Edexcel GCSE Higher November 2024 Paper 1 (non-calculator)
20 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 818.4 ÷ 1.2
(3 marks)
Question 2 (4 marks)
The table shows the probabilities that a biased dice will land on 3, on 4, on 5 and on 6
Number on dice 1 2 3 4 5 6 Probability 0.10 0.30 0.05 0.25 Karim assumes that the probabilities that the dice will land on 1 and on 2 are the same.
Karim rolls the biased dice 500 times.
(a)
Assuming Karim is right, work out an estimate for the number of times the dice will
land on 2(3 marks)
(b)
Karim is wrong.
The probability that the dice will land on 2 is greater than the probability that the dice
will land on 1How does this information affect your answer to part (a)?
(1 mark)
Question 3 (5 marks)
(a)
Work out 31/2 – 11/6
Give your answer as a mixed number.(2 marks)
(b)
Show that 51/4 ÷ 21/3 = 21/4
(3 marks)
Question 4 (3 marks)
ABCD is a parallelogram.
Diagram: Parallelogram ABCD with A at the top left, B at the top right, C at the bottom right and D at the bottom left, and the diagonal AC. Angle BAC is marked e. Angle ADC is marked 3e.
All angles are measured in degrees.
Find an expression, in terms of e, for the size of angle CAD.
Give a reason for each stage of your working.(3 marks)
Question 5 (4 marks)
A car travelled 4.96 miles at an average speed of 30.4 miles per hour.
(a)
Work out an estimate for the time taken by the car.
Give your answer in minutes.(3 marks)
(b)
Is your answer to part (a) an underestimate or an overestimate?
Give a reason for your answer.(1 mark)
Question 6 (4 marks)
Here is a pentagon.
Diagram: A pentagon. Its interior angles are marked a, b, c, d, e, going round clockwise from the corner on the left.
Angle a = angle c
Angle b = 155°
Angle d is three times the size of angle c
Angle e is two times the size of angle cWork out the size of angle a
(4 marks)
Question 7 (1 mark)
The graph shows the volume of water, V litres, in a tank at time t seconds.
Diagram: A graph of volume (V litres, 0 to 20) against time (t seconds, 0 to 50). A straight line goes down from 20 litres at 0 seconds to 0 litres at 50 seconds.
What does the gradient of this graph represent?
(1 mark)
Question 8 (3 marks)
The diagram shows a solid triangular prism on a horizontal floor.
Diagram: A solid triangular prism lying on a horizontal floor on one of its rectangular faces. The front edge on the floor is labelled 2 m; hidden edges are dashed.
pressure = dfracforcearea The face in contact with the floor is a rectangle of width 2 m.
The pressure on the floor due to the prism is 80 newtons/m²
The force exerted by the prism on the floor is 720 newtons.Work out the length of the prism.
(3 marks)
Question 9 (6 marks)
The cumulative frequency graph gives information about the marks that 60 students got in a test.
Diagram: A cumulative frequency graph for the marks of 60 students. The S-shaped curve starts at (8, 0) and rises to (74, 60), passing through about (10, 3), (20, 10), (30, 23), (40, 42), (50, 53), (60, 55), (70, 58).
(a)
For these 60 students
the highest mark was 74
the lowest mark was 8On the grid below, draw a box plot for the distribution of the marks.
Diagram: A blank squared grid above a Mark axis from 0 to 80, for drawing a box plot.
(3 marks)
(b)
The pass mark for the test was 40
Sian says,
“30% of the 60 students passed the test.”
Is Sian correct?
You must show how you get your answer.(3 marks)
Question 10 (4 marks)
(a)
Work out 25^(1/2) × 8^(1/3)
(2 marks)
(b)
Find the value of (1/32)^(3/5)
(2 marks)
Question 11 (5 marks)
(a)
Kate was asked to factorise x² + 5x + 6 in the form (x + a)(x + b)
Kate says,
“The sum of a and b must be 6 and the product of a and b must be 5”
Explain what is wrong with Kate’s statement.
(1 mark)
(b)
Factorise fully 2m² – 2
(2 marks)
(c)
Factorise fully ax + bx – ay – by
(2 marks)
Question 12 (4 marks)
A, B and C are three solid spheres.
Sphere A has a volume of 64 cm³
Sphere B has a volume of 125 cm³The radius of sphere C is 50% of the radius of sphere B.
Work out the ratio of the surface area of sphere A to the surface area of sphere C.
Give your answer in the form a : b where a and b are integers.(4 marks)
Question 13 (5 marks)
Here are two cuboids.
Diagram: Two cuboids. Cuboid A has height x + 2, width 2x – 1 and depth x – 1. Cuboid B has height x + 3, width 2x and depth x – 3.
All lengths are measured in centimetres.
The volume of cuboid A is 142 cm³ greater than the volume of cuboid B.
Work out the value of x.
(5 marks)
Question 14 (3 marks)
ABC is a triangle.
Diagram: Triangle ABC. AB is horizontal at the top with A on the left; C is below A, a little to its left. AC = 3√2 cm, angle ABC = 30° and angle ACB = 45°.
Work out the length of AB.
(3 marks)
Question 15 (4 marks)
OXYZ is a parallelogram.
Diagram: Parallelogram OXYZ with O at the bottom left, Z at the bottom right, X above O and Y above Z. The diagonal OY is drawn. M is marked on OY and N on OZ.
overrightarrowOY = mathbfa and overrightarrowOZ = mathbfb
M is the point on OY such that OM : MY = 1 : 3
N is the point on OZ such that ON : NZ = 1 : 2Work out the ratio XN : MN
You must show all your working.(4 marks)
Question 16 (6 marks)
(a)
Rationalise the denominator of dfrac15√5
Give your answer in its simplest form.
(2 marks)
(b)
Write dfrac√75 – 21 + 2√3 in the form dfraca – b√3c where a, b and c are integers.
(4 marks)
Question 17 (4 marks)
A, B and C are points on a circle, centre O.
Diagram: A circle centre O. A is on the upper left of the circle, B on the right and C at the bottom. Chords AB, AC and BC are drawn, and radii OA and OB. CD is a tangent at C, going to the right.
CD is a tangent to the circle.
Angle BCD = 40°
Angle OAB = 3 × angle OACWork out the size of angle ACD.
Write down any circle theorems that you use.(4 marks)
Question 18 (4 marks)
f(x) = (5x – 3)/4
(a)
Find f⁻¹(x)
(2 marks)
(b)
For all values of x
g(x) = (x – 1)² and h(x) = 1 – 2x
Work out the value of gh(5)
(2 marks)
Question 19 (4 marks)
In the semi-finals of a chess tournament,
player A will play player B
and player C will play player D.The two winners will then play each other in the final.
The probability that player A will win against player B is 0.6
The probability that player A will win against player C is 0.5
The probability that player A will win against player D is 0.3
The probability that player C will win against player D is 0.2Work out the probability that player A will win the chess tournament.
(4 marks)
Question 20 (4 marks)
C is the circle with equation x² + y² = 4
Find an equation of the tangent to C at the point (p, 1) where p > 0
Give your answer in the form y + √ax = b where a and b are integers.
You must show all your working.(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.