Edexcel GCSE Higher June 2019 Paper 3 (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 (5 marks)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 5, 6, 8, 9}
B = {2, 6, 9}(a)
Diagram: A blank Venn diagram: two overlapping circles, A and B, inside a rectangle labelled ℰ.
Complete the Venn diagram to represent this information.
(3 marks)
(b)
A number is chosen at random from the universal set ℰ.
Find the probability that the number is in the set A ∩ B
(2 marks)
Question 2 (3 marks)
Katy invests £200 000 in a savings account for 4 years.
The account pays compound interest at a rate of 1.5% per annum.
Calculate the total amount of interest Katy will get at the end of 4 years.
(3 marks)
Question 3 (3 marks)
The table shows information about the heights of 80 plants.
Height (h cm) Frequency 10 < h ≤ 20 7 20 < h ≤ 30 13 30 < h ≤ 40 14 40 < h ≤ 50 12 50 < h ≤ 60 16 60 < h ≤ 70 18 (a)
Find the class interval that contains the median.
(1 mark)
(b)
On the grid, draw a frequency polygon for the information in the table.
Diagram: A blank grid. Height (h cm) from 0 to 70 across, frequency from 0 to 20 up.
(2 marks)
Question 4 (2 marks)
Sean has drawn a time series graph to show the numbers, in thousands, of visitors to a
fun park.Diagram: A time series graph of the number of visitors to a fun park, in thousands. Across: 2016 quarters 2, 3, 4; 2017 quarters 2, 3, 4; 2018 quarters 2, 3, 4 (no quarter 1 is labelled). Up the side the scale is labelled 6, 6.5, 7, 7.5, 8, 8.5, 9, 10, equally spaced. Crosses at 10.2, 8, 8.4, 9.8, 7, 8, 8.9, 7 thousand are joined with a smooth curve.
Write down two things that are wrong or could be misleading with this graph.
(2 marks)
Question 5 (4 marks)
The diagram shows a hexagon.
The hexagon has one line of symmetry.Diagram: Hexagon ABCDEF with AB at the top and ED at the bottom, wider than AB. FA and BC are marked equal with one dash, EF and CD with two dashes. Angle ABC is marked 117°.
FA = BC
EF = CD
Angle ABC = 117°Angle BCD = 2 × angle CDE
Work out the size of angle AFE.
You must show all your working.(4 marks)
Question 6 (5 marks)
Jeremy has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a bottom.
The tank has a diameter of 1.6 m and a height of 1.8 m.Diagram: A cylinder standing on one end. An arrow across the top shows the diameter, 1.6 m; an arrow down the right side shows the height, 1.8 m.
Jeremy has 7 tins of paint.
Each tin of paint covers 5 m²Has Jeremy got enough paint to cover completely the 3 tanks?
You must show how you get your answer.(5 marks)
Question 7 (2 marks)
Work out √((2.5 × sin 43°)/(8.2² – 50.5))
Give your answer correct to 3 significant figures.
(2 marks)
Question 8 (2 marks)
(a)
ABC is a right-angled triangle.
Diagram: Right-angled triangle ABC with the right angle at B. B is at the top, A is down to the left and C is further down to the right. AB is 6 cm and AC, the longest side, is 8 cm.
Here is Sarah’s method to find the length of BC.
BC² = AB² + AC²
phantomBC² = 6² + 8²
phantomBC² = 100
BC = 10What mistake has Sarah made in her method?
(1 mark)
(b)
Diagram: A squared grid. Point C is marked. Triangle PQR has P 2 right and 4 up from C, Q 4 right and 4 up from C, R 4 right and 0 up from C. Triangle XYZ has X 5 right and 10 up from C, Y 10 right and 10 up from C, Z 10 right and 0 up from C. Dashed lines join C to X, Y, Z.
Roy is going to enlarge triangle PQR with centre C and scale factor 11/2
He draws triangle XYZ.Explain why Roy’s diagram is not correct.
(1 mark)
Question 9 (3 marks)
A company has to make a large number of boxes.
The company has 6 machines.
All the machines work at the same rate.
When all the machines are working, they can make all the boxes in 9 days.The table gives the number of machines working each day.
day 1 day 2 day 3 all other days Number of machines working 3 4 5 6 Work out the total number of days taken to make all the boxes.
(3 marks)
Question 10 (3 marks)
Marie invests £8000 in an account for one year.
At the end of the year, interest is added to her account.Marie pays tax on this interest at a rate of 20%
She pays £28.80 tax.Work out the percentage interest rate for the account.
(3 marks)
Question 11 (3 marks)
In May 2019, the distance between Earth and Mars was 3.9 × 10⁷ km.
In May 2019, a signal was sent from Earth to Mars.
Assuming that the signal sent from Earth to Mars travelled at a speed of 3 × 10⁵ km per second,(a)
how long did the signal take to get to Mars?
(2 marks)
(b)
The speed of the signal sent from Earth to Mars in May 2019 was actually less than
3 × 10⁵ km per second.How will this affect your answer to part (a)?
(1 mark)
Question 12 (1 mark)
Patrick has to work out the exact value of 64^(1/4)
Patrick says,
“1/4 of 64 is 16 so 64^(1/4) = 16”
Explain what is wrong with what Patrick says.
(1 mark)
Question 13 (4 marks)
The density of ethanol is 1.09 g/cm³
The density of propylene is 0.97 g/cm³60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze.
Work out the density of the antifreeze.
Give your answer correct to 2 decimal places.(4 marks)
Question 14 (4 marks)
The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD.
Diagram: Rectangle ABDE with AB along the top and AE down the left side. Triangle AFE is on the left side, with F to the left, and triangle BCD is on the right side, with C to the right. AF and BC are 24 cm. Angle FAE and angle CBD are 30°.
area of rectangle ABDE = area of triangle AFE + area of triangle BCD
AB : AE = 1 : 3
Work out the length of AE.
(4 marks)
Question 15 (2 marks)
The graph of the curve C with equation y = f(x) is transformed to give the graph of
the curve S with equation y = f(-x) – 3The point on C with coordinates (7, 2) is mapped to the point Q on S.
Find the coordinates of Q.
(2 marks)
Question 16 (3 marks)
Here are the first six terms of a quadratic sequence.
–1 5 15 29 47 69
Find an expression, in terms of n, for the nth term of this sequence.
(3 marks)
Question 17 (2 marks)
Here are four graphs.
Graph A
Diagram: Graph A: a wave through O. From the left it starts on the x-axis, dips below it, rises through O to a peak, then falls back to the x-axis.
Graph B
Diagram: Graph B: two curves, top right and bottom left, getting closer to the axes but never touching them.
Graph C
Diagram: Graph C: a curve starting at O and rising to the right, steeply at first and then less and less steeply.
Graph D
Diagram: Graph D: a curve just above the x-axis on the left, crossing the y-axis above O and rising more and more steeply to the right.
The graphs represent four different types of function f.
Match each description of the function in the table to the letter of its graph.
Description of function Graph f(x) is inversely proportional to x f(x) is a trigonometrical function f(x) is an exponential function f(x) is directly proportional to √x (2 marks)
Question 18 (6 marks)
(a)
Show that (2x + 1)(x + 3)(3x + 7) can be written in the form ax³ + bx² + cx + d
where a, b, c and d are integers.(3 marks)
(b)
Solve (1 – x)² < 9/25
(3 marks)
Question 19 (5 marks)
D = (u²)/2a
u = 26.2 correct to 3 significant figures
a = 4.3 correct to 2 significant figures
(a)
Calculate the upper bound for the value of D.
Give your answer correct to 6 significant figures.
You must show all your working.(3 marks)
(b)
The lower bound for the value of D is 78.6003 correct to 6 significant figures.
By considering bounds, write down the value of D to a suitable degree of accuracy.
You must give a reason for your answer.(2 marks)
Question 20 (5 marks)
Solve algebraically the simultaneous equations
x² – 4y² = 9
3x + 4y = 7(5 marks)
Question 21 (4 marks)
The histogram gives information about the distribution of the weights of some onions
grown by a farmer.Diagram: A histogram. Weight (grams) across from 0 to 210, frequency density up from 0 to 10. Bars: 0 to 60 at height 2, 60 to 90 at height 5, 90 to 120 at height 9, 120 to 135 at height 6, 135 to 180 at height 2.
Onions less than 60 grams in weight are used for pickling.
Onions greater than 120 grams in weight are sold at the market.
The rest of the onions are sent to a food processing factory.A pie chart is drawn using the information above to show what the farmer does with
the onions he grows.Diagram: A pie chart with three sectors: sent to the food processing factory (angle x°, starting at the top and going clockwise), sold at the market, and used for pickling.
The angle of the sector for the onions sent to the food processing factory is x°.
Work out the value of x.
(4 marks)
Question 22 (4 marks)
The diagram shows a circle, centre O.
Diagram: Coordinate axes with a circle, centre O. A straight line from B (16, 0) on the x-axis touches the circle at A, below the x-axis. Angle OBA is 30°. Point P (3p, p) is marked with a cross on the circle, above the x-axis and to the right of the y-axis.
AB is the tangent to the circle at the point A.
Angle OBA = 30°Point B has coordinates (16, 0)
Point P has coordinates (3p, p)Find the value of p.
Give your answer correct to 1 decimal place.
You must show all your working.(4 marks)
Question 23 (5 marks)
The diagram shows the positions of three towns, Acton (A), Barston (B) and Chorlton (C).
Diagram: Three towns. B is 8 km from A on a bearing of 037° (the angle from north at A is 37°). C is 9 km from B on a bearing of 150° (the angle from north at B, measured clockwise, is 150°). North lines are drawn at A, B and C.
Barston is 8 km from Acton on a bearing of 037°
Chorlton is 9 km from Barston on a bearing of 150°Find the bearing of Chorlton from Acton.
Give your answer correct to 1 decimal place.
You must show all your working.(5 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.