Edexcel GCSE Higher June 2018 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 (5 marks)
(a)
Simplify m³ × m⁴
(1 mark)
(b)
Simplify (5np³)³
(2 marks)
(c)
Simplify (32q⁹r⁴)/(4q³r)
(2 marks)
Question 2 (3 marks)
(a)
Find the lowest common multiple (LCM) of 40 and 56
(2 marks)
(b)
A = 2³ × 3 × 5 B = 2² × 3 × 5²
Write down the highest common factor (HCF) of A and B.
(1 mark)
Question 3 (3 marks)
The line L is shown on the grid.
Diagram: A straight line L on a grid, x from –1 to 5 and y from –7 to 2. It goes from (–0.333333333, –6.999999999) up to (2.666666667, 2.000000001), crossing the y-axis at –6.
Find an equation for L.
(3 marks)
Question 4 (5 marks)
Raya buys a van for £8500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £531.25 each month.Find the ratio of the deposit Raya pays to the total of the 12 equal payments.
Give your answer in its simplest form.(5 marks)
Question 5 (6 marks)
(a)
Complete the table of values for y = x² – x – 6
x –3 –2 –1 0 1 2 3 y 6 –6 (2 marks)
(b)
On the grid, draw the graph of y = x² – x – 6 for values of x from –3 to 3
Diagram: A graph.
(2 marks)
(c)
Use your graph to find estimates of the solutions to the equation x² – x – 6 = -2
(2 marks)
Question 6 (3 marks)
A force of 70 newtons acts on an area of 20 cm²
pressure = dfracforcearea The force is increased by 10 newtons.
The area is increased by 10 cm²Helen says,
“The pressure decreases by less than 20%”
Is Helen correct?
You must show how you get your answer.(3 marks)
Question 7 (2 marks)
Diagram: A grid with x from 0 to 8 and y from 0 to 11. Shape A has corners (3, 4), (3, 10), (6, 10) and (6, 7). A cross marks the point (0, 1).
Enlarge shape A by scale factor 1/3 centre (0, 1)
(2 marks)
Question 8 (4 marks)
60 people were asked if they prefer to go on holiday in Britain or in Spain or in Italy.
38 of the people were male.
11 of the 32 people who said Britain were female.
8 males said Italy.
12 people said Spain.One of the females is chosen at random.
What is the probability that this female said Spain?
(4 marks)
Question 9 (4 marks)
Jean invests £12 000 in an account paying compound interest for 2 years.
In the first year the rate of interest is x%
At the end of the first year the value of Jean’s investment is £12 336In the second year the rate of interest is x/2%
What is the value of Jean’s investment at the end of 2 years?
(4 marks)
Question 10 (3 marks)
The vector a and the vector b are shown on the grid.
Diagram: A grid with x from 0 to 9 and y from 0 to 7. Vector a is an arrow from (3, 4) to (4, 6). Vector b is an arrow from (7, 7) to (8, 4).
(a)
On the grid, draw and label vector –2a
(1 mark)
(b)
Work out mathbfa + 2mathbfb as a column vector.
(2 marks)
Question 11 (3 marks)
f and g are functions such that
f(x) = 2/(x²) and g(x) = 4x³
(a)
Find f(–5)
(1 mark)
(b)
Find fg(1)
(2 marks)
Question 12 (2 marks)
Graph A
Diagram: Graph A: a curve starting at O, rising steeply then more and more slowly.
Graph B
Diagram: Graph B: a straight line through O, sloping up.
Graph C
Diagram: Graph C: a curve falling from top left to bottom right, getting closer to the axes but never touching them.
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 letter y propto x y propto x² y propto √x y propto 1/x (2 marks)
Question 13 (4 marks)
Diagram: A circle with centre O. B is on the left, C at the top, D at the lower right and A at the bottom left. The quadrilateral ABCD is drawn with the diagonal BD, and the radius OD. FDE is a straight line touching the circle at D, with E up to the right and F down to the left. Angle BAD is marked y° and angle ODB is marked x°.
A, B, C and D are points on the circumference of a circle, centre O.
FDE is a tangent to the circle.(a)
Show that y – x = 90
You must give a reason for each stage of your working.(3 marks)
(b)
Dylan was asked to give some possible values for x and y.
He said,
“y could be 200 and x could be 110, because 200 – 110 = 90”
Is Dylan correct?
You must give a reason for your answer.(1 mark)
Question 14 (3 marks)
The distance-time graph shows information about part of a car journey.
Diagram: A distance-time graph. Time from 0 to 8 seconds across, distance travelled from 0 to 160 metres up. The graph is a straight line from (0, 0) to (4, 20), then curves upwards more and more steeply, through about (5, 30), (6, 52) and (7, 100), reaching 160 metres just before 8 seconds.
Use the graph to estimate the speed of the car at time 5 seconds.
(3 marks)
Question 15 (5 marks)
A darts team is going to play a match on Saturday and on Sunday.
The probability that the team will win on Saturday is 0.45If they win on Saturday, the probability that they will win on Sunday is 0.67
If they do not win on Saturday, the probability that they will win on Sunday is 0.35(a)
Complete the probability tree diagram.
Diagram: A probability tree diagram. The first branches are for Saturday: win (0.45) and not win (blank). After each, branches for Sunday: win (blank) and not win (blank) after a win; win (blank) and not win (blank) after not a win.
(2 marks)
(b)
Find the probability that the team will win exactly one of the two matches.
(3 marks)
Question 16 (5 marks)
(a)
On the grid, draw the graph of x² + y² = 12.25
Diagram: A blank grid, x and y each from –7 to 7.
(2 marks)
(b)
Hence find estimates for the solutions of the simultaneous equations
x² + y² = 12.25
2x + y = 1(3 marks)
Question 17 (4 marks)
The histogram shows information about the times taken by some students to finish a puzzle.
Diagram: A histogram. Time taken (t minutes) across from 0 to 60, frequency density up from 0 to 1. Bars: 0 to 5 at height 0.8, 5 to 15 at height 0.4, 15 to 25 at height 0.6, 25 to 30 at height 1, 30 to 50 at height 0.2.
(a)
Complete the frequency table for this information.
Time taken (t minutes) Frequency 0 < t ≤ 5 4 5 < t ≤ 15 15 < t ≤ 25 25 < t ≤ 30 30 < t ≤ 50 (2 marks)
(b)
Find an estimate for the lower quartile of the times taken to finish the puzzle.
(2 marks)
Question 18 (4 marks)
ABCDEFGH is a cuboid.
Diagram: A cuboid ABCDEFGH. ABCD is the base: A at the back left, B at the back right, C at the front right and D at the front left. F, G, H and E are above A, B, C and D. The edges AB, BC and BG are hidden (dashed).
AB = 7.3 cm
CH = 8.1 cm
Angle BCA = 48°Find the size of the angle between AH and the plane ABCD.
Give your answer correct to 1 decimal place.(4 marks)
Question 19 (5 marks)
Shape S is one quarter of a solid sphere, centre O.
Shape S
Diagram: Shape S: a quarter of a sphere. Its two flat faces are half circles that meet along a diameter through the centre O; the rest of its surface is curved.
Diagram: A sphere with its centre marked and a radius r drawn from the centre to the surface.
Volume of sphere = 4/3π r³
Surface area of sphere = 4π r²The volume of S is 576π cm³
Find the surface area of S.
Give your answer correct to 3 significant figures.
You must show your working.(5 marks)
Question 20 (2 marks)
(a)
Martin did this question.
Rationalise the denominator of dfrac142 + √3
Here is how he answered the question.
dfrac142 + √3 = dfrac14 × (2 – √3)(2 + √3)(2 – √3) = dfrac28 – 14√34 + 2√3 – 2√3 + 3
= dfrac28 – 14√37 = 4 – 2√3Martin’s answer is wrong. Find Martin’s mistake.
(1 mark)
(b)
Sian did this question.
Rationalise the denominator of dfrac5√12
Here is how she answered the question.
dfrac5√12 = dfrac5√12√12 × √12 = dfrac5 × 3√212 = dfrac5√24
Sian’s answer is wrong. Find Sian’s mistake.
(1 mark)
Question 21 (5 marks)
Jackson is trying to find the density, in g/cm³, of a block of wood.
The block of wood is in the shape of a cuboid.He measures
the length as 13.2 cm, correct to the nearest mm
the width as 16.0 cm, correct to the nearest mm
the height as 21.7 cm, correct to the nearest mmHe measures the mass as 1970 g, correct to the nearest 5 g.
By considering bounds, work out the density of the wood.
Give your answer to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.