Pre Public Examination

GCSE Mathematics (Edexcel style) March 2017 Higher Tier Paper 1H

Worked Solutions

Name ……………………………………………………………… Class ………………………………………………………………

TIME ALLOWED 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES

Answer all the questions.

Read each question carefully. Make sure you know what you have to

do before starting your answer.

You are NOT permitted to use a calculator in this paper.

Do all rough work in this book.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each

question or part question on the Question Paper.

You are reminded of the need for clear presentation in your answers.

The total number of marks for this paper is 80. © The PiXL Club Limited 2017 This resource is strictly for the use of member schools for as long as they remain members of The

PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after

membership ceases. Until such time it may be freely used within the member school. All opinions

and contributions are those of the authors. The contents of this resource are not connected with nor

endorsed by any other company, organisation or institution.

Qu

estion

Ma

rk

Ou

t of

1 3

2 5

3 5

4 6

5 6

6 4

7 3

8 2

9 3

10 1

11 2

12 3

13 4

14 3

15 4

16 2

17 4

18 3

19 5

20 3

21 3

22 3

23 3

Total 80

2

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

Question 1.

Work out 3

- 1

-

=

-

M1

=

M1

1

A1

(Total 3 mark)

Question 2.

The graph gives the values of y for values of x from 0 to 8.

(a) (i) Give an interpretation of the intercept of the graph on the y-axis.

When x = 0 y = 1.5 or starting point is 1.5 C1

(ii) Give an interpretation of the gradient of the graph.

For every one value of x, y increases by 0.5 C1

(2)

1

2

3

4

5

6

3 4 5 6 7 8 1 2 0

y

x

3

(b) Find the equation of the straight line in the form y = m x + c

Gradient 0.5 ÷ 1 = 0.5 M1

y = 0.5x + C M1

y = 0.5x + 1.5 A1

(3)

(Total 5 marks)

Question 3.

The diagram shows the plan of a field.

The farmer sells the field for £3 per square metre.

Work out the total amount of money the farmer should get for the field.

100 × 75 = 7500 P1

160 – 75 = 85

100 – 30 = 70 M1

(85 × 70) ÷ 2 = 2975 M1

7500 + 2975 = 10475 M1

10475 × 3 = 31425

£31425 A1

(Total 5 marks)

4

Question 4.

Here is part of a railway timetable.

Departure Times

Newcastle

0840

0935

1040

1122

York

0943

1034

1144

1225

Leeds

1010

–

1210

–

Derby

1124

1157

1324

1355

Birmingham

1215

1315

1415

1515

A train leaves Newcastle at 1040.

(a) How long is the journey to Birmingham for this train?

Give your answer in hours and minutes.

10.40 to 11.00 is 20min P1

11.00 to 14.00 is 3hrs M1

14.00 to 14.15 is 15min

3hrs + 20min + 15min

3hrs 35mins A1

(3)

(b) The train ticket from York to Derby costs £64 plus 2.5% booking fee.

Workout how much a ticket from York to Derby will cost in total.

64 ÷ 10 = 6.40 P1

6.40 ÷ 2 = 3.20

3.20 ÷ 2 = 1.60 P1

64 + 1.60 =

£65.60 A1

(3)

(Total 6 marks)

5

Question 5.

The diagram shows a rectangular garden with a path around the edge.

Farhan is going to cover the path with rectangular tiles.

Each tile is 25 cm by 10 cm.

He chooses to tile the path in white, red and black colours.

The ratio of the number of white tiles to the number of red tiles to the number of black tiles will be 5 : 3 : 4.

(a) Assuming there are no gaps between the tiles, how many tiles of each colour will Farhan need?

800 × 220 = 176000

500 × 130 = 65000 B1

176000 – 65000 = 111000cm2

25 × 10 = 250cm2

111000 ÷ 250 = 444 tiles M1

444 ÷ 12 = 37 1 part M1

37 × 5 = 185 white tiles M1

37 × 3 = 111 red tiles

37 × 4 = 148 black tiles

white tiles 185

red tiles 111

black tiles 148 A1

(5)

Farhan is told that he should leave gaps between the tiles.

(b) If Farhan leaves gaps between the tiles, how could this affect the number of tiles he needs?

He will need less tiles C1

(1)

(Total 6 marks)

8m

2.2m

5m

1.3m Lawn

6

Question 6.

Judy drove from her home to the airport.

She waited at the airport. Then she drove home.

Here is the distance-time graph for Judy’s complete journey.

(a) What is the distance from Judy’s home to the airport?

40km B1

(1)

(b) For how many minutes did Judy wait at the airport?

45 minutes B1

(1)

(c) Work out Judy’s average speed on her journey home from the airport.

Give your answer in kilometres per hour.

40 ÷ 0.5 M1

80 kilometres per hour A1

(2)

(Total 4 marks)

7

Question 7.

Write 420 as a product of its prime factors.

M1 for a correct start to a factor tree (2 correct branches)

M1 for a fully correct tree or correct factors as a list

2 × 2× 3 × 5 × 7 A1

(Total 3 marks)

Question 8.

Shape A is translated by the vector ( ) to make Shape B.

Shape B is then translated by the vector ( ) to make Shape C.

Describe the single transformation that maps Shape A onto Shape C.

3 + -5 = -2

-4 + -1 = -5 M1

( ) A1

(Total 2 marks)

42 10

6 7 2 5

3 2

420

8

Question 9.

To complete a task in 15 days a company needs 4 people each working for 8 hours per day.

The company decides to have 5 people each working for 6 hours per day.

Assume that each person works at the same rate.

How many days will the task take to complete?

You must show your working.

4 × 8 = 32

32 × 15 = 480hrs P1

5 × 6 = 30hrs is one day M1

480 ÷ 30

16 days A1

(Total 3 marks)

Question 10.

Find the value of

1/

1/√

= 5

1/52 =

1/25 A1

(Total 1 mark)

9

Question 11.

The table shows information about the heights of 40 bushes.

Height

(h cm)

Cumulative

Frequency

170 h < 175 5

170 h < 180 23

170 h < 185 35

170 h < 190 39

170 h < 195 40

On the grid below, draw a cumulative frequency graph for your table.

B1 for at least 3 points plotted correctly

B1 for correct cumulative graph drawn

(Total 2 marks)

40

30

20

10

0170 175 180 185 190 195

Height ( cm)h

Cumulative

frequency

X

X

X

X X

10

Question 12.

In a sale, the price of a television is reduced.

The television has a normal price of £1235.

The television has a sale price of £988.

Work out the percentage reduction in the price of the television.

988 ÷ 1235 P1

(988 ÷ 1235) × 100 = 80% M1

100 – 80

20% A1

(Total 3 marks)

Question 13.

Prove that (n + 1)2– (n – 1)

2 + 1 is always odd for all positive integer values of n.

(n + 1)2– (n – 1)

2 + 1

n2 + 2n + 1 – (n

2 -2n +1) + 1 P1

n2 + 2n + 1 – n

2 + 2n -1 + 1 M1

4n + 1 M1

Any number multiplied by 4 is even. Add 1 will make it odd number. C1

(Total 4 marks)

11

Question 14.

Write 0.3 ̇ ̇ as a fraction in its simplest form.

x = 0.3 ̇ ̇

10x = 3. ̇ ̇

1000x = 356. ̇ ̇ M1

990x = 353 M1

x =

A1

(Total 3 marks)

Question 15.

The equation of a curve is y = f(x) where f(x) = x2– 8x + 21.

Write down the coordinates of the minimum point of this curve.

f(x) = x2– 8x + 21

f(x) = (x – 4)2 – 16 + 21 P1

f(x) = (x – 4)2 + 5 P1

Substitute x = 4, f(x) = (4 – 4)2 + 5

y = 5 M1

(4,5) A1

(Total 4 marks)

12

Question 16.

Expand (3x + 1) (2x – 2) (3x + 4)

(3x + 1) (2x – 2) (3x + 4)

(6x2 – 4x – 2) (3x + 4) M1

18x3 + 24x

2 - 12x

2 – 16x – 6x – 8

18x3 + 12x

2 – 22x – 8 A1

(Total 2 marks)

13

Question 17.

The tangent DB is extended to T.

The line AO is added to the diagram. Angle TBA = 62° and BDC = 40°

(a) Work out the value of x.

The angle between a tangent and a radius is 90° therefore OBT is 90.

ABO = 90 – 62 = 28° M1

AOB is isosceles triangle therefore angle ABO=OAB.

AOB = 180 – (28+28)

124° A1

(2)

(b) Work out the value of y.

360 – (90+90+40) = 140

360 – (140+124) = 96 M1

180 – 96 = 84

84 ÷ 2 =

42° A1

(2)

(Total 4 marks)

14

Question 18.

In the diagram, the lines AC and BD intersect at E.

AB and DC are parallel and AB = DC.

Prove that triangles ABE and CDE are congruent.

Angle BAC = ACD alternate angles are equal. P1

Angle ABD = BDC alternate angles are equal P1

AB = DC

Therefore AAS both triangles are congruent. C1

(Total 3 marks)

x

x y

y

15

Question 19.

Solve these simultaneous equations

y2 + x

2 = 10

y = x – 2

(x – 2)2 + x

2 = 10 P1

2x2 – 4x – 6 = 0 M1

(2x – 6) (x + 1) = 0 M1

x = 3 & x = -1 M1

Substitute into y = x – 2

y = 1 and y = -3

x = 3 y = 1

or x = -1 y = -3 A1

(Total 5 marks)

16

Question 20.

Express (2 – 3)2 in the form b + c3, where b and c are integers to be found.

(2 – 3) (2 – 3) P1

4 – 23 – 23 + 3 M1

7 – 43 A1

(Total 3 marks)

17

Question 21.

The curve with equation y = f(x) is translated so that the point at (0, 0) is mapped onto the point (2, 0).

(a) Find an equation of the translated curve.

y = f(x – 2) B1

(1)

(b) Write down the coordinates of the minimum point of the curve with the equation

y = f(x + 5) + 6

3 – 5 = -2

-4 + 6 = 2

(-2 , 2) A2

(2)

(Total 3 marks)

18

Question 22.

(a) How many plants are represented by the histogram?

(10 × 1.5) + (5 × 5) + (10 × 2.5) + (10 × 2) + (5 × 1)

15 + 25 + 25 + 20 + 5 = 90

90 B1

(1)

(b) Estimate the median height of the plants.

90 ÷ 2 = 45

Use graph to find height of 45th

plant M1

22 A1

(2)

(Total 3 marks)

19

Question 23.

There are three different types of sandwiches on a shelf.

There are:

4 egg sandwiches,

5 cheese sandwiches

and 2 ham sandwiches.

Erin takes at random 2 of these sandwiches.

Work out the probability that she takes 2 different types of sandwiches.

1 – (CC + HH + EE) P1

10

4

11

5 +

10

1

11

2 +

10

3

11

4 P1

1 -

or

A1

(Total 3 marks)

TOTAL FOR PAPER IS 80 MARKS