Edexcel GCSE Higher November 2018 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 (3 marks)
(a)
Write 7357 correct to 3 significant figures.
(1 mark)
(b)
Work out dfrac√(17 + 4²)7.3²
Write down all the figures on your calculator display.
(2 marks)
Question 2 (3 marks)
Last year Jo paid £245 for her car insurance.
This year she has to pay £883 for her car insurance.Work out the percentage increase in the cost of her car insurance.
(3 marks)
Question 3 (5 marks)
(a)
Complete this table of values for y = x² + x – 4
x –3 –2 –1 0 1 2 3 y –2 –4 –2 (2 marks)
(b)
On the grid, draw the graph of y = x² + x – 4 for values of x from –3 to 3
Diagram: A grid with x from –3 to 3 and y from –10 to 15.
(2 marks)
(c)
Use the graph to estimate a solution to x² + x – 4 = 0
(1 mark)
Question 4 (6 marks)
Fran asks each of 40 students how many books they bought last year.
The chart below shows information about the number of books bought by each of the 40 students.
Diagram: Bar chart. 0 to 4: 11. 5 to 9: 8. 10 to 14: 13. 15 to 19: 6. 20 to 24: 2.
(a)
Work out the percentage of these students who bought 20 or more books.
(2 marks)
(b)
Show that an estimate for the mean number of books bought is 9.5
You must show all your working.(4 marks)
Question 5 (4 marks)
Lara is a skier.
She completed a ski race in 1 minute 54 seconds.
The race was 475 m in length.Lara assumes that her average speed is the same for each race.
(a)
Using this assumption, work out how long Lara should take to complete a 700 m race.
Give your answer in minutes and seconds.(3 marks)
(b)
Lara’s average speed actually increases the further she goes.
How does this affect your answer to part (a)?
(1 mark)
Question 6 (4 marks)
ABC is a right-angled triangle.
Diagram: A right-angled triangle ABC with the right angle at C. CA is along the bottom, 14 cm long, and B is above C.
AC = 14 cm.
Angle C = 90°size of angle B : size of angle A = 3 : 2
Work out the length of AB.
Give your answer correct to 3 significant figures.(4 marks)
Question 7 (2 marks)
The table gives information about the speeds of 70 cars.
Speed (s mph) Frequency 0 < s ≤ 10 14 10 < s ≤ 20 18 20 < s ≤ 30 26 30 < s ≤ 40 12 Draw a frequency polygon for this information.
Diagram: A blank grid: speed (mph) from 0 to 45 across, frequency from 0 to 30 up.
(2 marks)
Question 8 (5 marks)
The diagram shows a solid metal cuboid.
The areas of three of the faces are marked on the diagram.
The lengths, in cm, of the edges of the cuboid are whole numbers.Diagram: A cuboid. The area of the front face is 45 cm², the top face 27 cm² and the side face 15 cm².
The metal cuboid is melted and made into cubes.
Each of the cubes has sides of length 2.5 cm.Work out the greatest number of these cubes that can be made.
(5 marks)
Question 9 (8 marks)
(a)
Expand and simplify (x – 2)(2x + 3)(x + 1)
(3 marks)
(b)
(y⁴ × yⁿ)/(y²) = y⁻³
Find the value of n.
(2 marks)
(c)
Solve 5x² – 4x – 3 = 0
Give your solutions correct to 3 significant figures.(3 marks)
Question 10 (4 marks)
f(x) = 4sin x°
(a)
Find f(23)
Give your answer correct to 3 significant figures.(1 mark)
(b)
g(x) = 2x – 3
Find fg(34)
Give your answer correct to 3 significant figures.(2 marks)
(c)
h(x) = (x + 4)²
Ivan needs to solve the following equation h(x) = 25
He writes
(x + 4)² = 25
x + 4 = 5
x = 1This is not fully correct.
Explain why.
(1 mark)
Question 11 (2 marks)
Sketch the graph of y = tan x° for 0 ≤ x ≤ 360
Diagram: Blank axes for a sketch: x from 0 to 360, marked every 90, and y with no scale.
(2 marks)
Question 12 (4 marks)
Here is a pyramid with a square base ABCD.
Diagram: A pyramid with a square base ABCD and vertex T at the top. A is at the front left, D at the front, C on the right and B at the back. The edges AB, BC and TB are hidden and drawn dashed.
AB = 5 m
The vertex T is 12 m vertically above the midpoint of AC.
Calculate the size of angle TAC.
(4 marks)
Question 13 (2 marks)
The number of animals in a population at the start of year t is P_t
The number of animals at the start of year 1 is 400Given that
P_t + 1 = 1.01P_t
work out the number of animals at the start of year 3
(2 marks)
Question 14 (3 marks)
y is inversely proportional to x³
y = 44 when x = aShow that y = 5.5 when x = 2a
(3 marks)
Question 15 (3 marks)
Prove algebraically that the difference between the squares of any two consecutive odd
numbers is always a multiple of 8(3 marks)
Question 16 (5 marks)
Here is a shaded shape ABCD.
Diagram: A shaded shape ABCD made from a sector of a circle with centre O and a triangle. The curved edge is the major arc from C round through B to A. Straight edges join A to D and D to C, and O, C and D lie on a straight line. The radii OA and OC are drawn dashed.
The shape is made from a triangle and a sector of a circle, centre O and radius 6 cm.
OCD is a straight line.AD = 14 cm
Angle AOD = 140°
Angle OAD = 24°Calculate the perimeter of the shape.
Give your answer correct to 3 significant figures.(5 marks)
Question 17 (5 marks)
The table shows information about the distances 570 students travelled to a university
open day.Distance (d miles) Frequency 0 < d ≤ 20 120 20 < d ≤ 50 90 50 < d ≤ 80 120 80 < d ≤ 150 140 150 < d ≤ 200 100 (a)
Draw a histogram for the information in the table.
Diagram: A blank grid: distance (miles) from 0 to 250 across, and no scale up.
(3 marks)
(b)
Estimate the median distance.
(2 marks)
Question 18 (5 marks)
A high speed train travels a distance of 487 km in 3 hours.
The distance is measured correct to the nearest kilometre.
The time is measured correct to the nearest minute.By considering bounds, work out the average speed, in km/minute, of the train to a
suitable degree of accuracy.
You must show all your working and give a reason for your answer.(5 marks)
Question 19 (5 marks)
Solve algebraically the simultaneous equations
2x² – y² = 17
x + 2y = 1(5 marks)
Question 20 (2 marks)
Diagram: Triangle A on a grid, with corners at (–4, 1), (–3, 1) and (–3.5, 4).
Triangle A is transformed by the combined transformation of a rotation of 180° about the
point (-2, 0) followed by a translation with vector ( -3 , 2 )One point on triangle A is invariant under the combined transformation.
Find the coordinates of this point.
(2 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.