Eduqas GCSE Maths Component 2H Higher November 2022 question paper

Nathan and Lucy make and sell wooden items for gardens.

(a)

Nathan makes and sells benches, tables and tool sheds. Last year, the profit he made from selling these items was in the following ratio.

benches: tables: tool sheds 2: 3: 7

(a)(i)

What fraction of his profit did Nathan make from selling benches and tables?

[1]

Answer

(a)(ii)

His total profit was £18 072.

How much profit did Nathan make from the sale of tool sheds?

[2]

Answer

(b)

$Question 1, shown as an image$

[2]

Answer

(a)

Moeen uses the midpoint of each group to calculate an estimate of the mean mass of these buzzards. He does this correctly.

Calculate Moeen’s answer.

[3]

Answer

(b)

Deeta decides to estimate the mean mass of these buzzards. She uses the values 600, 700, 800 and 900 rather than the midpoints.

Explain why her method is unlikely to give a good estimate of the mean mass.

[1]

Answer

Debbie collects data about a group of 20 people.

Her data is: • the total number of years for which they have owned a pet • the number of visits they have each made to their doctor in the last year.

The scatter graph shows her results and her attempt to draw a line of best fit for the data.

Total number of years of pet ownership

(a)

Make a criticism of Debbie’s line of best fit.

[1]

Answer

(b)

Debbie says,

Is Debbie correct?

Yes No

Explain how you decide.

[1]

Answer

Janet invests £5000 in a savings account for 9 years.

She makes no further payments into or out of her account in this time.

For the first 5 years, her investment earns 2% compound interest per year. After this, the interest rate decreases to 1·3% compound interest per year.

How much is Janet’s investment worth at the end of the 9 years?

[4]

Answer

(a)

Circle the correct conversion of 7 m³ to cm³.

0 · 000 07 0 · 07 700 70 000 7 000 000

[1]

Answer

(b)

The diagram shows a shape made from a trapezium and a circle.

The parallel sides of the trapezium are tangents to the circle. The diameter of the circle is 30 cm.

The ratio of the white area to the shaded area is as follows.

white area: shaded area 1: k

Find the value of k.

Show all your working and give your answer correct to 1 significant figure.

[6]

Answer

(a)

Solve 5x maths symbol 4 2x 6 .

[2]

Answer

(b)

Solve 4x maths symbol 3 17.

[2]

Answer

(c)

Solve the following simultaneous equations. Use an algebraic (not graphical) method.

You must show all your working.

[3]

Answer

The diagram shows a rhombus, ABCD. AC and BD intersect at E. The length of maths symbol AC is 12 cm. BCE is 35°.

Find the perimeter of ABCD.

[6]

Answer

The table shows some of the values of h maths symbol 3(t 1)(t 4) for 0t5.

t	0	1	2	3	4	5
h 3(t 1)(t 4)		18	18		0

(a)

Complete the table above.

[2]

Answer

(b)

On the graph paper below, draw the graph of h maths symbol 3(t 1)(t 4) for 0t5.

[2]

Answer

(c)

Derek throws a ball upwards from a point above horizontal ground. The height, h metres, of the ball above the ground t seconds after Derek throws it is

(c)(i)

What is the height of the ball above the ground at the start of Derek’s throw?

[1]

Answer

(c)(ii)

How many seconds after Derek throws the ball does it first hit the ground?

[1]

Answer

(c)(iii)

How many seconds after Derek throws the ball is it at its maximum height?

[1]

Answer

(c)(iv)

What is the maximum height of the ball above the ground?

[1]

Answer

The diagram shows the interior length, width and height of a wooden crate.

Jake fills the crate with solid beeswax cylinders. They each have a length of 32 cm.

$Question 9, shown as an image$

Jake calculates the total mass of the cylinders to be more than 70 kg. Is he correct?

Yes No

Show how you decide.

[7]

Answer

Max bought a new computer.

In the first year, the value of Max’s computer decreased by 19·8%. In the second year, the value of Max’s computer decreased by 6·5% of its value at the end of the first year.

Find the overall percentage decrease in the value of Max’s computer at the end of the second year.

You must show all your working.

[4]

Answer

Two groups of people, A and B, take part in a fun run.

Everyone in the groups completes the run.

The table gives a summary of the times, t minutes, taken by group A.

Minimum	Maximum	Median	Lower Quartile	Inter-quartile range
15·2	23·2	19·4	16·8	4·2

(a)

On the grid below, draw a box plot to represent this data.

[3]

Answer

(b)

The box plot below gives a summary of the times, t minutes, taken by group B.

Marcie makes two statements using information from the box plots. Are Marcie’s statements correct? Explain how you decide.

(b)(i)

“On average, runners in group B ran faster than runners in group A.”

Correct
Not correct

[1]

Answer

(b)(ii)

“There is a greater proportion of runners who took less than 17 minutes in

$Question 11, shown as an image$

Correct
Not correct

[1]

Answer

The equation 2x³ maths symbol x² 12 0 has a solution between 1 and 2.

Use trial and improvement to find this solution correct to 1 decimal place.

[4]

Answer

(a)

What is the lower bound of the height of the wall?

[1]

Answer

(b)

A builder measures the lengths of two pieces of wood. He uses a tape measure.

The lengths are 2·85 metres and 1·90 metres, both correct to the nearest centimetre.

Calculate the greatest total length of the two pieces of wood.

Give your answer in metres.

[3]

Answer

Dora has two boxes, A and B.

The boxes contain beads which are identical in shape.

Box A contains 9 green, 6 red and 5 yellow beads. Box B contains 12 red and 8 yellow beads.

Dora takes a bead at random from box A. If the bead is: • green, she puts it back in box A • red or yellow, she puts it in box B. She then takes a bead at random from box B.

(a)

Complete the tree diagram.

[3]

Answer

(b)

Find the probability that Dora takes two beads of the same colour.

[3]

Answer

In this question all lengths are in metres.

This shape is made from two rectangles. The area of this shape is 10 m².

(a)

Show that 3x² maths symbol 2x 1 0.

[3]

Answer

(b)

Calculate the value of the perimeter of this shape.

You must show all your working.

[5]

Answer

OABC is a parallelogram. OA = a and OC = c. D is the midpoint of AB and E is the midpoint of OD.

(a)

Find OD in terms of a and c.

[1]

Answer

(b)

Find OE in terms of a and c.

[1]

Answer

(c)

Find CE in terms of a and c.

Give your answer in its simplest form.

[2]

Answer

The diagram shows a cuboid, ABCDEFGH.

Calculate the length of the diagonal, DF.

[3]

Answer

(a)

The diagram shows a sketch of the graph of y maths symbol f (x). The point A has coordinates (–3, 0), the point B has coordinates (–1, 1).

(a)(i)

Sketch the graph of y maths symbol f (x) on the axes below. You must indicate the coordinates of the new positions of the points A and B.

[2]

Answer

(a)(ii)

Sketch the graph of y maths symbol f (x) 2 on the axes below.

You must indicate the coordinates of the new positions of the points A and B.

[2]

Answer

(b)

The diagram shows a sketch of the circle with equation x² maths symbol y² 289.

Write down the coordinates of point C.

[1]

Answer

$Question 19, shown as an image$

In triangle ABC, AB = 7 cm, AC = 9 cm and ABC maths symbol = 61°. ACD is a straight line. Find BCD.

[4]

Answer

The diagram shows a sector of a circle, centre maths symbol O, radius 12 cm. AOB is 55°.

(a)

Find the area of the shaded region.

[4]

Answer

(b)

Find the perimeter of the shaded region.

[6]

Answer

$Question 21, shown as an image$

(a)

Show algebraically that the x-coordinates of the points of intersection of

• the curve with equation y maths symbol g(x), and • the line with equation y h¹(x),

are solutions of the equation

[3]

Answer

(b)

Use an algebraic method to find the x-coordinates of the points of intersection of

• the curve y maths symbol g(x), and • the line y h¹(x).

Give your answers correct to 2 decimal places.

You must show all your working.

[3]

Answer

The diagram shows the velocity, v metres per second, of a particle t seconds after it passes a fixed point.

$Question 22, shown as an image$

(a)

Calculate an estimate of the acceleration of the particle when t = 3·5 seconds.

[3]

Answer

(b)

Use five vertical strips of equal width to estimate the distance travelled by the particle in

the first 5 seconds after it passes the fixed point.

[4]

Answer

Eduqas C300 · Component 2H

Question 1

Question 2

Question 3

Question 4

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Question 6

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Question 10

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Question 22