Edexcel GCSE Higher November 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)
Use your calculator to work out the value of
√((208.3 – 15.7)/(5.694 + 1.8²))
Write down all the digits on your calculator display.
(2 marks)
Question 2 (3 marks)
The scatter graph shows information about some ships.
It shows the length and the width of each ship.Diagram: A scatter graph of width (m) against length (m) for 13 ships, lengths from 120 to 240 m and widths from 10 to 35 m. The crosses go up from bottom left to top right.
(a)
What type of correlation does this scatter graph show?
(1 mark)
(b)
Draw a line of best fit on the scatter graph.
(1 mark)
(c)
A different ship has a length of 194 metres.
Use your line of best fit to find an estimate for the width of this ship.
(1 mark)
Question 3 (3 marks)
London Zurich Choci bar Choci bar 200 g 360 g £3.50 7.20 Swiss francs In London, a 200 g Choci bar costs £3.50
In Zurich, a 360 g Choci bar costs 7.20 Swiss francs.The exchange rate is £1 = 1.25 Swiss francs.
In which city is the Choci bar the better value for money, in London or in Zurich?
You must show how you get your answer.(3 marks)
Question 4 (2 marks)
ℰ = {odd numbers between 0 and 20}
A = {3, 9, 15, 17}
B = {5, 7, 11, 13, 17, 19}Tom was asked to draw a Venn diagram for this information.
Here is his answer.Diagram: Tom’s Venn diagram: a rectangle for ℰ with two overlapping circles, A and B. Only in A: 3, 9, 15, 17. In both: 17. Only in B: 5, 7, 11, 13, 19. Nothing is written outside the circles.
Write down two things Tom should do to make his answer fully correct.
(2 marks)
Question 5 (4 marks)
(a)
Complete the table of values for y = x² – 2x – 3
x –2 –1 0 1 2 3 4 y 0 –3 (2 marks)
(b)
On the grid, draw the graph of y = x² – 2x – 3 for values of x from –2 to 4
Diagram: A grid with x from –2 to 4 and y from –5 to 6.
(2 marks)
Question 6 (4 marks)
The cost of a first class stamp increased from 76p to 85p.
The cost of a second class stamp increased from 65p to 66p.Filip says,
“The percentage increase in the cost of a first class stamp is more than 7 times
the percentage increase in the cost of a second class stamp.”Is Filip correct?
You must show all your working.(4 marks)
Question 7 (5 marks)
The diagram shows triangle ABC.
Diagram: Triangle ABC with AB across the bottom and C at the top. AC is labelled 2x + 11, BC is labelled 4x – 4 and AB is labelled 2x + 5. AC and BC are marked as equal.
In the diagram, all measurements are in centimetres.
AC = BC
The perimeter of the triangle is 72 cm.
Work out the area of the triangle.
(5 marks)
Question 8 (2 marks)
1.25 × 10⁻¹² = k × (4 × 10⁻²⁰)
Work out the value of k.
Give your answer in standard form.(2 marks)
Question 9 (3 marks)
The diagram shows two congruent regular 9-sided polygons.
ABCD is a quadrilateral.Diagram: Two congruent regular 9-sided polygons side by side, sharing one edge. B is the top end of the shared edge. A is the next corner of the left polygon after B and C is the next corner of the right polygon after B. ABCD is a quadrilateral above B, with D at the top.
Show that ABCD is not a square.
(3 marks)
Question 10 (4 marks)
Use algebra to solve the simultaneous equations
4x – 5y = 20
6x + 7y = -57You must show all your working.
(4 marks)
Question 11 (2 marks)
Diagram: A grid with x from –6 to 7 and y from –4 to 8. Triangle A has corners (2, 7), (5, 7), (5, 1). Triangle B has corners (0, 4), (2, 4), (2, 0).
Describe fully the single transformation that maps triangle A onto triangle B.
(2 marks)
Question 12 (5 marks)
The diagram shows a solid cylinder with base radius 3 cm and height 8 cm.
It also shows a solid cube with side length h cm.Diagram: A solid cylinder with base radius 3 cm and height 8 cm, and a solid cube with side length h cm.
The cylinder is made from steel with a density of 7.86 g/cm³
The cube is made from brass with a density of 8.5 g/cm³The mass of the cylinder is equal to the mass of the cube.
Work out the value of h.
Give your answer correct to 1 decimal place.(5 marks)
Question 13 (5 marks)
Here is a table of values of x and y.
x 2 4 6 8 y 0 4 8 12 Nadia says that y is directly proportional to x because the value of y increases by 4 as
the value of x increases by 2(a)
Is Nadia correct?
You must give a reason for your answer.(1 mark)
(b)(i)
w is directly proportional to the square root of t.
w = 140 when t = 64
Calculate the value of w when t = 7.84
(3 marks)
(ii)
On the axes below, sketch a graph to show the relationship between w and t.
Diagram: Empty axes: w up, t across, origin O.
(1 mark)
Question 14 (2 marks)
There are 10 football teams in a league.
Each team plays every other team 4 times.Work out the total number of games played.
(2 marks)
Question 15 (6 marks)
(a)
Here are the first five terms of a quadratic sequence.
3 20 47 84 131
Find an expression, in terms of n, for the nth term of this sequence.
(3 marks)
(b)
The terms of a different sequence are given by the rule u_n + 1 = ku_n + k where k is
a constant.Given that u_1 = 9 and u_2 = 4
find the value of u_4
(3 marks)
Question 16 (4 marks)
The histogram gives information about the distances that 60 teachers travelled to school
on Monday.
The histogram is incomplete.Diagram: An incomplete histogram of the distances teachers travelled to school. Bars: 0 to 5 miles, frequency density 2.2; 10 to 20 miles, frequency density 1.5; 30 to 50 miles, frequency density 0.3.
11 of the teachers travelled between 0 miles and 5 miles.
None of the teachers travelled a distance greater than 50 miles.The number of teachers who travelled between 5 miles and 10 miles is the same as the
number of teachers who travelled between 20 miles and 30 miles.Complete the histogram.
(4 marks)
Question 17 (3 marks)
Show that (6x – y)/10xy + 1/2x – (2y – 7x)/5xy simplifies to k/y where k is an integer.
(3 marks)
Question 18 (3 marks)
A, B and C are three points on a circle, centre O.
Diagram: A circle with centre O, marked with a dot. A, B and C are on the circle, with the chords BA and BC drawn.
BA = BC
Prove that OB bisects angle ABC.
(3 marks)
Question 19 (5 marks)
T = w/(a – c)
w = 435 correct to the nearest 5
a = 9.8 correct to 2 significant figures.
c = 2.5 correct to 2 significant figures.By considering bounds, calculate the value of T to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer.(5 marks)
Question 20 (3 marks)
VABC is a solid pyramid.
ABC is an equilateral triangle.Diagram: A triangular pyramid VABC with V at the top. The base ABC is an equilateral triangle: A at the front left, B at the front right and C at the back. AC is a hidden edge, drawn dashed. M is the midpoint of AB, and a dotted line joins M to C. F is a point marked on MC, directly below V.
M is the midpoint of AB.
F is the point on MC such that MF : FC = 1 : 2The vertex V is vertically above F.
VA = VB = VCVF = 8 cm Angle VCM = 52°
Work out the side length of the equilateral triangle ABC.
Give your answer correct to 1 decimal place.(3 marks)
Question 21 (5 marks)
The point P has coordinates (–4, 5)
The point Q has coordinates (6, –6)
The point R has coordinates (k, k + 3)Given that angle PRQ is a right angle,
find the possible values of k.
You must show all your working.(5 marks)
Question 22 (5 marks)
There are only red counters and yellow counters in a box.
3/5 of the counters are red.Sophie takes at random two counters from the box.
The probability that the two counters are the same colour is 41/80
Work out the number of yellow counters in the box.
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.