Eduqas GCSE Maths Component 2H Higher November 2020 question paper

(a)

[2]

Answer

(b)

Emma buys another car for £8495. Its value decreases by 16% each year.

What is the car’s value after 11 years?

[3]

Answer

This pattern is made from a regular seven-sided polygon surrounded by squares and isosceles triangles.

Show that the value of x is 64·3 correct to 1 decimal place.

You must show all your working.

[4]

Answer

Rashid plays a game. Each time he can score 1 point, 5 points or 10 points. The table shows the probability of each outcome.

Points	Probability
1	0·80
5	0·15
10	0·05

Rashid plays the game 40 times.

How many times does he expect to score more than 1 point?

[3]

Answer

[3]

Answer

The graph shows the number of copies of a local newspaper sold over a 25-year period.

(a)

Eva uses the graph to predict that about 10 thousand newspapers will be sold in 2025.

Explain why her prediction may not be reliable.

[1]

Answer

(b)

The ratio of adults who read news online to those who do not is 16: 9. The adult population of the UK is about 52 000 000.

Calculate an estimate of the number of adults in the UK who read news online.

[2]

Answer

[5]

Answer

Cheng stands at O and rolls a ball along the horizontal ground.

The ball stops at point B, which: • is equidistant from X and Y, • lies on the bisector of angle XOY.

Use a ruler and a pair of compasses to construct suitable lines and arcs to show the position of point B.

Construction arcs must be clearly shown.

[5]

Answer

The diagram shows two right-angled triangles.

(a)

Calculate the value of x.

[3]

Answer

(b)

Calculate the value of y.

[3]

Answer

The speed limit on a road is decreased from 70mph to 50 mph. The road is 7·3 miles long.

How much longer does it take to travel along the road at 50 mph than at 70 mph?

Give your answer in minutes correct to 1 decimal place.

[4]

Answer

(a)

10. (a) 7476 football supporters watched the first match of the season.

The ratio of men: women: children was 10: 8: 3.

Show that 712 more men than women watched the match.

[2]

Answer

(b)

At the second match of the season, the ratio of adults: children was 5: 3. At the third match, $fraction$ of the supporters were adults. At which of these two matches was the proportion of adults higher?

You must show your working.

Second match
Third match

[2]

Answer

A full bottle containing 1 litre of cooking oil has mass 1270 g. 400 ml of cooking oil is used.

The bottle with the remaining cooking oil has mass 900 g.

Calculate the mass of the empty bottle.

[4]

Answer

The graph shows part of a quadratic curve.

(a)

Use the graph to write down the minimum value of y.

[1]

Answer

(b)

The curve cuts the x-axis at (1·4, 0) and (a, 0).

Calculate the value of a.

[2]

Answer

$Question 13, shown as an image$

[3]

Answer

n is a positive integer.

Prove that, for all possible values of n, (2n – 1)² is an odd number.

[2]

Answer

The mean of the data in the frequency table below is 2·7.

x	Frequency
1	a
2	5
3	1
4	b
5	2
6	3
Total	30

Work out the values of a and b.

You must show all your working.

[5]

Answer

(a)

A cone has vertical height 20 cm. The volume of the cone is 2400 cm³.

Calculate L, the slant height of the cone.

[4]

Answer

(b)

Cones A and B are mathematically similar.

The diameter of the base of cone A is 12 cm. The diameter of the base of cone B is 18 cm.

The total surface area of cone A is 300 cm².

Calculate the total surface area of cone B.

[3]

Answer

A rectangle has:

• length y cm, • perimeter 30 cm, • area 55 cm².

(a)

Form an equation in y and show that it can be simplified to y² maths symbol 15y 55 0.

[3]

Answer

(b)(i)

Use the quadratic formula to solve the equation given in part (a). Give your answers correct to 2 decimal places.

You must show all your working.

[3]

Answer

(b)

(b)(ii)

Interpret your answers in terms of the rectangle.

[1]

Answer

A pet hotel is allowed to have a maximum of 10 pets at one time. It takes only cats and dogs. Each cat requires 1 unit of accommodation and each dog requires 3 units of accommodation. For the hotel to make a profit, there must be at least 15 units occupied each day.

Let x be the number of cats and y the number of dogs in the pet hotel.

(a)

Two inequalities that represent this information are x maths symbol 0 and y 0.

Write down two further inequalities that represent the information.

[2]

Answer

(b)

[3]

Answer

(c)

One Wednesday there are enough pets staying for the hotel to make a profit.

What is the fewest number of dogs that could be in the hotel?

[1]

Answer

(a)

19. (a) Freya records how long each of 40 people can hold their breath. The results are shown in the table.

Time, s (seconds)	Frequency
0 s 20	5
20 s 30	13
30 s 45	10
45 s 70	7
70 s 100	5

Freya wants to draw a histogram for this data. This is the graph she draws.

Has Freya drawn a histogram?

Yes No

Give a reason for your answer.

[1]

Answer

(b)

In one month, 2000 patients visited a doctors’ surgery. This histogram shows information about the length of time, t minutes, these 2000 patients spent at the surgery.

The group 0 maths symbol t 5 represents 120 patients.

How many patients are represented by the group 30 maths symbol t 40?

[2]

Answer

(a)

20. (a) On any working day, the probability that Don oversleeps in the morning is 0·3.

When he oversleeps, the probability that he catches his train to work is 0·25. When Don does not oversleep, he always catches his train.

Work out the probability that, on a randomly chosen working day, Don catches his train

to work.

[3]

Answer

(b)

Don sometimes spends his evenings watching films, playing computer games, or doing both.

On any evening the probability that Don: • watches films is 0·25, • plays computer games is 0·45, • does neither is three times the probability that he does both.

(b)(i)