Edexcel GCSE Maths Paper 2: Calculator Higher November 2021 question paper 1MA1/2H

Write down the inequality shown on this number line.

On the number line below, show the inequality –3 y 4

Find the Highest Common Factor (HCF) of 60 and 84

Find the Lowest Common Multiple (LCM) of 24 and 40

Sam drives his car on a journey. Here is the travel graph for the first 15 minutes of his journey.

Work out Sam’s speed, in km/h, for the first 15 minutes of his journey.

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.

Complete the table of values for y = x² – 2x + 2

On the grid, draw the graph of y = x² – 2x + 2 for values of x from –2 to 4

Use your graph to find estimates of the solutions of the equation x² – 2x + 2 = 4

Here is a right‑angled triangle.

The shaded shape below is made from two of these triangles.

Work out the perimeter of the shaded shape. Give your answer correct to 3 significant figures.

ABC is a right‑angled triangle.

Work out the length of BC. Give your answer correct to 1 decimal place.

PQR is a right‑angled triangle.

Work out the size of the angle marked x. Give your answer correct to 1 decimal place.

Liquid A has a density of 1.8 g/cm³ Liquid B has a density of 1.2 g/cm³ 80 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.

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.

The box plot shows information about the length of time, in minutes, some people waited to see a doctor at a hospital on Monday.

Work out the interquartile range of the information in the box plot.

Becky says, “50% of the people waited for at least 2 hours.”

Is Becky correct? Explain why.

The table gives information about the length of time, in minutes, some people waited to see a doctor at the same hospital on Tuesday.

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.

Louise invests £ x in Better Investments for 3 years. Sadiq invests £x in County Bank for 3 years.

At 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.

Here is a sketch of the line L.

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

Find the coordinates of R.

Find an equation of the line that is perpendicular to L and passes through Q.

Expand and simplify (x – 2)(3 x + 2)(2 x + 3)

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.

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.

Here is triangle ABC.

Find the length of BC. Give your answer correct to 3 significant figures.

Find the area of triangle ABC. Give your answer correct to 3 significant figures.

The values of x₁, x₂ and x₃ 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.

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.

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.

18Here is a graph of y = sin x for 0 ≤ x 360

Using this graph, find estimates of all four solutions of

The graph of y = sin x is reflected in the x‑axis.

Write down an equation of the reflected graph.

Here is a graph of y = f(x)

On the grid, draw the graph of y = f(x – 2)

A, B and C are three spheres. The volume of sphere A is 125 cm³ The volume of sphere B is 27 cm³ The 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.

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 0.6 A 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.

21The time period, T seconds, of a simple pendulum of length lcm is given by the formula

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.