Edexcel GCSE Higher November 2023 Paper 2 (calculator)
21 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 (6 marks)
(a)
Expand and simplify 3(2y – 5) + 7(y + 2)
(2 marks)
(b)
Factorise fully 6x² + 15x
(2 marks)
(c)
Make g the subject of the formula f = 3g + 11
(2 marks)
Question 2 (4 marks)
Karen is organising a party for a charity.
She spends
£100 on food
£120 on a hall
£80 on a DJ.Karen sells 54 tickets for the party.
Each ticket costs £7.50Work out the percentage profit Karen makes for the charity.
(4 marks)
Question 3 (2 marks)
Andrew invests £4500 in a savings account for 2 years.
The account pays compound interest at a rate of 3.4% per year.Calculate how much Andrew has in this savings account at the end of the 2 years.
(2 marks)
Question 4 (3 marks)
Solve 5x – 14 = 52 – x
(3 marks)
Question 5 (4 marks)
Chris, Debbie and Errol share some money in the ratio 3 : 4 : 2
Debbie gets £120
Chris then gives some of his share to Debbie and some of his share to Errol.
The money that Chris, Debbie and Errol each have is now in the ratio 2 : 5 : 3
How much money did Chris give to Errol?
(4 marks)
Question 6 (2 marks)
The bearing of port B from port A is 147°
Work out the bearing of port A from port B.
(2 marks)
Question 7 (4 marks)
The diagram shows an empty tank in the shape of a cylinder.
Diagram: A cylinder with radius 15 cm and height 43 cm.
The cylinder has radius 15 cm and height 43 cm.
Water flows into the tank at a rate of 0.47 litres per minute.
Calculate the number of minutes it will take to completely fill the tank.
Give your answer correct to the nearest minute.(4 marks)
Question 8 (2 marks)
A number x is written correct to 2 significant figures.
The result is 1.9Complete the error interval for x.
ldotsldots ≤ x < ldotsldots
(2 marks)
Question 9 (3 marks)
Expand and simplify (x + 7)(x – 2)(x + 3)
(3 marks)
Question 10 (5 marks)
Shakir has to complete two tests.
He can either pass or fail each test.The probability that he will pass the first test is 0.87
If he passes the first test the probability he will pass the second test is 0.94
If he fails the first test the probability he will pass the second test is 0.73(a)
Complete the probability tree diagram for this information.
Diagram: Probability tree diagram. First test: pass 0.87, fail blank. Second test: all four branches blank.
(2 marks)
(b)
Work out the probability that Shakir passes at least one of the tests.
(3 marks)
Question 11 (2 marks)
Graph A
Diagram: Graph A: a straight line through O, sloping up.
Graph B
Diagram: Graph B: a curve falling from top left to bottom right, getting closer to the axes but never touching them.
Graph C
Diagram: Graph C: a curve starting at O, rising steeply then more and more slowly.
Graph D
Diagram: Graph D: a curve starting at O, rising slowly then more and more steeply.
The graphs of y against x represent four different types of proportionality.
Match each type of proportionality in the table to the correct graph.
Type of proportionality Graph y propto x² y propto x y propto 1/x y propto √x (2 marks)
Question 12 (3 marks)
A is the point with coordinates (7, 13)
B is the point with coordinates (–3, 21)
C is the point with coordinates (15, 23)M is the midpoint of AB.
N is the midpoint of BC.Work out the distance between M and N.
Give your answer correct to 1 decimal place.(3 marks)
Question 13 (3 marks)
Prove algebraically that 0.07̇23̇ can be written as 241/3330
(3 marks)
Question 14 (5 marks)
y is proportional to x²
y = 3 when x = 0.5x is inversely proportional to w
x = 2 when w = 0.2Find the value of y when w = 2
(5 marks)
Question 15 (6 marks)
The incomplete table and the incomplete histogram give information about the times taken by some students to run a race.
Time (t seconds) Frequency 10 < t ≤ 12 12 < t ≤ 16 10 16 < t ≤ 19 15 19 < t ≤ 21 9 21 < t ≤ 26 7 Diagram: An incomplete histogram with no scale on the frequency density axis. Bars: 10 to 12 seconds, 3 small squares tall; 12 to 16 seconds, 5 small squares tall; 16 to 19 seconds, 10 small squares tall.
None of these students had a time for the race such that t ≤ 10 or t > 26
(a)
Use the histogram to complete the table.
(1 mark)
(b)
Use the table to complete the histogram.
(2 marks)
(c)
The histogram below gives information about the times taken by 43 students to run a different race.
Diagram: A graph.
Work out an estimate for the median of the times taken by these 43 students to run the race.
(3 marks)
Question 16 (4 marks)
ABCD is a trapezium.
Diagram: Trapezium ABCD with AD parallel to BC and the diagonal BD drawn. AB = 7.9 cm, BC = 15.3 cm, angle DAB = 112° and angle ADB = 42°.
AD is parallel to BC.
Calculate the area of triangle BCD.
Give your answer correct to 1 decimal place.(4 marks)
Question 17 (6 marks)
(a)
Show that the equation x³ + 2x – 6 = 0 has a solution between x = 1 and x = 2
(2 marks)
(b)
Show that the equation x³ + 2x – 6 = 0 can be rearranged to give x = 6/(x² + 2)
(1 mark)
(c)
Starting with x_0 = 1.45
use the iteration formula x_n + 1 = 6/(x_n² + 2) twice to find an estimate for the solution of x³ + 2x – 6 = 0
Give your answer correct to 4 decimal places.(3 marks)
Question 18 (4 marks)
Diagram: Quadrilateral ABCD with the midpoints E on AB, F on BC, G on CD and H on DA marked.
ABCD is a quadrilateral.
E, F, G and H are the midpoints of AB, BC, CD and DA.
overrightarrowAH = mathbfa overrightarrowAE = mathbfb overrightarrowDG = mathbfc
Prove, using vectors, that EFGH is a parallelogram.
(4 marks)
Question 19 (4 marks)
The functions f and g are such that
f(x) = (2x + 3)² and g(x) = 2x – 1
(a)
Find gf(-3)
(2 marks)
(b)
Find g⁻¹(x)
(2 marks)
Question 20 (4 marks)
Write
14/(3x – 21) + Big[(x + 4) ÷ (2x² – 6x – 56)/(2x + 3)Big]
in the form (ax + b)/(cx + d) where a, b, c and d are integers.
(4 marks)
Question 21 (4 marks)
Vicky has a collection of medals.
The Venn diagram gives information about the number of medals in her collection where
ℰ = {all medals}
A = {English medals}
B = {gold medals}Diagram: Venn diagram with sets A and B inside the universal set. Only A: 7x – 11. A and B: x. Only B: 5x – 3. Outside both circles: 34.
Vicky is going to take at random a medal from her collection.
Given that the medal is gold, the probability that the medal is English is 2/11
Work out the number of medals in Vicky’s collection.
(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.