Edexcel GCSE Higher November 2019 Paper 3 (calculator)
24 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 (4 marks)
(a)
Expand and simplify (x + 5)(x – 9)
(2 marks)
(b)
Factorise fully 9x² + 6x
(2 marks)
Question 2 (3 marks)
(a)
Use your calculator to work out
dfrac29² – 4.6√(35 – 1.9³)
Write down all the figures on your calculator display.
(2 marks)
(b)
Write your answer to part (a) correct to 4 significant figures.
(1 mark)
Question 3 (2 marks)
The scatter graph shows information about the marks a group of students got in a Science
test and in a Maths test.Diagram: A scatter graph of Maths test mark against Science test mark for 12 students, both from 0 to 60. The crosses go up from bottom left to top right.
Jamie got a mark of 34 in the Science test.
Using the scatter graph, find an estimate for Jamie’s mark in the Maths test.
(2 marks)
Question 4 (3 marks)
The table gives information about the times taken, in seconds, by 18 students to run a race.
Time (t seconds) Frequency 5 < t ≤ 10 1 10 < t ≤ 15 2 15 < t ≤ 20 7 20 < t ≤ 25 8 Work out an estimate for the mean time.
Give your answer correct to 3 significant figures.(3 marks)
Question 5 (1 mark)
Write 37 cm³ in mm³
(1 mark)
Question 6 (4 marks)
Nimer was driving to a hotel.
He looked at his Sat Nav at 13 30Time 13 30 Distance to destination 65 miles Nimer arrived at the hotel at 14 48
Work out the average speed of the car from 13 30 to 14 48
You must show all your working.(4 marks)
Question 7 (3 marks)
(a)
Write 32 460 000 in standard form.
(1 mark)
(b)
Write 4.96 × 10⁻³ as an ordinary number.
(1 mark)
(c)
Asma was asked to compare the following two numbers.
A = 6.212 × 10⁸ and B = 4.73 × 10⁹
She says,
“6.212 is bigger than 4.73 so A is bigger than B.”
Is Asma correct?
You must give a reason for your answer.(1 mark)
Question 8 (4 marks)
The diagram shows a regular pentagon and a parallelogram.
Diagram: A regular pentagon with its bottom side horizontal. A parallelogram sits inside it on the same bottom line, sharing the bottom left corner. The parallelogram’s angle at its top left corner is 117°. The angle x is at the bottom left corner, between the side of the pentagon and the slanting side of the parallelogram.
Work out the size of the angle marked x.
You must show all your working.(4 marks)
Question 9 (2 marks)
Diagram: A grid with x and y from –1 to 10. Triangle A has corners (1, 1), (1, 3) and (2, 3). A cross marks the point (0, 1).
Enlarge triangle A by scale factor 2.5 with centre (0, 1)
(2 marks)
Question 10 (4 marks)
(a)
Solve (9 + x)/7 = 11 – x
(3 marks)
(b)
Simplify (4(y + 3)³)/((y + 3)²)
(1 mark)
Question 11 (3 marks)
The probability tree diagram shows the probabilities that Bismah will be late for work on
two days next week.Diagram: Probability tree diagram: Monday then Tuesday.
Calculate the probability that Bismah will be late on exactly one of the two days.
(3 marks)
Question 12 (3 marks)
The stem and leaf diagram shows information about the heights, in cm, of 23 sunflowers.
Diagram: Stem and leaf diagram. Stem 17, leaves 3 4 9; Stem 18, leaves 6 8 8; Stem 19, leaves 0 0 1 4 6 7 8; Stem 20, leaves 1 4 7 7 9 9; Stem 21, leaves 4 8 8 9. Key: 17 | 3 represents 173 cm.
On the grid, draw a box plot for this information.
Diagram: A blank grid for a box plot, with a scale for height from 170 to 220 cm.
(3 marks)
Question 13 (4 marks)
Liquid A and liquid B are mixed together in the ratio 2 : 13 by volume to make liquid C.
Liquid A has density 1.21 g/cm³
Liquid B has density 1.02 g/cm³A cylindrical container is filled completely with liquid C.
The cylinder has radius 3 cm and height 25 cm.Work out the mass of the liquid in the container.
Give your answer correct to 3 significant figures.
You must show all your working.(4 marks)
Question 14 (4 marks)
A group of people went to a restaurant.
Each person chose one starter and one main course.starter main course soup lasagne prawns curry the number of people who chose soup : the number of people who chose prawns = 2 : 3
Of those who chose soup,
the number of people who chose lasagne : the number of people who chose curry = 5 : 3Of those who chose prawns,
the number of people who chose lasagne : the number of people who chose curry = 1 : 5What fraction of the people chose curry?
You must show how you get your answer.(4 marks)
Question 15 (3 marks)
Prove algebraically that the sum of the squares of any two consecutive even numbers is
always a multiple of 4(3 marks)
Question 16 (3 marks)
y is inversely proportional to the square of x.
y = 8 when x = 2.5
Find the negative value of x when y = 8/9
(3 marks)
Question 17 (4 marks)
Here is the graph of y = x² – 3
Diagram: The graph of y = x squared minus 3 for x from –4 to 4: a U-shaped curve with its lowest point at (0, –3), crossing the x-axis at about –1.7 and 1.7
Use the graph to find estimates for the solutions to the equation x² – 2x – 2 = 0
You must show how you get your solutions.(4 marks)
Question 18 (5 marks)
The diagram shows triangle ABC.
Diagram: Triangle ABC with AB = 3.4 cm, AC = 6.2 cm and BC = 6.1 cm. D is a point on BC, nearer to C, and the line AD is drawn.
AB = 3.4 cm AC = 6.2 cm BC = 6.1 cm
D is the point on BC such that
size of angle DAC = 2/5 × size of angle BCA
Calculate the length DC.
Give your answer correct to 3 significant figures.
You must show all your working.(5 marks)
Question 19 (3 marks)
The graph shows information about part of a cyclist’s journey.
Diagram: A distance-time graph. A curve starts at the origin and gets steeper: about 1 metre at 2 seconds, 4.5 metres at 4 seconds, 10 metres at 6 seconds and 20 metres at about 8.4 seconds.
Work out an estimate of the speed, in m/s, of the cyclist at time 6 seconds.
(3 marks)
Question 20 (2 marks)
Here are the first five terms of a sequence.
–1 0 3 8 15
Find an expression, in terms of n, for the nth term of this sequence.
(2 marks)
Question 21 (2 marks)
When a biased coin is thrown 4 times, the probability of getting 4 heads is 16/81
Work out the probability of getting 4 tails when the coin is thrown 4 times.
(2 marks)
Question 22 (4 marks)
Show that (7x – 14)/(x² + 4x – 12) ÷ (x – 6)/(x³ – 36x) simplifies to ax where a is an integer.
(4 marks)
Question 23 (5 marks)
The diagram shows a sector OACB of a circle with centre O.
The point C is the midpoint of the arc AB.The diagram also shows a hollow cone with vertex O.
The cone is formed by joining OA and OB.Diagram: A sector OACB of a circle with centre O. The sector is the large part of the circle: its angle AOB is a reflex angle. C is halfway round the arc from A to B.
Diagram: A cone with vertex O. A and B are together on the edge of the circular base, and C is opposite them.
Volume of cone = 1/3π r²h
Curved surface area of cone = π rlDiagram: A cone with its slant height l, its vertical height h and its base radius r marked.
The cone has volume 56.8 cm³ and height 3.6 cm.
Calculate the size of angle AOB of sector OACB.
Give your answer correct to 3 significant figures.
You must show all your working.(5 marks)
Question 24 (5 marks)
OXYZ is a parallelogram.
Diagram: Parallelogram OXYZ with O at the bottom left, X at the bottom right, Y at the top right and Z at the top left. The diagonal OY is drawn. P is on OX, and the line from Z to P crosses OY at R.
overrightarrowOX = mathbfa
overrightarrowOY = mathbfbP is the point on OX such that OP : PX = 1 : 2
R is the point on OY such that OR : RY = 1 : 3Work out, in its simplest form, the ratio ZP : ZR
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.