Edexcel GCSE Higher June 2024 Paper 2 (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)
ABC is a right-angled triangle.
Diagram: A diagram.
Work out the length of CB.
Give your answer correct to 3 significant figures.(2 marks)
Question 2 (3 marks)
(a)
Write 90 as a product of its prime factors.
(2 marks)
(b)
A = 2² × 3
B = 2 × 3²
Write down the lowest common multiple (LCM) of A and B.
(1 mark)
Question 3 (2 marks)
The number of hours, H, that some machines take to make 5000 bottles is given by
H = 72/n where n is the number of machines.
On Monday, 6 machines made 5000 bottles.
On Tuesday, 9 machines made 5000 bottles.The machines took more time to make the bottles on Monday than on Tuesday.
How much more time?
(2 marks)
Question 4 (4 marks)
There are only red discs, blue discs and yellow discs in a bag.
There are 24 yellow discs in the bag.Mel is going to take at random a disc from the bag.
The probability that the disc will be yellow is 0.16the number of red discs : the number of blue discs = 5 : 4
Work out the number of red discs in the bag.
(4 marks)
Question 5 (6 marks)
(a)
Complete the table of values for y = x² – x
x –2 –1 0 1 2 3 y 6 0 2 (2 marks)
(b)
On the grid, draw the graph of y = x² – x for values of x from –2 to 3
Diagram: A graph.
(2 marks)
(c)
Use your graph to find estimates for the solutions of the equation x² – x = 4
(2 marks)
Question 6 (4 marks)
Andy, Luke and Tina share some sweets in the ratio 1 : 6 : 14
Tina gives 3/7 of her sweets to Andy.
Tina then gives 121/2\% of the rest of her sweets to Luke.
Tina says,
“Now all three of us have the same number of sweets.”Is Tina correct?
You must show how you get your answer.(4 marks)
Question 7 (4 marks)
ABCD is a quadrilateral.
Diagram: A diagram.
All angles are measured in degrees.
Show that ABCD is a trapezium.
(4 marks)
Question 8 (3 marks)
A playground is in the shape of a right-angled triangle.
Diagram: Right-angled triangle PQR with the right angle at Q: PQ along the bottom, QR going up.
Dan makes a scale drawing of the playground.
He uses a scale of 1 cm represents 5 mThe area of the playground on the scale drawing is 28 cm²
The real length of QR is 40 mWork out the real length of PQ.
(3 marks)
Question 9 (2 marks)
A number N is rounded to 2 significant figures.
The result is 7.3(a)
Write down the least possible value of N.
(1 mark)
(b)
Leila says,
“The value of N cannot be greater than 7.349 because 7.350 would round up to 7.4”Is Leila correct?
You must give a reason for your answer.(1 mark)
Question 10 (3 marks)
The diagram shows two right-angled triangles.
Diagram: A diagram.
All lengths are measured in centimetres.
Given that
sin a = tan b
work out the value of x.
(3 marks)
Question 11 (7 marks)
The frequency table gives information about the weights of 60 parcels.
Weight (w kg) Frequency Cumulative frequency 0 < w ≤ 2 7 2 < w ≤ 4 21 4 < w ≤ 6 15 6 < w ≤ 8 11 8 < w ≤ 10 6 (a)
Complete the cumulative frequency column of the table.
(1 mark)
(b)
On the grid, draw a cumulative frequency graph for your table.
Diagram: A graph.
(2 marks)
(c)
Use your graph to find an estimate for the interquartile range.
(2 marks)
(d)
Use your graph to find an estimate for the number of these parcels with a weight greater than 7.4 kg.
(2 marks)
Question 12 (4 marks)
f is inversely proportional to d²
f = 3.5 when d = 8
(a)
Find an equation for f in terms of d.
(2 marks)
(b)
Find the positive value of d when f = 10
Give your answer correct to 3 significant figures.(2 marks)
Question 13 (3 marks)
Diagram: A graph.
On the grid, shade the region R that satisfies all the following inequalities.
x ≤ 2 y ≥ -3 y ≤ 2x + 1 3x + 2y ≤ 6
Label the region R.
(3 marks)
Question 14 (6 marks)
The graph shows the velocity of a car, in metres per second, t seconds after it starts to slow down.
Diagram: A curve falling from 25 m/s at t = 0, through 16 at t = 2, 9 at t = 4 and 4 at t = 6, flattening to 0 at t = 10.
(a)
Calculate an estimate for the acceleration of the car when t = 5
You must show all your working.(3 marks)
(b)
Work out an estimate for the distance the car travels in the first 6 seconds after it starts to slow down.
Use 3 strips of equal width.(3 marks)
Question 15 (2 marks)
Given that a is a prime number, rationalise the denominator of dfrac1√a + 1
Give your answer in its simplest form.
(2 marks)
Question 16 (2 marks)
Solve (4x – 3)(x + 5) < 0
(2 marks)
Question 17 (4 marks)
L, M and P are three similar solid cylinders made from the same material.
Diagram: Three similar cylinders: L, a larger M, and a small P.
L has a mass of 64 g
M has a mass of 125 gM has a total surface area of 144 cm²
P has a total surface area of 16 cm²Work out
height of cylinder L : height of cylinder M : height of cylinder P
(4 marks)
Question 18 (5 marks)
There are only 4 red counters, 3 yellow counters and 1 green counter in a bag.
Tony takes at random three counters from the bag.
Work out the probability that there are now more yellow counters than red counters in the bag.
You must show all your working.(5 marks)
Question 19 (5 marks)
The diagram shows quadrilateral OACB.
Diagram: Quadrilateral OACB with AC parallel to OB. M is on OA, N is on BC.
M is the midpoint of OA.
N is the point on BC such that BN : NC = 4 : 5overrightarrowOA = mathbfa overrightarrowOB = mathbfb overrightarrowAC = kmathbfb where k is a positive integer.
(a)
Express overrightarrowMN in terms of k, mathbfa and mathbfb.
Give your answer in its simplest form.(4 marks)
(b)
Is MN parallel to OB?
Give a reason for your answer.(1 mark)
Question 20 (3 marks)
The curve C has equation y = 2x² – 12x + 7
Find the coordinates of the turning point on C.
(3 marks)
Question 21 (2 marks)
The graph of y = g(x) is shown on the grid.
Diagram: A graph.
On the grid, draw the graph of y = g(-x) + 2
(2 marks)
Question 22 (4 marks)
A and B are points on a circle, centre O.
Diagram: A circle centre O. From P outside it, two tangents touch the circle at A and B; the tangent through A goes on to M and the one through B to N.
MAP and NBP are tangents to the circle.
Prove that AP = BP
(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.