Eduqas GCSE Maths Component 1H Higher November 2020 question paper

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Peter and Paula record the number of cars in each of two airport car parks, A and B, between 8 a.m. and 12 noon one Saturday morning. This was done to find out if there was a peak time for parking during that period. The table shows the data they collected.

Time	8 a.m.	9 a.m.	10 a.m.	11 a.m.	12 noon
Number of cars in car park A	178	179	183	180	179
Number of cars in car park B	176	175	181	177	176

Paula draws this graph to represent the data.

Peter says, “This graph is not sensible as it does not show the data fairly.”

(a)

What has been done in the drawing of the graph that has made Peter think this?

[1]

Answer

(b)

What error might this lead to, for people who do not look carefully at the graph?

[1]

Answer

Lena makes a fruit drink by mixing orange juice, pineapple juice and sparkling water in the ratio

orange: pineapple: water = 3: 2: 7.

(a)

What fraction of the mix is water?

[1]

Answer

(b)

Lena pours 300 ml of her fruit drink into a glass.

How much pineapple juice is in Lena’s glass?

[2]

Answer

$Question 3, shown as an image$

Give your answer as a mixed number in its simplest form.

[3]

Answer

(a)

4. (a) Simplify 18 maths symbol ÷ 9.

[1]

Answer

(b)

The diagram shows two circles, one inside the other.

The radius of the outer circle is 6 cm. The radius of the inner circle is 5 cm.

Work out the area of the shaded region.

Give your answer in terms of maths symbol .

$Question 4, shown as an image$

[3]

Answer

$Question 5, shown as an image$

A camera is attached to a tripod.

The tripod has a weight of 34 N. The camera has a weight of 20 N.

Each foot of the tripod is a rectangle with length 3 cm and width 2 cm.

Work out the pressure exerted by the tripod and camera on the ground.

You must show all your working.

$Question 5, shown as an image$

[5]

Answer

(a)

6. (a) Eric currently spends £36 each week playing ten pin bowling. He wants to decrease this amount by $fraction$ He writes:

(a)(i)

Explain why Eric’s method is not correct.

[1]

Answer

(a)(ii)

[1]

Answer

(b)

Three integers a, b and c are in the ratios

a: b = 9: 2 and b: c = 6: 7.

It is known that a + b + c = 200.

Find the integers a, b and c.

$Question 6, shown as an image$

[3]

Answer

Ivan is part of a team making bags of free items to give away at a college open evening.

He has: • 140 discount vouchers, • 56 pencils, • 280 sweets to share between all his bags.

He uses all the vouchers, all the pencils and all the sweets. He makes as many bags as possible. The contents of each bag are the same.

How many bags does Ivan make and what does each bag contain?

$Question 7, shown as an image$

[5]

Answer

A line L has equation y maths symbol 12 4x.

Write down the equation of a different line that is parallel to L.

[1]

Answer

(a)(i)

xy maths symbol 1

Explain why neither x nor y can be zero.

[1]

Answer

(a)

(a)(ii)

On the axes below, sketch the graph of y maths symbol $fraction$

[2]

Answer

(a)(iii)

[1]

Answer

(b)

[2]

Answer

(a)

10. (a) Solve.10 maths symbol x 1 7x 9 x

[3]

Answer

(b)

Factorise and hence solve x² maths symbol 3x 18 0.

[3]

Answer

Jan’s hobbies are sewing and gardening. Each week the probability that she spends: • Monday evening sewing (S) is 0·3, • time gardening on Friday (G) is 0·6. These events are independent. The tree diagram shows this information.

Calculate the probability that, in a randomly selected week,

(a)

Jan spends Monday evening sewing but does not spend time gardening on Friday,

[2]

Answer

(b)

Jan does not spend Monday evening sewing but does spend time gardening on Friday.

[2]

Answer

(a)

12. (a) Find the next term of this sequence.

$Question 12, shown as an image$

[2]

Answer

(b)

$Question 12, shown as an image$

Find and simplify the 3rd term of this sequence.

[2]

Answer

(c)

Find the nth term of this sequence.

1·5, 3, 5·5, 9, 13·5,...

[2]

Answer

(a)

13. (a)

$Question 13, shown as an image$

Draw a diagram on the grid above to represent p + 2q.

[2]

Answer

(b)

OA = 3a and OB = 6b. The sides of triangles OAB and OCD are in the ratio 3: 1.

By writing AB and CD in terms of a and b, decide whether CD is parallel to AB.

Parallel
Not Parallel

Show how you decide.

[3]

Answer

(a)

14. $Question 14, shown as an image$

[2]

Answer

(b)(i)

Find the positive value of 1616 $fraction$

[1]

Answer

(b)

(b)(ii)

$Question 14, shown as an image$

[2]

Answer

(c)

Estimate the value of. maths symbol 3·910⁶ ³ 1

Give your answer in standard form.

[3]

Answer

(d)

$Question 14, shown as an image$

[2]

Answer

(a)

15. (a) The diagram shows the distribution of the heights, in cm, of 100 Firebird Marigold plants.

(a)(i)

How many of these Firebird Marigold plants had a height of less than 25 cm?

[1]

Answer

(a)(ii)

Use the diagram to complete the table for these Firebird Marigold plants.

[3]

Answer

(b)

This box plot shows the distribution of the heights, in cm, of 100 Marvel Marigold plants.

(b)(i)

The tallest Firebird Marigold plant had a height of 49 cm. The range of the heights of the Firebird Marigold plants was exactly 27 cm.

Use this information and the information from part (a) to draw the box plot for the

Firebird Marigold plants on the grid above.

[2]

Answer

(b)(ii)

Jules wants to buy one of these types of Marigold for her garden. She wants as many as possible of her plants to be at least 30 cm tall.

Should Jules buy Marvel Marigold or Firebird Marigold plants?

Marvel Marigold
Firebird Marigold

Give a reason for your decision.

[1]

Answer

A tennis club has 240 members.

They each played a senior, main or junior event in one of three competitions, A, B or C.

Of the club members: • 110 played in A, • 30 played in a junior event, • 25 played in the senior event in B, • no junior played in C, • 40 of those who played in C were in the main event.

The number of members who played in a senior event was 150% more than those who played in a junior event. The ratio of members who played in B and C was B: C = 6: 7. The probability that a member played in the junior event in A was 0·1.

A member is selected at random from the club.

Use the table to help you to find the probability that this member played in a Main event or played in B but not both.

You must show all your working.

$Question 16, shown as an image$

[6]

Answer

The diagram shows a sketch of a letter L.

This letter is first, reflected in the line x = 4, then reflected in the x-axis and finally

$Question 17, shown as an image$

Describe the single transformation that is equivalent to these 3 transformations. You may use this grid to help you.

[3]

Answer

(a)

18. (a)

Points A, B, C, P, Q and R lie on the circumference of the circle, centre O.

Show that triangle ABC is congruent to triangle PQR.

Give a reason for each step of your answer.

[3]

Answer

(b)

[1]

Answer

[2]

Answer

(a)

Find the number of different ways in which this can be done.

[2]

Answer

(b)

One of her tokens is pink and another is green.

Find the number of arrangements where the middle token is pink or green.

[2]

Answer

(a)

21. $Question 21, shown as an image$

Show that f maths symbol ¹x 1 has no solutions.

[3]

Answer

(b)

g maths symbol x 5^x

$Question 21, shown as an image$

[4]

Answer

Calculate the length of AC.

Give your answer as a surd in its simplest form.

[5]

Answer

In this question, all lengths are in centimetres.

The diagram shows a sketch of a circle, centre O. Points A, B, C, D, E and F lie on the circumference of the circle. Triangles AOB, BOC, COD, DOE, EOF and FOA are congruent.

$Question 23, shown as an image$

Calculate the perimeter of the hexagon ABCDEF.

You must justify any decisions that you make.

[4]

Answer

The velocity, v m/s of a particle, t seconds after it begins to move is given by

$Question 24, shown as an image$

(a)

The diagram shows the graph of the velocity of this particle.

Velocity,

Find an estimate for the acceleration of the particle at t = 6.

[3]

Answer

(b)

Velocity,

(b)(i)

Use five vertical strips of equal width to calculate an estimate of the area of the

shaded region.

[4]

Answer

(b)(ii)

What does this area represent?

[1]

Answer

(a)

[3]

Answer

(b)

Write down the coordinates of the turning point of the curve. y maths symbol x² 8x

Turning point = (_........,_........)

[2]

Answer

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Eduqas C300 · Component 1H

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