Edexcel GCSE Higher June 2023 Paper 3 (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 (4 marks)
(a)
Simplify (m²)³
(1 mark)
(b)
Simplify x⁵ × x⁸
(1 mark)
(c)
Expand 4p(p² + 3p)
(2 marks)
Question 2 (5 marks)
Jonny wants to know how much coffee he will need for 800 people at a meeting.
Each person who drinks coffee will drink 2 cups of coffee.
10.6 g of coffee is needed for each cup of coffee.
Jonny assumes 68% of the people will drink coffee.(a)
Using this assumption, work out the amount of coffee Jonny needs.
Give your answer correct to the nearest gram.(4 marks)
(b)
Jonny’s assumption is wrong.
72% of the people will drink coffee.How does this affect your answer to part (a)?
(1 mark)
Question 3 (5 marks)
ACF and ADG are straight lines.
BCD and EFG are parallel lines.Diagram: A diagram.
Show that triangle ACD is isosceles.
Give a reason for each stage of your working.(5 marks)
Question 4 (2 marks)
It takes 14 hours for 5 identical pumps to fill a water tank.
How many hours would it take 4 of these pumps to fill another water tank of the same size?(2 marks)
Question 5 (3 marks)
A and B are numbers such that
A = 2² × 3⁴ × 7
B = 3² × 7²
(a)
Find the highest common factor (HCF) of A and B.
(1 mark)
(b)
Find the lowest common multiple (LCM) of A and B.
(2 marks)
Question 6 (3 marks)
Lava flows from a volcano at a constant rate of 11.9 m³/s
How many days does it take for 67 205 600 m³ of lava to flow from the volcano?
Give your answer correct to the nearest day.(3 marks)
Question 7 (2 marks)
Here is the graph of y = x² – 2x – 2
Diagram: The graph of y = x squared minus 2x minus 2, for x from –2 to 4.
(a)
Write down the coordinates of the turning point on the graph of y = x² – 2x – 2
(1 mark)
(b)
Write down an estimate for one of the roots of x² – 2x – 2 = 0
(1 mark)
Question 8 (2 marks)
A solid cuboid is made of metal.
The metal has a density of 9 g/cm³
The volume of the cuboid is 72 cm³Work out the mass of the cuboid.
(2 marks)
Question 9 (2 marks)
Some people were asked if they wanted a new television.
70% of the people said yes.
80% of the people who said yes wanted a television with a large screen.What percentage of the people asked said they wanted a television with a large screen?
(2 marks)
Question 10 (3 marks)
ABD is a triangle.
C is a point on BD.Diagram: A diagram.
Work out the length of DC.
Give your answer correct to 1 decimal place.(3 marks)
Question 11 (5 marks)
The table shows some information about the heights of a group of adults.
Height least height 169 cm greatest height 186 cm median 177 cm lower quartile 174 cm upper quartile 180 cm (a)
On the grid, draw a box plot for the information in the table.
Diagram: Adults: blank grid.
(3 marks)
(b)
The box plot below shows the distribution of the heights of a group of teenagers.
Diagram: Teenagers: lowest 157.5, lower quartile 165, median 169, upper quartile 171, highest 178.
Compare the distribution of the heights of the adults with the distribution of the heights of the teenagers.
(2 marks)
Question 12 (3 marks)
Show that (x – 1)(x + 3)(x – 5) can be written in the form ax³ + bx² + cx + d
where a, b, c and d are integers.(3 marks)
Question 13 (3 marks)
An expression for the nth term of the sequence of triangular numbers is (n(n + 1))/2
Prove that the sum of any two consecutive triangular numbers is a square number.
(3 marks)
Question 14 (4 marks)
OAB is a triangle.
OBC is a sector of a circle, centre O.Diagram: A diagram.
Calculate the area of OBC.
Give your answer correct to 3 significant figures.(4 marks)
Question 15 (3 marks)
(a)
Factorise a² – b²
(1 mark)
(b)
Show that 2⁴⁰ – 1 is the product of two consecutive odd numbers.
(2 marks)
Question 16 (2 marks)
Diagram: A graph.
On the grid, enlarge triangle T by scale factor -2 with centre of enlargement (–2, –2)
(2 marks)
Question 17 (4 marks)
Here is a distance-time graph.
Diagram: A curve starting at the origin and getting steeper: about 4 metres at 1 second, 14 at 2, 32 at 3 and 90 at 4 seconds.
(a)
Find an estimate of the gradient of the graph at time 2.5 seconds.
You must show how you get your answer.(3 marks)
(b)
What does the gradient of the graph represent?
(1 mark)
Question 18 (5 marks)
A solid frustum is made by removing a small cone from a large cone
as shown in the diagram.Diagram: A frustum: a cone with slant height 10 cm (marked from the apex to the base) and base radius 3 cm, with a small cone of slant height 6 cm (dashed) removed from the top.
Curved surface area of cone = π rl
Diagram: A cone with slant height l and base radius r.
The slant height of the small cone is 6 cm.
The slant height of the large cone is 10 cm.
The radius of the base of the large cone is 3 cm.Calculate the total surface area of the frustum.
Give your answer correct to 3 significant figures.(5 marks)
Question 19 (1 mark)
Sana needs to draw the graph of y = 3^x for 0 ≤ x ≤ 4
She draws the graph shown on the grid.
Diagram: A curve from the origin, rising more and more steeply through about (1, 3), (2, 9) and (3, 27) to (4, 81).
Write down one thing Sana has done wrong.
(1 mark)
Question 20 (3 marks)
Prove algebraically that 0.12̇3̇ can be written as 61/495
(3 marks)
Question 21 (4 marks)
Solve 1/(x + 4) + 3/(2 – 2x) = 1
(4 marks)
Question 22 (3 marks)
Given that the vector a( 2 , 6 ) + b( 8 , 2 ) is parallel to the vector ( 13 , 6 )
find an expression for b in terms of a.
(3 marks)
Question 23 (4 marks)
A circle has equation x² + y² = 25
The point P with coordinates (–3, 4) lies on the circle.Alex says that the tangent to the circle at P crosses the x-axis at the point (–8, 0)
Is Alex correct?
You must show how you get your answer.(4 marks)
Question 24 (5 marks)
There is a total of y counters in a box.
There are x pink counters and 5 blue counters in the box.
The rest of the counters are green.x : y = 1 : 3
Freda takes at random two counters from the box.
Find, in terms of x, an expression for the probability that Freda takes two counters of the same colour.
Give your answer as a fraction in the form (ax² + bx + c)/(dx² + ex) where a, b, c, d and e
are integers.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.