Edexcel GCSE Higher June 2017 Paper 3 (calculator)
20 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 = {odd numbers less than 30}
A = {3, 9, 15, 21, 27}
B = {5, 15, 25}(a)
Complete the Venn diagram to represent this information.
Diagram: Venn diagram with sets and . Only : . Both: . Only : . Neither: .
(4 marks)
(b)
A number is chosen at random from the universal set, ℰ.
What is the probability that the number is in the set A ∪ B?
(2 marks)
Question 2 (3 marks)
Solve the simultaneous equations
3x + y = -4
3x – 4y = 6(3 marks)
Question 3 (2 marks)
The table shows some information about the dress sizes of 25 women.
Dress size Number of women 8 2 10 9 12 8 14 6 (a)
Find the median dress size.
(1 mark)
(b)
3 of the 25 women have a shoe size of 7
Zoe says that if you choose at random one of the 25 women, the probability that she has either a shoe size of 7 or a dress size of 14 is 9/25 because
3/25 + 6/25 = 9/25
Is Zoe correct?
You must give a reason for your answer.(1 mark)
Question 4 (5 marks)
Daniel bakes 420 cakes.
He bakes only vanilla cakes, banana cakes, lemon cakes and chocolate cakes.2/7 of the cakes are vanilla cakes.
35% of the cakes are banana cakes.
The ratio of the number of lemon cakes to the number of chocolate cakes is 4 : 5Work out the number of lemon cakes Daniel bakes.
(5 marks)
Question 5 (4 marks)
In the diagram, AB, BC and CD are three sides of a regular polygon P.
Diagram: Three sides AB, BC and CD of polygon P. A square stands on AB and another on CD, outside P. Below BC is a regular 12-sided polygon, which shares side BC with P.
Show that polygon P is a hexagon.
You must show your working.(4 marks)
Question 6 (4 marks)
The density of apple juice is 1.05 grams per cm³.
The density of fruit syrup is 1.4 grams per cm³.
The density of carbonated water is 0.99 grams per cm³.25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and
280 cm³ of carbonated water to make a drink with a volume of 320 cm³.Work out the density of the drink.
Give your answer correct to 2 decimal places.(4 marks)
Question 7 (2 marks)
ABC is a right-angled triangle.
Diagram: A right-angled triangle ABC. CB is horizontal, with C on the left, and A is straight below B. The right angle is at B. CA, the sloping side, is 15 cm. The angle at C is 23°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.(2 marks)
Question 8 (4 marks)
A square, with sides of length x cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.The area of the circle is 49 cm²
Work out the value of x.
Give your answer correct to 3 significant figures.(4 marks)
Question 9 (5 marks)
The box plot shows information about the distribution of the amounts of money spent by
some male students on their holidays.Diagram: A box plot grid with a money scale from £0 to £1000. Male students: smallest 20, lower quartile 150, median 250, upper quartile 330, largest 750. The Female row is empty.
(a)
Work out the interquartile range for the amounts of money spent by these male students.
(2 marks)
(b)
The table below shows information about the distribution of the amounts of money spent
by some female students on their holidays.Money spent (£) Smallest 60 Lower quartile 180 Median 300 Upper quartile 350 Largest 650 On the grid above, draw a box plot for the information in the table.
(2 marks)
(c)
Chris says,
“The box plots show that the female students spent more money than the male students.”
Is Chris correct?
Give a reason for your answer.(1 mark)
Question 10 (3 marks)
Naoby invests £6000 for 5 years.
The investment gets compound interest of x% per annum.
At the end of 5 years the investment is worth £8029.35Work out the value of x.
(3 marks)
Question 11 (2 marks)
Jeff is choosing a shrub and a rose tree for his garden.
At the garden centre there are 17 different types of shrubs and some rose trees.Jeff says,
“There are 215 different ways to choose one shrub and one rose tree.”
Could Jeff be correct?
You must show how you get your answer.(2 marks)
Question 12 (3 marks)
The points A, B, C and D lie in order on a straight line.
AB : BD = 1 : 5
AC : CD = 7 : 11
Work out AB : BC : CD
(3 marks)
Question 13 (4 marks)
Diagram: A grid with x from –7 to 7 and y from –4 to 4, with three straight lines: y = –2 (horizontal), a line through (0, 0) and (2, 2), and a less steep line through (–2, 0) and (0, 1). The shaded triangle has corners at (–6, –2), (–2, –2) and (2, 2).
Write down the three inequalities that define the shaded region.
(4 marks)
Question 14 (6 marks)
(a)
Simplify (x² – 16)/(2x² – 5x – 12)
(3 marks)
(b)
Make v the subject of the formula w = (15(t – 2v))/v
(3 marks)
Question 15 (5 marks)
Diagram: Triangle ABC. AB is along the bottom and is labelled (2x – 1) metres. BC is labelled (x + 3) metres. The angle at B, between AB and BC, is 45°.
The area of triangle ABC is 6√2 m².
Calculate the value of x.
Give your answer correct to 3 significant figures.(5 marks)
Question 16 (5 marks)
Using x_n + 1 = -2 – 4/(x_n²) with x_0 = -2.5
(a)
find the values of x_1, x_2 and x_3
(3 marks)
(b)
Explain the relationship between the values of x_1, x_2 and x_3 and the equation x³ + 2x² + 4 = 0
(2 marks)
Question 17 (5 marks)
A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.
Jake finds out that the track is 270 km long.
He assumes that the track has been measured correct to the nearest 10 km.(a)
Could the average speed of the train have been greater than 160 km/h?
You must show how you get your answer.(4 marks)
(b)
Jake’s assumption was wrong.
The track was measured correct to the nearest 5 km.Explain how this could affect your decision in part (a).
(1 mark)
Question 18 (5 marks)
Diagram: A circle with centre O. B is on the circle on the left. D is outside the circle on the right, joined to O by a dashed line. Lines from D touch the circle at A, at the top, and C, at the bottom. OA and OC are radii, each labelled 5 cm.
A, B and C are points on a circle of radius 5 cm, centre O.
DA and DC are tangents to the circle.
DO = 9 cmWork out the length of arc ABC.
Give your answer correct to 3 significant figures.(5 marks)
Question 19 (3 marks)
Solve 2x² + 3x – 2 > 0
(3 marks)
Question 20 (4 marks)
The equation of a curve is y = a^x
A is the point where the curve intersects the y-axis.(a)
State the coordinates of A.
(1 mark)
(b)
The equation of circle C is x² + y² = 16
The circle C is translated by the vector ( 3 , 0 ) to give circle B.
Draw a sketch of circle B.
Label with coordinates
the centre of circle B
and any points of intersection with the x-axis.(3 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.