Edexcel GCSE Higher November 2021 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 (4 marks)
The scatter graph shows information about the volume of traffic and the carbon monoxide level at a point on a road each day for 22 days.
Diagram: A scatter graph of carbon monoxide level (mg/m³) against volume of traffic (number of cars) for 22 days. The crosses go up from bottom left to top right, except one cross at (100, 18), which is far above the others.
One point is an outlier.
(a)
Write down the coordinates of this point.
(1 mark)
(b)
For another day, 370 cars pass the point on the road.
Estimate the carbon monoxide level for this day.
(2 marks)
(c)
Alfie says,
“Because there is an outlier, there is no correlation.”
Is Alfie correct?
You must give a reason for your answer.(1 mark)
Question 2 (4 marks)
Natalie makes potato cakes in a restaurant.
She mixes potato, cheese and onion so thatweight of potato : weight of cheese : weight of onion = 9 : 2 : 1
Natalie needs to make 6000 g of potato cakes.
Cheese costs £2.25 for 175 g.
Work out the cost of the cheese needed to make 6000 g of potato cakes.
(4 marks)
Question 3 (4 marks)
(a)
Write 4.5 × 10⁵ as an ordinary number.
(1 mark)
(b)
Write 0.007 in standard form.
(1 mark)
(c)
Work out 4.2 × 10³ + 5.3 × 10²
Give your answer in standard form.(2 marks)
Question 4 (4 marks)
A water tank is empty.
Anil needs to fill the tank with 2400 litres of water.Company A supplies water at a rate of 8 litres in 1 minute 40 seconds.
Company B supplies water at a rate of 2.2 gallons per minute.1 gallon = 4.54 litres
Company A would take more time to fill the tank than Company B would take to fill the tank.
How much more time?
Give your answer in minutes correct to the nearest minute.(4 marks)
Question 5 (3 marks)
The first four terms of a Fibonacci sequence are
a 2a 3a 5a
The sum of the first five terms of this sequence is 228
Work out the value of a.
(3 marks)
Question 6 (4 marks)
In a bag there are only red counters, blue counters, green counters and pink counters.
A counter is going to be taken at random from the bag.The table shows the probabilities of taking a red counter or a blue counter.
Colour red blue green pink Probability 0.05 0.15 The probability of taking a green counter is 0.2 more than the probability of taking
a pink counter.(a)
Complete the table.
(2 marks)
(b)
There are 18 blue counters in the bag.
Work out the total number of counters in the bag.
(2 marks)
Question 7 (4 marks)
The diagram shows a sector OPQR of a circle, centre O and radius 8 cm.
Diagram: A quarter circle OPQR with centre O and radius 8 cm: OP goes right, OR goes down, and the angle at O is a right angle. The chord PR and the arc PQR enclose a shaded segment.
OPR is a triangle.
Work out the area of the shaded segment PQR.
Give your answer correct to 3 significant figures.(4 marks)
Question 8 (2 marks)
(a)
Using the axes below, sketch a graph to represent the statement
y is directly proportional to x
Diagram: Empty axes: y up, x across, origin O.
(1 mark)
(b)
Using the axes below, sketch a graph to represent the statement
y is inversely proportional to x
Diagram: Empty axes: y up, x across, origin O.
(1 mark)
Question 9 (3 marks)
On Monday, 12 people took 5 hours to clean a number of cars.
On Tuesday, 15 people cleaned the same number of cars.(a)
Assuming that all the people worked at the same rate,
work out how many hours the 15 people took to clean the cars.(2 marks)
(b)
The assumption is wrong.
How might this affect the time taken for the 15 people to clean the cars?
(1 mark)
Question 10 (4 marks)
The diagram shows two right-angled triangles ACB and DEB.
Diagram: Right-angled triangle ACB with the right angle at C. D is on AB and E is on CB, with DE perpendicular to CB.
AD = 9 cm
DE = 2 cm
DB = 6 cmCalculate the length of CB.
Give your answer correct to 2 decimal places.(4 marks)
Question 11 (2 marks)
Freya writes down the value of x, correct to 1 decimal place.
She writes x = 6.4
Complete the error interval for x.
ldotsldots ≤ x < ldotsldots
(2 marks)
Question 12 (2 marks)
(ax⁶)^(1/n) = 7x³
Work out the value of a and the value of n.
(2 marks)
Question 13 (5 marks)
A pattern is made from four identical rectangles.
The sides of the rectangles are parallel to the axes.Diagram: Four identical rectangles in a staircase: a flat one with A at its bottom left corner, an upright one on its right end, a flat one to the right of the top of that, and an upright one on its right end with B at its top left corner. C is the top right corner of the first rectangle.
Point A has coordinates (3, 4)
Point B has coordinates (11, 20)
Point C is marked on the diagram.Work out the coordinates of C.
You must show all your working.(5 marks)
Question 14 (4 marks)
Olivia and Jessica have in total half as many sweets as Fran and Gary have in total.
Fran and Gary share their sweets in the ratio 2 : 3
Olivia and Jessica share their sweets in the ratio 9 : 1Fran got w sweets.
Gary got x sweets.
Olivia got y sweets.
Jessica got z sweets.Find, in its simplest form, w : x : y : z
(4 marks)
Question 15 (3 marks)
The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container.
Diagram: A curve falling from about 41.6 litres at t = 0: about 19.3 litres at 10 seconds, 10.8 at 20, 6.2 at 30, 3.7 at 40 and 2.2 at 51 seconds, getting less steep.
Using the graph, work out an estimate for the rate at which the water is flowing out of the container when t = 12
You must show your working.(3 marks)
Question 16 (4 marks)
The curve C has equation y = x² + 3x – 3
The line L has equation y – 5x + 4 = 0Show, algebraically, that C and L have exactly one point in common.
(4 marks)
Question 17 (4 marks)
x is directly proportional to the square of y.
y is directly proportional to the cube of z.z = 2 when x = 32
Find a formula for x in terms of z.
(4 marks)
Question 18 (4 marks)
OABC is a trapezium.
Diagram: Trapezium OABC with AB parallel to OC. OA is a, AB is b and OC is 3b. D is on OB and E is on BC, joined by a line.
overrightarrowOA = mathbfa
overrightarrowAB = mathbfb
overrightarrowOC = 3mathbfbD is the point on OB such that OD : DB = 2 : 3
E is the point on BC such that BE : EC = 1 : 4Work out the vector overrightarrowDE in terms of mathbfa and mathbfb.
Give your answer in its simplest form.(4 marks)
Question 19 (3 marks)
At the start of year n, the number of animals in a population is P_n
At the start of the following year, the number of animals in the population is P_n + 1 whereP_n + 1 = kP_n
At the start of 2017 the number of animals in the population was 4000
At the start of 2019 the number of animals in the population was 3610Find the value of the constant k.
(3 marks)
Question 20 (2 marks)
Pat throws a fair coin n times.
Find an expression, in terms of n, for the probability that Pat gets at least 1 head and at least 1 tail.
(2 marks)
Question 21 (4 marks)
Here is a speed-time graph showing the speed, in metres per second, of an object t seconds after it started to move from rest.
Diagram: A curve starting at 0 and getting less steep: 4 m/s at 1 second, 6 at 2, 7.2 at 3, 7.8 at 4 and 8 at 5 seconds, then level at 8.
(a)
Using 3 trapeziums of equal width, work out an estimate for the area under the graph between t = 1 and t = 4
(3 marks)
(b)
What does this area represent?
(1 mark)
Question 22 (3 marks)
Show that (6x³)/((9x² – 144)) ÷ (2x⁴)/(3(x – 4)) can be written in the form 1/(x(x + r)) where r is an integer.
(3 marks)
Question 23 (4 marks)
ABC is a triangle.
Diagram: Triangle ABC with D on BC. AD splits angle BAC into two equal angles, each x°.
D is the point on BC such that angle BAD = angle DAC = x°
Prove that AB/BD = AC/DC
(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.