Edexcel GCSE Higher November 2022 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)
Write 500 as a product of powers of its prime factors.
(3 marks)
Question 2 (4 marks)
(a)
Work out 13/5 + 21/4
Give your answer as a mixed number.(2 marks)
(b)
Show that 22/3 ÷ 6 = 4/9
(2 marks)
Question 3 (2 marks)
Simplify (2⁻⁵ × 2⁸)²
Give your answer as a power of 2(2 marks)
Question 4 (2 marks)
Work out 0.004 × 0.32
(2 marks)
Question 5 (2 marks)
A car factory is going to make four different car models A, B, C and D.
80 people are asked which of the four models they would be most likely to buy.
The table shows information about the results.Car model Number of people A 23 B 15 C 30 D 12 The factory is going to make 40 000 cars next year.
Work out how many model B cars the factory should make next year.
(2 marks)
Question 6 (6 marks)
Rizwan writes down three numbers a, b and c
a : b = 1 : 3
b : c = 6 : 5(a)(i)
Find a : b : c
(2 marks)
(ii)
Express a as a fraction of the total of the three numbers a, b and c
(2 marks)
(b)
Emma writes down three numbers m, n and p
n = 2m
p = 5nFind m : p
(2 marks)
Question 7 (2 marks)
Diagram: A storage tank in the shape of a cuboid.
pressure = dfracforcearea A storage tank exerts a force of 10 000 newtons on the ground.
The base of the tank in contact with the ground is a 4 m by 2 m rectangle.Work out the pressure on the ground due to the tank.
(2 marks)
Question 8 (2 marks)
Two numbers m and n are such that
m is a multiple of 5
n is an even number
the highest common factor (HCF) of m and n is 7Write down a possible value for m and a possible value for n.
(2 marks)
Question 9 (4 marks)
(a)
Complete the table of values for y = 6x – x³
x y –3 9 –2 –1 0 1 2 4 3 –9 (2 marks)
(b)
On the grid, draw the graph of y = 6x – x³ for values of x from –3 to 3
Diagram: A blank grid with x from –3 to 3 and y from –10 to 10.
(2 marks)
Question 10 (4 marks)
Lina spins a biased 5-sided spinner 40 times.
Diagram: A spinner shaped like a regular pentagon, split into 5 equal triangles from its centre, numbered 2, 5, 3, 1, 4 going clockwise from the top right.
Here are her results.
Score Frequency 1 6 2 8 3 9 4 7 5 10 Lina is now going to spin the spinner another two times.
(a)
Work out an estimate for the probability that she gets a score of 5 both times.
(2 marks)
(b)
Derek is going to spin the spinner a large number of times.
Work out an estimate for the percentage of times Derek can expect to get a score of 1
(2 marks)
Question 11 (2 marks)
Diagram: A grid with x and y from 0 to 16. Shape P is a trapezium with corners (6, 14), (15, 14), (12, 8) and (9, 8). Shape Q is a smaller trapezium with corners (2, 6), (5, 6), (4, 4) and (3, 4).
Describe fully the single transformation that maps shape P onto shape Q.
(2 marks)
Question 12 (4 marks)
Solve the simultaneous equations
5x + 2y = 11
4x + 3y = 6(4 marks)
Question 13 (3 marks)
p is inversely proportional to t
Complete the table of values.
t 100 25 2 p 1 5 (3 marks)
Question 14 (3 marks)
The table shows information about the weights, in grams, of some potatoes.
Weight (w grams) Number of potatoes 50 < w ≤ 70 20 70 < w ≤ 80 50 80 < w ≤ 90 60 90 < w ≤ 110 30 On the grid, draw a histogram for this information.
Diagram: A blank grid: weight (w grams) from 40 to 120 across, frequency density up with no scale.
(3 marks)
Question 15 (3 marks)
The diagram shows a sector of a circle of radius 18 cm.
Diagram: A sector of a circle. Its two straight sides are radii, each labelled 18 cm, and the angle between them at the centre is labelled x degrees.
The length of the arc is 4π cm.
Work out the value of x.
(3 marks)
Question 16 (4 marks)
(a)
Prove that
(2m + 1)² – (2n – 1)² = 4(m + n) (m – n + 1)
(3 marks)
(b)
Sophia says that the result in part (a) shows that the difference of the squares of any two odd numbers must be a multiple of 4
Is Sophia correct?
You must give reasons for your answer.(1 mark)
Question 17 (2 marks)
Work out the value of (8/27)^(4/3)
(2 marks)
Question 18 (3 marks)
Diagram: A circle with centre O. A and B are points on the circle, and the radii OA and OB and the chord AB are drawn. The line DBC touches the circle at B. The angle AOB at the centre is marked x degrees.
A and B are points on a circle, centre O.
DBC is the tangent to the circle at B.
Angle AOB = x°Show that angle ABC = 1/2x°
You must give a reason for each stage of your working.(3 marks)
Question 19 (5 marks)
Solve 1/x – 1/(x + 1) = 4
Give your answer in the form a ± b√2 where a and b are fractions.
(5 marks)
Question 20 (3 marks)
Alfie has 11 cards.
He has3 blue cards
7 green cards
and 1 white card.Alfie takes at random 2 of these cards.
Work out the probability that he takes cards of different colours.
(3 marks)
Question 21 (2 marks)
Diagram: A sketch of a wave-shaped curve with no scale on the axes. It starts at its highest point on the y-axis, goes down through the x-axis to a lowest point P, back up to a highest point, down to another lowest point and back up.
The diagram shows a sketch of part of the curve with equation y = cos x°
P is a minimum point on the curve.Write down the coordinates of P.
(2 marks)
Question 22 (4 marks)
Here is a triangle ABC.
Diagram: Triangle ABC with AC = 6.5 cm along the bottom, BC = 10.7 cm, and angle BAC = 30°. B is far to the right of C, so the angle at C is obtuse.
Work out the value of sin ABC
Give your answer in the form m/n where m and n are integers.(4 marks)
Question 23 (5 marks)
Here are the first five terms of a geometric sequence.
√5 10 20√5 200 400√5
(a)
Work out the next term of the sequence.
(2 marks)
(b)
The 4th term of a different geometric sequence is dfrac5√24
The 6th term of this sequence is dfrac5√28Given that the terms of this sequence are all positive,
work out the first term of this sequence.
You must show all your working.(3 marks)
Question 24 (6 marks)
(a)
Here is a solid sphere and a solid cone.
Diagram: Top: A sphere with its centre marked. An arrow from the centre to the edge is labelled r. Below it: A cone with the centre of its base marked. An arrow from the centre to the edge of the base is labelled r, and an arrow beside it from the base to the top is labelled h.
Volume of sphere = 4/3π r³
Volume of cone = 1/3π r² hAll measurements are in cm. The volume of the sphere is equal to the volume of the cone.
Find r : h
Give your answer in its simplest form.(2 marks)
(b)
Here is a different solid sphere and a different solid cone.
Diagram: Top: A sphere with its centre marked. An arrow from the centre to the edge is labelled r. Below it: A cone with the centre of its base marked. An arrow from the centre to the edge of the base is labelled r, and an arrow along its sloping side is labelled l.
Surface area of sphere = 4π r²
Curved area of cone = π rlAll measurements are in cm. The surface area of the sphere is equal to the total surface area of the cone.
Find r : h
Give your answer in the form 1 : √n where n is an integer.(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.