Edexcel GCSE Higher June 2023 Paper 2 (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)
(a)
Work out the value of dfrac25 – √43.876 + 2.1²
Write down all the figures on your calculator display.
(2 marks)
(b)
Work out the value of the reciprocal of 0.625
(1 mark)
Question 2 (2 marks)
Write 60 as a product of its prime factors.
(2 marks)
Question 3 (1 mark)
There are 48 counters in a bag.
There are only red counters and blue counters in the bag.number of red counters : number of blue counters = 1 : 2
Helen has to work out how many red counters are in the bag.
She says,“There are 24 red counters in the bag because 1 is half of 2 and 24 is half of 48”
Is Helen correct?
You must give a reason for your answer.(1 mark)
Question 4 (6 marks)
-2 ≤ n < 5
n is an integer.
(a)
Write down the greatest possible value of n.
(1 mark)
(b)
On the number line below, show the inequality -4 ≤ m < 1
Diagram: A number line for m from -6 to 6.
(2 marks)
(c)
Solve 2/5g – 4 < 6
(3 marks)
Question 5 (4 marks)
Here is a triangle and a rectangle.
Diagram: A right-angled triangle with base 8 and height 6x, and a rectangle 5 wide and 4x – 1 tall.
All measurements are in centimetres.
The area of the triangle is 10 cm² greater than the area of the rectangle.
Work out the value of x.
(4 marks)
Question 6 (3 marks)
Last year a family recycled 800 kg of household waste.
57% of this waste was paper and glass.weight of paper recycled : weight of glass recycled = 12 : 7
Calculate the weight of glass the family recycled.
(3 marks)
Question 7 (2 marks)
A number, d, is rounded to 1 decimal place.
The result is 12.7Complete the error interval for d.
……… ≤ d < ………
(2 marks)
Question 8 (4 marks)
Tamsin buys a house with a value of £150 000
The value of Tamsin’s house increases by 4% each year.Rachel buys a house with a value of £160 000
The value of Rachel’s house increases by 1.5% each year.At the end of 2 years, whose house has the greater value?
You must show how you get your answer.(4 marks)
Question 9 (3 marks)
The cumulative frequency table gives information about the ages of 80 people working for a company.
Age (a years) Cumulative frequency 20 < a ≤ 30 20 20 < a ≤ 40 48 20 < a ≤ 50 64 20 < a ≤ 60 75 20 < a ≤ 70 80 (a)
On the grid, draw a cumulative frequency graph for this information.
Diagram: A graph.
(2 marks)
(b)
Use your graph to find an estimate for the median age.
(1 mark)
Question 10 (4 marks)
A biased dice is thrown 60 times.
The table shows information about the number that the dice lands on each time.Number on dice 1 2 3 4 5 6 Frequency 12 7 8 9 9 15 Gethin throws the dice twice.
(a)
Work out an estimate for the probability that the dice will land on 6 both times.
(3 marks)
(b)
Sally is going to throw the same dice n times and record the number it lands on each time.
She will use her results to work out a more reliable estimate for the probability in part (a).What can you say about the value of n?
(1 mark)
Question 11 (4 marks)
Use algebra to solve the simultaneous equations
2x + 6y = 5
3x – 4y = -12(4 marks)
Question 12 (4 marks)
The points A, B, C and D lie on a circle, centre O.
ABCD is a rectangle.Diagram: Rectangle ABCD inside a circle, centre O, with all four corners on the circle. AB is 8 cm and BC is 10 cm.
AB = 8 cm BC = 10 cm
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.(4 marks)
Question 13 (4 marks)
ABC is a triangle.
Diagram: Triangle ABC with AB = 15 cm, AC = 18 cm and angle ABC = 70°.
Calculate the size of angle BAC.
Give your answer correct to 1 decimal place.(4 marks)
Question 14 (3 marks)
Show that (x² – x – 6)/(2x² – 5x – 3) can be written in the form (ax + b)/(cx + d) where a, b, c and d are integers.
(3 marks)
Question 15 (3 marks)
Here are the first four terms of a quadratic sequence.
3 9 17 27
Find an expression, in terms of n, for the nth term of this sequence.
(3 marks)
Question 16 (4 marks)
The histogram gives information about the number of hours some students used their phones last week.
The histogram is incomplete.Diagram: An incomplete histogram with no scale on the frequency density axis. Bars: 0 to 20 hours, 8 small squares tall; 20 to 30 hours, 18 small squares tall; 30 to 40 hours, 14 small squares tall.
28 students used their phones for between 30 and 40 hours.
24 students used their phones for between 40 and 60 hours.(a)
Use this information to complete the histogram.
(2 marks)
(b)
No student used their phone for more than 60 hours.
Work out the total number of students.
(2 marks)
Question 17 (4 marks)
(a)
Show that the equation x⁴ – x² – 5 = 0 can be written in the form x = 4√(x² + 5)
(1 mark)
(b)
Starting with x_0 = 1.5
use the iteration formula x_n + 1 = 4√(x_n² + 5) three times to find an estimate for a solution of x⁴ – x² – 5 = 0(3 marks)
Question 18 (3 marks)
2a : 5c = 6 : 25
4b : 7c = 20 : 21
Show that a + b : b + c = 17 : 20
(3 marks)
Question 19 (3 marks)
ABC is a right-angled triangle.
Diagram: Right-angled triangle ABC with the right angle at B. AB = 9.3 cm is vertical, AC = 12.6 cm is the hypotenuse, and the angle x is at C.
AB = 9.3 cm correct to the nearest mm.
AC = 12.6 cm correct to the nearest mm.Calculate the lower bound for the size of the angle marked x.
You must show all your working.(3 marks)
Question 20 (4 marks)
ORT is a triangle.
Diagram: Triangle ORT. The side OT has an arrow from O to T labelled a; the side RT has an arrow from R to T labelled b. M is a point on OR.
overrightarrowOT = mathbfa overrightarrowRT = mathbfb
M is the point on OR such that OM : MR = 2 : 3
Express overrightarrowMT in terms of mathbfa and mathbfb.
Give your answer in its simplest form.(4 marks)
Question 21 (2 marks)
Here is the graph of y = f(x)
Diagram: The graph of y = f(x): straight lines joining (–3, 0), (–2, 1), (–1, 1) and (0, 0).
(a)
On the grid below, draw the graph of y = f(x) – 4
Diagram: A graph.
(1 mark)
(b)
On the grid below, draw the graph of y = f(-x)
Diagram: A graph.
(1 mark)
Question 22 (2 marks)
There are only blue pens and red pens in a box.
The number of blue pens is four times the number of red pens.Rita takes at random one pen from the box.
She records the colour of the pen and then replaces it in the box.Rita does this n times, where n ≥ 2
Write down an expression, in terms of n, for the probability that Rita gets a blue pen at least once and a red pen at least once.
(2 marks)
Question 23 (3 marks)
Here are three similar triangles, ABG, ACF and ADE.
Diagram: A large triangle ADE with apex A. B and C are on AD, G and F are on AE, and GB, FC and ED are parallel lines across the triangle.
ABCD and AGFE are straight lines.
AB : BC : CD = 1 : 2 : 3
Show that
area of ABG : area of BCFG : area of CDEF = 1 : 8 : 27
(3 marks)
Question 24 (5 marks)
The diagram shows 8 identical regular octagons joined to enclose a shaded shape.
Diagram: Eight identical regular octagons in a ring, each joined edge to edge to the next. The shaded shape they enclose is a square with a right-angled triangle on the middle of each side.
Each octagon has sides of length a.
Find, in terms of a, an expression for the area of the shaded shape.
Give your answer in the form p(2 + √2)a² where p is an integer.
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.