Edexcel GCSE Higher November 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 (6 marks)
ℰ = {even numbers between 1 and 25}
A = {2, 8, 10, 14}
B = {6, 8, 20}
C = {8, 18, 20, 22}(a)
Complete the Venn diagram for this information.
Diagram: A blank Venn diagram: three overlapping circles A, B, C inside a rectangle labelled ℰ.
(4 marks)
(b)
A number is chosen at random from ℰ.
Find the probability that the number is a member of A ∩ B.
(2 marks)
Question 2 (2 marks)
Sean has information about the height, in cm, and the weight, in kg, of each of ten rugby players.
He is asked to draw a scatter graph and a line of best fit for this information.
Here is his answer.
Diagram: A scatter graph of Weight (kg) against Height (cm). Along the bottom the labels are 140, 160, 170, 180, 190, 200, equally spaced. Up the side: 85, 90, 95, 100, 105. Ten crosses, at (175, 89), (179, 93), (179, 88), (183, 96), (184, 93), (185, 99), (186, 100), (190, 102), (191, 103), (192, 100). A straight line is drawn from the bottom left corner (140, 85) to the top right corner (200, 105).
Sean has plotted the points accurately.
Write down two things that are wrong with his answer.
(2 marks)
Question 3 (4 marks)
BEG is a triangle.
Diagram: Two parallel lines, ABC above and DEF below, both marked with arrows and rising slightly to the right. B is on the upper line and E is on the lower line. Triangle BEG has G to the right, between the lines. Angle CBG is 35°, angle BED is 110°, angle GEF is 25°, and angle BGE is marked x.
ABC and DEF are parallel lines.
Work out the size of angle x.
Give a reason for each stage of your working.(4 marks)
Question 4 (5 marks)
Northern Bank has two types of account.
Both accounts pay compound interest.Cash savings account Shares account Interest
2.5% per annumInterest
3.5% per annumAli invests £2000 in the cash savings account.
Ben invests £1600 in the shares account.(a)
Work out who will get the most interest by the end of 3 years.
You must show all your working.(4 marks)
(b)
In the 3rd year the rate of interest for the shares account is changed to 4% per annum.
Does this affect who will get the most interest by the end of 3 years?
Give a reason for your answer.(1 mark)
Question 5 (5 marks)
The diagram shows a floor in the shape of a trapezium.
Diagram: A trapezium. Its parallel sides are 10 m (top) and 16 m (bottom), and an arrow between them shows the height, 7 m.
£16.99
Diagram: A tin of paint, labelled 5 litres.
John is going to paint the floor.
Each 5 litre tin of paint costs £16.99
1 litre of paint covers an area of 2 m²John has £160 to spend on paint.
Has John got enough money to buy all the paint he needs?
You must show how you get your answer.(5 marks)
Question 6 (3 marks)
A is the point with coordinates (5, 9)
B is the point with coordinates (d, 15)The gradient of the line AB is 3
Work out the value of d.
(3 marks)
Question 7 (3 marks)
(a)
Write the number 0.000 086 23 in standard form.
(1 mark)
(b)
Work out dfrac3.2 × 10³ + 5.1 × 10⁻² 4.3 × 10⁻⁴
Give your answer in standard form, correct to 3 significant figures.
(2 marks)
Question 8 (3 marks)
Diagram: A grid with x and y from –6 to 6. Triangle P has corners (–1, 3), (3, 3) and (3, 5).
Triangle P is reflected in the line y = -x to give triangle Q.
Triangle Q is reflected in the line x = -1 to give triangle R.Describe fully the single transformation that maps triangle R to triangle P.
(3 marks)
Question 9 (2 marks)
Martin truncates the number N to 1 digit.
The result is 7Write down the error interval for N.
(2 marks)
Question 10 (5 marks)
Robert makes 50 litres of green paint by mixing litres of yellow paint and litres of
blue paint in the ratio 2 : 3Yellow paint is sold in 5 litre tins.
Each tin of yellow paint costs £26
Blue paint is sold in 10 litre tins.
Each tin of blue paint costs £48Robert sells all the green paint he makes in 10 litre tins.
He sells each tin of green paint for £66.96Work out Robert’s percentage profit on each tin of green paint he sells.
(5 marks)
Question 11 (3 marks)
In a restaurant there are
9 starter dishes
15 main dishes
8 dessert dishesJanet is going to choose one of the following combinations for her meal.
a starter dish and a main dish
or a main dish and a dessert dish
or a starter dish, a main dish and a dessert dish
Show that there are 1335 different ways to choose the meal.
(3 marks)
Question 12 (6 marks)
(a)
Write (4x² – 9)/(6x + 9) × 2x/(x² – 3x) in the form (ax + b)/(cx + d) where a, b, c and d are integers.
(3 marks)
(b)
Express 3/(x + 1) + 1/(x – 2) – 4/x as a single fraction in its simplest form.
(3 marks)
Question 13 (3 marks)
The diagram shows a circle and an equilateral triangle.
One side of the equilateral triangle is a diameter of the circle.
The circle has a circumference of 44 cm.Diagram: A circle with its centre marked. An equilateral triangle stands on a diameter of the circle, with its top corner outside the circle.
Work out the area of the triangle.
Give your answer correct to 3 significant figures.(3 marks)
Question 14 (2 marks)
On the grid, sketch the curve with equation y = 2^x
Give the coordinates of any points of intersection with the axes.Diagram: A pair of axes, x and y, crossing at O. There is no scale.
(2 marks)
Question 15 (1 mark)
The equation of a circle is x² + y² = 42.25
Find the radius of the circle.
(1 mark)
Question 16 (4 marks)
There are only red counters and blue counters in a bag.
Joe takes at random a counter from the bag.
The probability that the counter is red is 0.65
Joe puts the counter back into the bag.Mary takes at random a counter from the bag.
She puts the counter back into the bag.(a)
What is the probability that Joe and Mary take counters of different colours?
(2 marks)
(b)
There are 78 red counters in the bag.
How many blue counters are there in the bag?
(2 marks)
Question 17 (5 marks)
p and q are two numbers such that p > q
When you subtract 5 from p and subtract 5 from q the answers are in the ratio 5 : 1
When you add 20 to p and add 20 to q the answers are in the ratio 5 : 2Find the ratio p : q
Give your answer in its simplest form.(5 marks)
Question 18 (4 marks)
The straight line mathbfL_1 passes through the points with coordinates (4, 6) and (12, 2)
The straight line mathbfL_2 passes through the origin and has gradient –3The lines mathbfL_1 and mathbfL_2 intersect at point P.
Find the coordinates of P.
(4 marks)
Question 19 (5 marks)
Solve 22 < (m² + 7)/4 < 32
Show all your working.
(5 marks)
Question 20 (5 marks)
Here is a frustum of a cone.
Diagram: A solid cone of height 6.4 cm and base diameter 7.2 cm. A small cone of height 3.2 cm (dashed) is removed from the top, leaving a frustum. Heights 3.2 cm and 3.2 cm are marked on the right.
Volume of sphere = 4/3π r³ Volume of cone = 1/3π r² h
The diagram shows that the frustum is made by removing a cone with height 3.2 cm from
a solid cone with height 6.4 cm and base diameter 7.2 cm.The frustum is joined to a solid hemisphere of diameter 7.2 cm to form the solid S shown
below.Diagram: Solid S: the frustum, height 3.2 cm, standing on a hemisphere of diameter 7.2 cm.
The density of the frustum is 2.4 g/cm³
The density of the hemisphere is 4.8 g/cm³Calculate the average density of solid S.
(5 marks)
Question 21 (4 marks)
Diagram: Two circles crossing at A and R. The first has centre O and passes through A, B, R and P, with AOB a diameter. The second passes through A, O, R and C. CPA, CRB and AOB are straight lines.
A, B, R and P are four points on a circle with centre O.
A, O, R and C are four points on a different circle.
The two circles intersect at the points A and R.CPA, CRB and AOB are straight lines.
Prove that angle CAB = angle ABC.
(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.