Eduqas GCSE Maths Component 2H Higher June 2018 question paper

Eduqas C300 · Component 2H

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Three friends, Jane, Caroline and Eddie, each throw the same dice 40 times.

Their results are shown in the table below.

(a)

[1]

Answer

(b)

What is the best estimate of the probability of scoring a 2 on this dice?

[2]

Answer

(c)

Using Jane’s, Caroline’s and Eddie’s results, how many times would you expect a

score greater than 4 to occur in 480 throws of this dice?

[2]

Answer

(a)

2. (a) Factorise a² + 5a – 14.

[2]

Answer

(b)

Factorise b² – 25.

[1]

Answer

(c)

$Question 2, shown as an image$

[2]

Answer

1 AU is 1 astronomical unit. 1 AU = 1·496 × 10⁸ km, which is the distance from the Sun to Earth.

The distance between the planet Mercury and Earth can vary from 0·515 AU to 1·48 AU.

Complete the statement below. Use kilometres written in standard form correct to 2 significant figures.

‘The distance between the planet Mercury and Earth can vary

from........ km to........ km.’

[3]

Answer

(a)

Copper: Tin: Nickel

_........:_........:_........

[4]

Answer

(b)

You must show all your working and give a reason for your answer.

Reason:

[3]

Answer

The tourist office in Trofenberg displays the snowfall data each month in a table.

The table shows snowfall in Trofenberg for each day during January.

Snowfall, s (cm)	Number of days
0 s 20	1
20 s 40	8
40 s 60	9
60 s 80	7
80 s 100	6

(a)

Calculate an estimate for the mean daily snowfall in Trofenberg for January.

You must show all your working.

[4]

Answer

(b)

There were 9 days when the snowfall was between 40 cm and 60 cm. On each of these days, the snowfall was actually between 57 cm and 59 cm.

Explain why the estimate for the mean daily snowfall in January may still be

fairly accurate.

[1]

Answer

(a)

Calculate the length x.

[3]

Answer

(b)

Calculate the size of angle y.

[3]

Answer

$Question 7, shown as an image$

Calculate how much change Sunita would get from £40 when buying 7 shower curtains and 5 rails.

You must use an algebraic method.

Sunita’s change from £40 would be_{…………........ ……….}

[6]

Answer

(a)

Is it possible to pour all the milk from the full carton into the bottle?

You must show all your working and give a reason for your answer.

Yes No

Reason:

[5]

Answer

(b)(i)

When evaluating your result in part (a), what assumption did you make?

[1]

Answer

(b)

(b)(ii)

[1]

Answer

Adanna wants to buy a ring.

The same ring could also be made from silver. The density of the silver in the ring would be 10·48 g/cm³.

Calculate the difference in the masses of the two rings.

Difference in mass is_{………........ ……} g

[4]

Answer

Filbert rides his bike at x km/h for 15 minutes.

He then rides at (x + 2) km/h for half an hour. The last section of his ride takes a further 15 minutes at (x – 4) km/h.

Show that the total distance of Filbert’s bike ride is x km.

You must show all your working.

[4]

Answer

(a)

11. (a) Wayne says, ‘6·5 m² is the same as 650 cm², because there are 100 cm in 1 metre.’

Maria says, ‘6·5 m² is the same as 65 000 cm².’

Explain why Maria is correct.

[1]

Answer

(b)(i)

The area of the water surface of Maria’s pond is 6·5 m². She measures the depth of the pond in 5 different places using a measuring stick. The 5 depths recorded by Maria are 120 cm, 120 cm, 130 cm, 140 cm and 140 cm.

Maria buys a liquid treatment for pond water. The instructions state:

Use 0·5 litres of this treatment for every 1 800 litres of pond water.

Calculate an approximate value for the quantity of the liquid treatment Maria needs to use in her pond. You must give units at each stage of your working and give your answer in litres.

You must show all your working.

[5]

Answer

(b)

(b)(ii)

Explain any decision you made in calculating an approximate value for the quantity of the liquid treatment needed.

What could be done to improve the accuracy of this value?

Explanation of decision:

Improvement:

[2]

Answer

In a sale the prices of all jackets are reduced by 22%.

In the final week of the sale, all jackets are reduced by a further 15% of the sale price.

Abigail buys a jacket in the final week of the sale for £42.50.

What was the original price of the jacket?

Give your answer correct to the nearest penny.

[4]

Answer

$Question 13, shown as an image$

Minimum mass is_{………........ ……} g

[3]

Answer

Lewis is organising a music festival for up to 200 people.

He has investigated the charges for booking bands. The band Rightjet gives its charges using a graph, as shown below.

(a)

Find the gradient of the graph and state the units of your answer.

[2]

Answer

(b)(i)

The band Draigetal charges a fee of £60 and an additional £3 per person. On the same axes as Rightjet, draw a graph to show Draigetal’s total charges

for up to 200 people.

[2]

Answer

(b)

(b)(ii)

Let t represent the total charge, in pounds, and p represent the number of people.

Hence, write down the equation of the line you have drawn in part (b)(i).

[1]

Answer

(c)

Lewis wonders,

Complete the following statement.

‘If........ people attend, the charge would be the same for having the band

Rightjet or the band Draigetal. This charge would be £........ ’

[2]

Answer

(a)

15. (a) £500 was invested in a savings account for Harry when he was born. The compound interest paid on this account was 2·1% per annum. On his 18^th birthday he was given the full amount from the savings account.

How much money did Harry receive?

Give your answer correct to the nearest penny.

[3]

Answer

(b)

Mina was given £x, which she invested in an account paying y% compound interest per annum. How much will Mina’s investment be worth after 6 years?

Give your answer as an expression in terms of x and y.

[2]

Answer

$Question 16, shown as an image$

Find the value of C when A = 130.

[2]

Answer

Find the n th term of the following sequence.

3, 7, 13, 21, 31, 43, ….

[2]

Answer

(a)

18. $Question 18, shown as an image$

You must show each stage of your working.

[1]

Answer

(b)

Use the iteration formula

$Question 18, shown as an image$

to find a solution of x² – 13x + 9 = 0 correct to 2 decimal places.

You must give all your calculated values of x_n+1.

[3]

Answer

Kai and his mum have mathematically similar suitcases.

Kai’s suitcase is smaller than his mum’s suitcase.

The label on Kai’s suitcase says it holds 66 litres.

What should the label on his mum’s suitcase say it holds?

His mum’s suitcase holds_{………........ ………} litres.

[2]

Answer

(a)

The total area of the composite shape is 47 cm².

Show that 6x² – 3x – 47 = 0.

[3]

Answer

(b)

Use the quadratic formula to solve 6x² – 3x – 47 = 0.

Give both of your answers correct to 2 decimal places.

[3]

Answer

(c)

Calculate the perimeter of the composite shape.

You must give a reason for any decision that you make.

Decision:

Reason:

Working:

Perimeter is_{………........ ……….} cm.

[3]

Answer

Use the method of completing the square to find the coordinates of the turning point of the

curve y = x² + 12x + 57.

Coordinates of the turning point (_........,_........)

[4]

Answer

A number of girls and boys with part-time jobs answered an online survey.

One of the questions asked how long they each spent working last Friday. Histograms of these results are shown on the opposite page.

(a)

Calculate an estimate for the number of girls who worked for 45 minutes or less

last Friday.

[2]

Answer

(b)

Fred uses the results of the survey to compare the percentages of girls and boys who worked 1 hour or more last Friday.

580 girls took part in the survey.

Complete the following statement.

........ % of girls compared with........ % of boys worked for 1 hour

or more last Friday.

[6]

Answer

[10]

Answer

Score on the dice