 0.36The two events are independent.
Work out the probability of passing the practical test.
(4 marks)
Question 17 (4 marks)
y is directly proportional to the square root of t.
y = 15 when t = 9t is inversely proportional to the cube of x.
t = 8 when x = 2Find a formula for y in terms of x.
Give your answer in its simplest form.(4 marks)
Question 18 (4 marks)
Work out the value of dfrac(54/9)^(-1/2) × (42/3)2⁻³
You must show all your working.(4 marks)
Question 19 (4 marks)
Solve 1/(2x – 1) + 3/(x – 1) = 1
Give your answer in the form dfracp ± √q2 where p and q are integers.
(4 marks)
Question 20 (4 marks)
The centre of a circle is the point with coordinates (–1, 3)
The point A with coordinates (6, 8) lies on the circle.
Find an equation of the tangent to the circle at A.
Give your answer in the form ax + by + c = 0 where a, b and c are integers.(4 marks)
Question 21 (5 marks)
The diagram shows three circles, each of radius 4 cm.
The centres of the circles are A, B and C such that ABC is a straight line and
AB = BC = 4 cm.Diagram: Three circles of the same radius with centres A, B and C equally spaced on a horizontal line. The middle circle passes through A and C; the outer circles touch at B. The two parts of the middle circle outside both outer circles, above and below B, are shaded.
Work out the total area of the two shaded regions.
Give your answer in terms of π(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.