Eduqas GCSE Maths Component 2H Higher November 2021 question paper

21 questions

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(a)

1. (a) Solve6x maths symbol 1 5 x.

[2]

Answer

(b)

Abby, Ben and Ceri are solving a puzzle.

Abby takes x seconds. Ben takes 5 seconds more than Abby. Ceri takes twice as long as Ben.

Ceri takes 116 seconds to solve the puzzle.

Use an algebraic method to find how long Abby takes to solve the puzzle.

You must show all your working.

Abby takes_........ seconds

[3]

Answer

Tori’s grandfather buys a gold coin for her on the day she is born.

The coin costs £130. The value of the coin is expected to increase by 6% each year.

What value is the coin expected to have on Tori’s 10th birthday?

Give your answer correct to the nearest penny.

Expected value of the coin £_........

[3]

Answer

The circumference of a circle is 40·841 cm.

Find the area of this circle.

You must show all your working.

[4]

Answer

(a)

4. (a) The diagram shows the side view of a design for a ramp to a building.

For the design to be approved, the angle of rise must not be more than 4·8°.

Use calculations to show that the design should be approved.

[3]

Answer

(b)

The diagram shows a concrete ramp to a different building. It was not approved and needs to be completely removed.

The ramp is a triangular prism and is 2·5 m wide.

How many cubic metres of concrete will need to be removed?

You must show all your working.

[5]

Answer

(a)

p and q are translation vectors with

$Question 5, shown as an image$

Shape A is mapped to shape B using p + 2q.

(a)(i)

Find the column vector which translates shape A to shape B.

[2]

Answer

(a)(ii)

Draw and label shape B on the grid on page 8.

[2]

Answer

(b)

Triangle C has vertices with coordinates (4, 3), (6, 5), (6, 0). After a single transformation, the vertices of triangle C are mapped to (3, 4), (5, 6), (0, 6).

Describe the transformation.

You may use this grid to help you

Transformation:_........

[2]

Answer

A tram company sells all-day tickets.

1 adult ticket and 4 child tickets cost a total of £16.30. 2 adult tickets and 3 child tickets cost a total of £19.10.

Use an algebraic method to find the total cost of 3 adult tickets and 1 child ticket.

[5]

Answer

(a)

7. (a) Expand and simplify.(x maths symbol 6)(7x+5)

[3]

Answer

(b)

Factorise.y² maths symbol 2y 8

[2]

Answer

The table shows the time, t minutes, taken by 600 people travelling to a flower show by car.

Time, t (minutes)	Frequency
20 t 40	68
40 t 80	186
80 t 100	238
100 t 150	108

(a)

Calculate an estimate of the mean travelling time for these 600 people.

You must show all your working.

[4]

Answer

(b)

Road works delayed each of these 600 people by 3 minutes.

What would the mean travelling time have been without these road works?

[1]

Answer

(a)

Complete the table above.

[1]

Answer

(b)

[2]

Answer

(c)

Write down the roots of.x² maths symbol 2x 3 0

[1]

Answer

(d)

Use your graph to solve the simultaneous equations

[3]

Answer

(a)

10. (a) Find the next term of each of the following sequences.

(a)(i)

2, 9, 11, 20, 31, 51,...

[1]

Answer

(a)(ii)

$Question 10, shown as an image$

[1]

Answer

(b)

Find the nth term of the following sequence.

2, 6, 12, 20, 30,...

[2]

Answer

(c)

The numbers 4, 6, and 8 are three consecutive even integers.

Complete the following proof to show that the sum of any three consecutive even integers

is a multiple of 6.

Proof:

Every even number is a multiple of 2.

Let the smallest of the three even numbers be 2n, where n is an integer.

The second of the three even numbers must be_........

and the third of the three even numbers must be_........

[3]

Answer

What was the purchase price of the car?

[4]

Answer

[4]

Answer

(a)

13. (a) Rita has a box containing 12 buttons, 5 are white (W) and the rest are blue (B). Rita takes 2 buttons from the box at random, without replacement.

Complete the tree diagram.

First Second

[3]

Answer

(b)

Calculate the probability that at least one of the buttons Rita takes from the box is white.

[2]

Answer

(c)

Rita puts the 2 buttons back into the box. She then takes 3 buttons from the box at random, without replacement. What is the probability that the second and the third buttons she takes are both blue?

[3]

Answer

At the end of 2020, the population, P₀, of a particular type of insect on an island was estimated to be 25 000.

Anwar and Irina are scientists studying these insects.

Anwar uses this iterative formula to predict the population of the insects, P_n, n years after the end of 2020.

P₀ = 25 000

P_n₊₁= 1·12P_n where n ≥ 0 and n is an integer

(a)

Use Anwar’s formula to predict the population at the end of 2021.

[1]

Answer

(b)

Use Anwar’s formula to predict the increase in population during the year 2025.

You must show all your working.

Increase in population =_........ insects

[3]

Answer

(c)

[2]

Answer

The diagram shows a candle. It is made by removing a small pyramid of wax from the top of a large pyramid of wax, to expose the wick.

Diagram not drawn to scale

The perpendicular height of the large pyramid is 24 cm. The base of the large pyramid is a square with sides 12 cm. The base of the small pyramid that is removed is a square with sides 2 cm.

The density of the candle wax is 0·9 g / cm³.

(a)

Calculate the mass of the candle.

State one assumption you make.

[7]

Answer

(b)

Describe the impact of your assumption on your answer to part (a).

[1]

Answer

Tom rides his motorbike for 187·5 miles, correct to the nearest $fraction$ mile. On this journey his motorbike uses 4·8 litres of fuel, correct to the nearest 0·4 litre. The fuel economy of Tom’s motorbike is k kilometres per litre.

What is the smallest possible value of k?

Smallest possible value of k is_........

[5]

Answer

(a)

17. (a) How many 8-digit numbers can be made using the digits 2, 3, 4, 5, 6, 7, 8, 9 when each

digit is used once?

[2]

Answer

(b)

How many 6-digit numbers which start with a prime number can be made using the digits

2, 3, 4, 5, 6, 7, 8, 9 when each digit may be used at most once?

[2]

Answer

The diagram shows Zac’s height from 8 to 18 years of age.

(a)

Find Zac’s rate of growth on his 17th birthday.

[1]

Answer

(b)

What is Zac’s average rate of growth per year between his 10th and 15th birthdays?

You must show all your working.

[3]

Answer

Solve the following equation.

Give your answers correct to 2 decimal places.

[7]

Answer

The diagram shows the journey of a small boat.

The boat sails from point P on a bearing of 030° for 50 km. When it reaches point Q, it changes direction and travels to point R on a bearing of 161° for 72 km.

(a)

[1]

Answer

(b)

The triangular area PQR is to be searched to locate a shipwreck.

Calculate this area.

[2]

Answer

(c)

Calculate the bearing of P from R.

Give your answer correct to the nearest degree.

[7]

Answer

The following probabilities are given for events A and B.

(a)

By drawing a Venn diagram or otherwise, find the probability that A occurs or B occurs

but they do not both occur.

[3]

Answer

(b)

Find.P(A' maths symbol B')

[2]

Answer

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Eduqas C300 · Component 2H

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