Edexcel GCSE Higher November 2021 Paper 2 (calculator)
21 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 down the inequality shown on this number line.
Diagram: A number line for x from -5 to 5, with an open circle at -1 and an arrow from it pointing right, drawn just above the number line.
(1 mark)
(b)
On the number line below, show the inequality -3 ≤ y < 4
Diagram: A number line for y from -5 to 5.
(2 marks)
Question 2 (4 marks)
(a)
Find the Highest Common Factor (HCF) of 60 and 84
(2 marks)
(b)
Find the Lowest Common Multiple (LCM) of 24 and 40
(2 marks)
Question 3 (5 marks)
Sam drives his car on a journey.
Here is the travel graph for the first 15 minutes of his journey.Diagram: Travel graph: time of day across, from 10 00 to 10 50; distance travelled in kilometres up the side, from 0 to 50. (10 00, 0 km) to (10 15, 20 km).
(a)
Work out Sam’s speed, in km/h, for the first 15 minutes of his journey.
(2 marks)
(b)
At 10 15 Sam stops for 10 minutes and then drives for 20 minutes at a speed of 75 km/h.
On the grid, complete the travel graph for Sam’s journey.
(3 marks)
Question 4 (6 marks)
(a)
Complete the table of values for y = x² – 2x + 2
x –2 –1 0 1 2 3 4 y 10 2 5 (2 marks)
(b)
On the grid, draw the graph of y = x² – 2x + 2 for values of x from –2 to 4
Diagram: A graph.
(2 marks)
(c)
Use your graph to find estimates of the solutions of the equation x² – 2x + 2 = 4
(2 marks)
Question 5 (4 marks)
Here is a right-angled triangle.
Diagram: A right-angled triangle with sides 8 mm and 10 mm next to the right angle.
The shaded shape below is made from two of these triangles.
Diagram: A shaded shape made from two copies of the triangle. The second triangle has its right angle at the top of the 8 mm side; its 10 mm side lies along the sloping side of the first triangle and its 8 mm side goes up from the right angle.
Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.(4 marks)
Question 6 (4 marks)
(a)
ABC is a right-angled triangle.
Diagram: A diagram.
Work out the length of BC.
Give your answer correct to 1 decimal place.(2 marks)
(b)
PQR is a right-angled triangle.
Diagram: A diagram.
Work out the size of the angle marked x.
Give your answer correct to 1 decimal place.(2 marks)
Question 7 (3 marks)
Liquid A has a density of 1.8 g/cm³
Liquid B has a density of 1.2 g/cm³80 cm³ of liquid A is mixed with 40 cm³ of liquid B to make 120 cm³ of liquid C.
Work out the density of liquid C.
(3 marks)
Question 8 (1 mark)
The grouped frequency table gives information about the time, in minutes, taken by 50 people to solve a puzzle.
Time (t minutes) Frequency 0 < t ≤ 10 5 10 < t ≤ 20 8 20 < t ≤ 30 12 30 < t ≤ 40 15 40 < t ≤ 50 7 50 < t ≤ 60 3 Brian was asked to draw a cumulative frequency table for this information.
This is the table that Brian drew.Time (t minutes) Cumulative frequency 0 < t ≤ 10 5 10 < t ≤ 20 13 20 < t ≤ 30 25 30 < t ≤ 40 40 40 < t ≤ 50 47 50 < t ≤ 60 50 Write down one thing that is wrong with this cumulative frequency table.
(1 mark)
Question 9 (4 marks)
The box plot shows information about the length of time, in minutes, some people waited to see a doctor at a hospital on Monday.
Diagram: Box plot: lowest 20, lower quartile 50, median 120, upper quartile 188, highest 200.
(a)
Work out the interquartile range of the information in the box plot.
(2 marks)
(b)
Becky says, “50% of the people waited for at least 2 hours.” Is Becky correct? Explain why.
(1 mark)
(c)
The table gives information about the length of time, in minutes, some people waited to see a doctor at the same hospital on Tuesday.
Waiting time (minutes) Shortest time 20 Lower quartile 50 Median 100 Upper quartile 140 Longest time 210 Becky was asked to compare the distribution of the lengths of times people waited on Monday with the distribution of the lengths of times people waited on Tuesday.
She wrote, “People had to wait longer on Tuesday than on Monday.”
Give one reason why Becky may be wrong.(1 mark)
Question 10 (4 marks)
Louise invests £x in Better Investments for 3 years.
Sadiq invests £x in County Bank for 3 years.Better Investments Compound Interest 2.5% per annum County Bank Compound Interest 2% per annum for the first two years
3.5% per annum for each extra yearAt the end of the 3 years, the value of Louise’s investment is £344 605
Work out the value of Sadiq’s investment at the end of the 3 years.
(4 marks)
Question 11 (5 marks)
Here is a sketch of the line L.
Diagram: A sketch of a straight line L sloping upwards. It crosses the x-axis at P(–6, 0) and the y-axis at Q(0, 3), and carries on up to the point R, marked with a cross.
The points P(-6, 0) and Q(0, 3) are points on the line L.
The point R is such that PQR is a straight line and PQ : QR = 2 : 3(a)
Find the coordinates of R.
(2 marks)
(b)
Find an equation of the line that is perpendicular to L and passes through Q.
(3 marks)
Question 12 (3 marks)
Expand and simplify (x – 2)(3x + 2)(2x + 3)
(3 marks)
Question 13 (2 marks)
In a school there are 16 teachers and 220 students.
Of these students 120 are girls and 100 are boys.One teacher, one girl and one boy are going to be chosen to represent the school.
Work out the number of different ways there are to choose one teacher, one girl and one boy.
(2 marks)
Question 14 (4 marks)
Diagram: A circle with B at the top. SBT is a straight line touching the circle at B. A is on the upper left of the circle, D on the left and C at the bottom right. The quadrilateral ABCD is drawn, with the chord BD. Angle ABD is marked 20°.
A, B, C and D are four points on a circle.
SBT is a tangent to the circle.
Angle ABD = 20°the size of angle BAD : the size of angle BCD = 3 : 1
Find the size of angle SBA.
Give a reason for each stage of your working.(4 marks)
Question 15 (5 marks)
Here is triangle ABC.
Diagram: Triangle ABC with C at the bottom left, B at the bottom right and A at the top. AC is 8 cm, AB is 11 cm and angle CAB is 72°.
(a)
Find the length of BC.
Give your answer correct to 3 significant figures.(3 marks)
(b)
Find the area of triangle ABC.
Give your answer correct to 3 significant figures.(2 marks)
Question 16 (4 marks)
(a)
Use the iteration formula x_n + 1 = 3√(10 – 2x_n) to find the values of x_1, x_2 and x_3
Start with x_0 = 2(3 marks)
(b)
The values of x_1, x_2 and x_3 found in part (a) are estimates of the solution of an equation of
the form x³ + ax + b = 0 where a and b are integers.Find the value of a and the value of b.
(1 mark)
Question 17 (4 marks)
Some people took part in the first round of a competition.
The histogram gives information about the scores of these people in the first round.
Diagram: A histogram of first round scores out of 40. Bars: 0 to 5, frequency density 0.8; 5 to 15, 1.6; 15 to 25, 2.2; 25 to 40, 1.2.
20% of the people got a score high enough for them to qualify for the second round.
Work out an estimate for the score needed to qualify for the second round.
You must show all your working.(4 marks)
Question 18 (4 marks)
(a)
Here is a graph of y = sin x° for 0 ≤ x ≤ 360
Diagram: The graph of y = sin x for x from 0 to 360 on a grid: up to 1 at 90, down through 180 to –1 at 270, and back to 0 at 360.
Using this graph, find estimates of all four solutions of
sin x° = 0.6 for 0 ≤ x ≤ 720
(2 marks)
(b)
The graph of y = sin x° is reflected in the x-axis.
Write down an equation of the reflected graph.(1 mark)
(c)
Here is a graph of y = f(x)
Diagram: The graph of y = f(x): straight lines from (–4, 1) down to (–2, –1), across to (–1, –1), then up to (2, 1).
On the grid, draw the graph of y = f(x – 2)
(1 mark)
Question 19 (3 marks)
A, B and C are three spheres.
The volume of sphere A is 125 cm³
The volume of sphere B is 27 cm³The ratio of the radius of sphere B to the radius of sphere C is 1 : 2
Work out the ratio of the surface area of sphere A to the surface area of sphere C.
(3 marks)
Question 20 (4 marks)
In a village,
if it rains on one day, the probability that it will rain on the next day is 0.8
if it does not rain on one day, the probability that it will rain on the next day is 0.6A weather forecaster says,
“There is a 70% chance that it will rain in the village on Monday.”Work out an estimate for the probability that it will rain in the village on Wednesday.
You must show all your working.(4 marks)
Question 21 (4 marks)
The time period, T seconds, of a simple pendulum of length l cm is given by the formula
T = 2π√(l/g)
Katie uses a simple pendulum in an experiment to find an estimate for the value of g.
Here are her results.
l = 52.0 correct to 3 significant figures.
T = 1.45 correct to 3 significant figures.Work out the upper bound and the lower bound for the value of g.
Use π = 3.142
You must show all your working.(4 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.