Edexcel GCSE Higher November 2017 Paper 2 (calculator)
23 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)
Solve 5x – 6 = 3(x – 1)
(3 marks)
Question 2 (3 marks)
Emily buys a pack of 12 bottles of water.
The pack costs £5.64Emily sells all 12 bottles for 50p each.
Work out Emily’s percentage profit.
Give your answer correct to 1 decimal place.(3 marks)
Question 3 (3 marks)
Hasmeet walks once round a circle with diameter 80 metres.
There are 8 points equally spaced on the circumference of the circle.
(a)
Diagram: A circle with 8 points marked on it by short lines across the circle, labelled A, B, C, D, E, F, G, H going clockwise from the top.
Find the distance Hasmeet walks between one point and the next point.
(2 marks)
(b)
Four of the points are moved, as shown in the diagram below.
Diagram: A circle with 8 points marked on it by short lines across the circle, labelled A, B, C, D, E, F, G, H going clockwise from the top.
Hasmeet walks once round the circle again.
Has the mean distance that Hasmeet walks between one point and the next point changed?
You must give a reason for your answer.(1 mark)
Question 4 (3 marks)
There are only blue cubes, yellow cubes and green cubes in a bag.
There are
twice as many blue cubes as yellow cubes
and four times as many green cubes as blue cubes.Hannah takes at random a cube from the bag.
Work out the probability that Hannah takes a yellow cube.
(3 marks)
Question 5 (2 marks)
Diagram: A coordinate grid with x and y from –7 to 7. Trapezium T has corners at (2, –1), (4, –1), (5, –2), (2, –2).
(a)
Rotate trapezium T 180° about the origin.
Label the new trapezium A.(1 mark)
(b)
Translate trapezium T by the vector ( -1 , -3 )
Label the new trapezium B.(1 mark)
Question 6 (4 marks)
(a)
p³ × p^x = p⁹
Find the value of x.
(1 mark)
(b)
(7²)^y = 7¹⁰
Find the value of y.
(1 mark)
(c)
100^a × 1000^b can be written in the form 10^w
Show that w = 2a + 3b
(2 marks)
Question 7 (5 marks)
ABCD is a trapezium.
Diagram: Trapezium ABCD with AD along the bottom and BC parallel to it, above. AD is 24 cm, BC is 10 cm and AB is 7.5 cm. A dashed line goes straight down from B to AD, at right angles to it, and is marked 6 cm.
Work out the size of angle CDA.
Give your answer correct to 1 decimal place.(5 marks)
Question 8 (3 marks)
Use your calculator to work out √((sin 25° + sin 40°)/(cos 25° – cos 40°))
(a)
Write down all the figures on your calculator display.
(2 marks)
(b)
Write your answer to part (a) correct to 2 decimal places.
(1 mark)
Question 9 (3 marks)
Yesterday it took 5 cleaners 41/2 hours to clean all the rooms in a hotel.
There are only 3 cleaners to clean all the rooms in the hotel today.
Each cleaner is paid £8.20 for each hour or part of an hour they work.
How much will each cleaner be paid today?
(3 marks)
Question 10 (3 marks)
Here is part of a distance-time graph for a car’s journey.
Diagram: A distance-time graph: time in seconds across, from 0 to 90; distance in metres up, from 0 to 700. Straight lines join (0 s, 0 m), (20 s, 360 m), (60 s, 560 m), (80 s, 560 m).
(a)
Between which two times does the car travel at its greatest speed?
Give a reason for your answer.(2 marks)
(b)
Work out this greatest speed.
(1 mark)
Question 11 (3 marks)
The pie charts give information about the ages, in years, of people living in two towns, Adley and Bridford.
Diagram: Two pie charts drawn to the same scale. Adley (radius 5 units): 0 – 19 70°, 20 – 39 65°, 40 – 59 115°, 60 – 79 90°, 80+ 20°. Bridford (radius 4 units): 0 – 19 60°, 20 – 39 75°, 40 – 59 80°, 60 – 79 120°, 80+ 25°.
Diagrams accurately drawn
The ratio of the number of people living in Adley to the number of people living in Bridford is given by the ratio of the areas of the pie charts.
What proportion of the total number of people living in these two towns live in Adley and are aged 0 – 19?
Give your answer correct to 3 significant figures.(3 marks)
Question 12 (3 marks)
Diagram: Two sides RS and ST of a regular 12-sided polygon meeting at S, with ST going right from S and RS going down to the left. A dashed line joins R and T.
RS and ST are 2 sides of a regular 12-sided polygon.
RT is a diagonal of the polygon.Work out the size of angle STR.
You must show your working.(3 marks)
Question 13 (5 marks)
At the beginning of 2009, Mr Veale bought a company.
The value of the company was £50 000Each year the value of the company increased by 2%.
(a)
Calculate the value of the company at the beginning of 2017
Give your answer correct to the nearest £100(2 marks)
(b)
At the beginning of 2009 the value of a different company was £250 000
In 6 years the value of this company increased to £325 000This is equivalent to an increase of x% each year.
Find the value of x.
Give your answer correct to 2 significant figures.(3 marks)
Question 14 (3 marks)
On the grid, shade the region that satisfies all these inequalities.
y > 1 x + y < 5 y > 2x
Label the region R.
Diagram: A graph.
(3 marks)
Question 15 (3 marks)
Tracey is going to choose a main course and a dessert in a cafe.
She can choose from 8 main courses and 7 desserts.Tracey says that to work out the number of different ways of choosing a main course and a dessert you add 8 and 7
(a)
Is Tracey correct?
You must give a reason for your answer.(1 mark)
(b)
12 teams play in a competition.
Each team plays each other team exactly once.Work out the total number of games played.
(2 marks)
Question 16 (2 marks)
Solve (x – 2)² = 3
Give your solutions correct to 3 significant figures.
(2 marks)
Question 17 (5 marks)
The table gives information about the heights of 150 students.
Height (h cm) Frequency 140 < h ≤ 150 15 150 < h ≤ 155 30 155 < h ≤ 160 51 160 < h ≤ 165 36 165 < h ≤ 180 18 (a)
On the grid, draw a histogram for this information.
Diagram: A blank grid with a horizontal and a vertical axis. There are no labels and no scale.
(3 marks)
(b)
Work out an estimate for the fraction of the students who have a height between
150 cm and 170 cm.(2 marks)
Question 18 (1 mark)
At time t = 0 hours a tank is full of water.
Water leaks from the tank.
At the end of every hour there is 2% less water in the tank than at the start of the hour.The volume of water, in litres, in the tank at time t hours is V_t
Given that
V_0 = 2000
V_t + 1 = kV_twrite down the value of k.
(1 mark)
Question 19 (4 marks)
A triangle has vertices P, Q and R.
The coordinates of P are (-3, -6)
The coordinates of Q are (1, 4)
The coordinates of R are (5, -2)M is the midpoint of PQ.
N is the midpoint of QR.Prove that MN is parallel to PR.
You must show each stage of your working.(4 marks)
Question 20 (5 marks)
Diagram: Sector OAC with centre O at the bottom, radius 10 m and angle 120° at O. A is on the left and C on the right. Lines from A and from C meet at B above the arc. The region between the arc AC and the lines AB and BC is shaded.
OAC is a sector of a circle, centre O, radius 10 m.
BA is the tangent to the circle at point A.
BC is the tangent to the circle at point C.Angle AOC = 120°
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.(5 marks)
Question 21 (4 marks)
There are 12 counters in a bag.
There is an equal number of red counters, blue counters and yellow counters in the bag.
There are no other counters in the bag.3 counters are taken at random from the bag.
(a)
Work out the probability of taking 3 red counters.
(2 marks)
(b)
The 3 counters are put back into the bag.
Some more counters are now put into the bag.
There is still an equal number of red counters, blue counters and yellow counters in the bag.
There are no counters of any other colour in the bag.3 counters are taken at random from the bag.
Is it now less likely or equally likely or more likely that the 3 counters will be red?
You must show how you get your answer.(2 marks)
Question 22 (5 marks)
The functions f and g are such that
f(x) = 5x + 3 g(x) = ax + b where a and b are constants.
g(3) = 20 and f⁻¹(33) = g(1)
Find the value of a and the value of b.
(5 marks)
Question 23 (5 marks)
S is a geometric sequence.
(a)
Given that (√x – 1), 1 and (√x + 1) are the first three terms of S, find the value of x.
You must show all your working.(3 marks)
(b)
Show that the 5th term of S is 7 + 5√2
(2 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.