Edexcel GCSE Higher June 2023 Paper 1 (non-calculator)
24 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 (3 marks)
Work out 8.46 ÷ 0.15
(3 marks)
Question 2 (3 marks)
Work out 73/8 – 21/2
Give your answer as a mixed number.(3 marks)
Question 3 (4 marks)
A cube has a total surface area of 150 cm²
Work out the volume of the cube.
(4 marks)
Question 4 (2 marks)
The table shows information about the daily rainfall in a town for 60 days.
Rainfall (R mm) Frequency 0 ≤ R < 5 8 5 ≤ R < 10 24 10 ≤ R < 15 13 15 ≤ R < 20 11 20 ≤ R < 25 4 Draw a frequency polygon for this information.
Diagram: A blank grid. Rainfall (R mm) from 0 to 25 across, frequency from 0 to 30 up.
(2 marks)
Question 5 (5 marks)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {odd numbers}
B = {square numbers}(a)
Complete the Venn diagram for this information.
Diagram: Venn diagram with sets A and B. Only A: . Both: . Only B: . Neither: .
(3 marks)
(b)
A number is chosen at random from the universal set ℰ
Find the probability that this number is in the set B’
(2 marks)
Question 6 (3 marks)
The scatter graph shows information about the ages and weights of some babies.
Diagram: A scatter graph of weight (kg) against age (months) for 25 babies. The crosses go up from bottom left to top right.
(a)
Describe the relationship between the age and the weight of the babies.
(1 mark)
(b)
Another baby has a weight of 5.8 kg
Using the scatter graph, find an estimate for the age of this baby.
(2 marks)
Question 7 (2 marks)
The price of a holiday increases by 20%
This 20% increase adds £240 to the price of the holiday.Work out the price of the holiday before the increase.
(2 marks)
Question 8 (3 marks)
The diagram shows a solid cylinder on a horizontal floor.
Diagram: A tall thin cylinder standing upright on a floor, with its height labelled 40 cm.
pressure = dfracforcearea The cylinder has a
volume of 1200 cm³
height of 40 cm.The cylinder exerts a force of 90 newtons on the floor.
Work out the pressure on the floor due to the cylinder.
(3 marks)
Question 9 (1 mark)
Diagram: Two straight lines on a grid, x from –5 to 15 and y from –15 to 5. The line 2y = 3x – 22 slopes up steeply; the line 2 – 2y = x slopes down gently. They cross once.
Use these graphs to solve the simultaneous equations
2 – 2y = x
2y = 3x – 22(1 mark)
Question 10 (4 marks)
Here is a pentagon.
Diagram: A pentagon ABCDE. Angle A is 120°, angle C is 110° and angle D is 135°. Angles B and E are not marked.
Angle AED = 4 × angle ABC
Work out the size of angle AED.
You must show all your working.(4 marks)
Question 11 (3 marks)
Write dfrac(6x⁵y³)² 3x²y⁷ × 4xy⁻³ in the form ax^by^c where a, b and c are integers.
(3 marks)
Question 12 (3 marks)
Martha plays a game twice.
The probability tree diagram shows the probabilities that Martha will win or lose
each game.Diagram: Probability tree diagram. 1st game: win 5/8, lose 3/8. 2nd game, after a win: win 2/9, lose 7/9. After a loss: win 2/9, lose 7/9.
Find the probability that Martha will lose at least one game.
(3 marks)
Question 13 (3 marks)
y is directly proportional to x.
y = 24 when x = 1.5
Work out the value of y when x = 5
(3 marks)
Question 14 (4 marks)
(a)
Write 1/16 in the form 4ⁿ where n is an integer.
(1 mark)
(b)
Work out the value of 8^(5/3) – 9^(3/2)
(3 marks)
Question 15 (3 marks)
The equation of line L_1 is y = 2x – 5
The equation of line L_2 is 6y + kx – 12 = 0
L_1 is perpendicular to L_2
Find the value of k.
You must show all your working.(3 marks)
Question 16 (4 marks)
Here is a sphere.
Diagram: A sphere with its radius r marked from the centre to the surface.
Surface area of sphere = 4π r²
3/8 of the surface area of this sphere is 75π cm²
Find the diameter of the sphere.
Give your answer in the form a√b where a is an integer and b is a prime number.(4 marks)
Question 17 (4 marks)
Make x the subject of the formula y = (4(2x – 7))/(5x + 3)
(4 marks)
Question 18 (4 marks)
7 kg of carrots and 5 kg of tomatoes cost a total of 480p
cost of 1 kg of carrots : cost of 1 kg of tomatoes = 5 : 9
Work out the cost of 1 kg of carrots and the cost of 1 kg of tomatoes.
(4 marks)
Question 19 (2 marks)
The menu in a restaurant has starters, main courses and desserts.
There are 5 starters.
There are 12 main courses.
There are x desserts.There are 420 different ways to choose one starter, one main course and one dessert.
Work out the value of x.
(2 marks)
Question 20 (5 marks)
For x ≥ 0, the functions f and g are such that
f(x) = 3x + 4 g(x) = dfrac√x + 25
(a)
Find g⁻¹(x)
(2 marks)
(b)
Solve gf(x) = 3
(3 marks)
Question 21 (4 marks)
A, B and D are points on a circle with centre O.
CDE is the tangent to the circle at D.Diagram: A circle with centre O and points A, B and D on it. Lines AB, BO, OD and AD are drawn, and the line CDE touches the circle at D. Angle ABO is 51° and angle BOD is 64°.
Work out the size of angle ADC.
Write down any circle theorems you use.(4 marks)
Question 22 (2 marks)
ABCDEFGH is a cuboid.
Diagram: A cuboid ABCDEFGH. ABCD is the base, with A at the front left and D at the front right. F, E, H and G are above A, D, C and B.
AF = 6.8 cm
FC = 13.6 cmWork out the size of the angle between FC and the plane ABCD.
(2 marks)
Question 23 (4 marks)
Write dfrac3√34 – √3 – dfrac2√3 in the form dfraca√3 + bc where a, b and c are integers.
(4 marks)
Question 24 (5 marks)
Find the set of possible values of x for which
4x² – 25 < 0 and 12 – 5x – 3x² > 0
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.