Edexcel GCSE Mathematics Intermediate Tier revision questions



St Edmund Campion Mathematics Department

Year 11 Intermediate

Revision Pack:

Answers

1. (a) A company has 27 offices.

The company buys a new fax machine for each office.

The cost of each fax machine is £238

Work out the cost of the 27 fax machines.

6426

£..................................

(3 marks)

(b) The cost of hiring a boat is £774

This cost is to be shared between a group of 43 people.

Work out each person’s share of the cost.

18

£..................................

(3 marks)

2. The first five terms of an arithmetic sequence are

1, 4, 7, 10, 13

(a) Write down the next two numbers in the sequence.

16, 19

..................................

(1 mark)

(b) Write down the 50th number in the sequence.

148

..................................

(2 marks)

(c) Write down an expression for the nth term of the sequence.

3n – 2

..................................

(2 marks)

3. A pen costs 25p from a retailer.

Sam bought 20 pens from the retailer.

He sold them at a profit of 20%

(a) Work out the total amount Sam received when all 20 of the pens had been sold.

£6.00

..................................

(3 marks)

(b) Work out the number of pens that can be bought from the retailer for £160.

640

..................................

(2 marks)

(c) Work out [pic] of £160.

£120

..................................

(3 marks)

4. ABC is a triangle.

AB = 9 cm, AC = 6 cm, Angle BAC = 64(

In the space below, make an accurate drawing of the triangle ABC.

Measure and records the length of the side BC.

9.7 cm

BC = ..................................

(4 marks)

5. Using ruler, compasses and pencil only, construct, in the space below, the triangle PQR with

PQ = 12 cm PR = 4 cm and the angle QPR = 90(.

Measure and record the length of QR.

QR = ..................................

(4 marks)

6. The diagram represents a bottle.

Water is to be poured into the bottle at a constant rate.

Sketch the graph of the height, h, of the water in the bottle against the time, t, as the water is being poured into the bottle.

h

t

(2 marks)

7. Jenny has a bag of 20 coloured beads.

6 of the beads are red, 8 of the beads are blue, 1 bead is white and the remainder of the beads are yellow.

Jenny selects a bead at random.

Work out the probability of the selected bead being

(i) white

1/20

...............................

(ii) red

3/10

...............................

(iii) either blue or yellow

13/20

...............................

(iv) not blue

3/5

...............................

(v) green

0

...............................

(7 marks)

8. A pencil costs 12 pence.

An eraser costs 25 pence.

Mrs Ellis bought x pencils and y erasers.

The total cost was C pence.

(a) Write a formula connecting C, x and y.

C = 12x + 25y

...............................

(2 marks)

C = 246 and y = 6

(b) Work out the value of x.

8

x = ...............................

(2 marks)

9. The table below provides information about the time taken by some ice cubes to melt at certain room temperatures.

|Room |9 |11.5 |13 |17 |18 |20 |21 |22 |

|Tempera| | | | | | | | |

|ture | | | | | | | | |

|((C) | | | | | | | | |

| | | | | | | | | |

|3000 | | | | | | | | |

| | | | | | | | | |

| | | | | | | | | |

| | | | | | | | | |

|2000 | | | | | | | | |

| | | | | | | | | |

| | | | | | | | | |

| | | | | | | | | |

|1000 | | | | | | | | |

| | | | | | | | | |

| | | | | | | | | |

| | | | | | | | | |

|O | | | | | | | | |

| | |5 | |10 | |

|Probability |0.23 |0.18 |0.26 |0.17 | |

(a) Work out the probability of the spinner stopping on section E when it is spun once.

0.16

..................................

(2 marks)

The spinner is to be spun 1000 times.

(b) Work out, with reasons, an estimate for the most likely number of times it will stop on Section A.

230

..................................

(2 marks)

15. The diagram shows the plan of a floor space.

(a) Work out the perimeter of the floor space.

32

.............................. m

(2 marks)

(b) Work out the area of the floor space.

83

.............................. m2

(2 marks)

16.

The diagram shows an oil tank in the shape of a cuboid.

The measurements of the oil tank are 40 cm by 60 cm by 40 cm.

Work out the volume of the oil tank.

96 000

.................................. cm3

(2 marks)

17. a) Draw the perpendicular bisector of the line AB

b) Draw the locus of all points equidistant from lines AC and AB

A B

(2 marks)

18. (a) Write the number 1500 as the product of its prime factors.

3

15

5

1500 2

10

100 5

2

10

5

1500 = 3 × 5 × 2 × 5 × 2 × 5 = 2² × 3 × 5³

22 ( 3 ( 53

..................................

(2 marks)

(b) Work out the Highest Common Factor of 1500 and 72

24

..................................

(3 marks)

1500 = 2 × 2 × 3 × 5 × 5 × 5

72 = 2 × 2 × 2 × 3 × 3

HCF = 2 × 2 × 3 = 12

19. Triangle A is shown on the grid.

Triangle A is enlarged, centre (0, 0), to obtain triangle B.

One side of triangle B has been drawn for you.

| | | | | |

|V( |V( |None |L |V ( |

The letters a, b and c represent lengths.

Tick (() each expression which could represent a volume.

(3 marks)

28. There are 120 students in Year 11 at Hardinge High School.

The table below provides information about the normal means by which these students travel to school.

|Means of travel |Frequency |Angle |

|Walk |30 |90 |

|Bus |40 |120 |

|Car |25 |75 |

|Cycle |16 |48 |

|Train |9 |27 |

(a) Draw a pie chart to represent this information.

(4 marks)

The Headteacher of Hardinge High School selects the name of one of the Year 11 students at random.

(b) Work out the probability of that selected student normally travelling to school by bus or car.

13/24

......................................

(2 marks)

29. Work out 45% of £240

108

£...................................(2 marks)

30. A survey is conducted of the speeds of 160 vehicles using a main road.

The results of the survey are given in the table below.

|Speed (s) in mph |Frequency |

| 0 < s ( 10 |4 |

|10 < s ( 20 |16 |

|20 < s ( 30 |23 |

|30 < s ( 40 |47 |

|40 < s ( 50 |38 |

|50 < s ( 60 |17 |

|60 < s ( 70 |12 |

|70 < s ( 80 |3 |

(a) Complete the cumulative frequency table for this data.

|Speed |Cumulative Frequency |

| up to 10 mph |44 |

| up to 20 mph |2020 |

| up to 30 mph |43 |

| up to 40 mph |90 |

| up to 50 mph |128 |

| up to 60 mph |145 |

| up to 70 mph |157 |

| up to 80 mph |160 |

(b) Draw the cumulative frequency diagram for this data.

(2 marks)

(c) Use your cumulative frequency diagram to work out estimates for

(i) the median speed of the vehicles

............................... mph

(ii) the median speed of the vehicles

............................... mph

(3 marks)

31. 200 students took a test.

The cumulative frequency graph gives information about their marks.

[pic]

The lowest mark scored in the test was 10.

The highest mark scored in the test was 60.

Use this information and the cumulative frequency graph to draw a box plot showing information about the students’ marks.

| | | |

| | | |

|2 |10 | |

|3 |30 | |

|4 |68 | |

|3.5 |46.375 | |

|3.4 |42.704 | |

|3.3 |39.237 | |

|3.2 |35.968 |Answer = 3.2 |

51. Sharon has 12 computer discs. Five of the discs are red.

Seven of the discs are black. She keeps all the discs in a box.

Sharon removes one disc at random. She records its colour and replaces it in the box.

Sharon removes a second disc at random, and again records its colour.

(a) Complete the tree diagram.

(b) Calculate the probability

that the two discs removed

i) will both be red,

ii) will be different colours.

52. The grouped frequency table shows information about the number of hours worked

by each of 200 headteachers in one week.

|Number of hours worked (t) |Frequency | | |

|0 < t ( 30 | 0 |15 |0 |

|30 < t ( 40 | 4 |35 |140 |

|40 < t ( 50 | 18 |45 |810 |

|50 < t ( 60 | 68 |55 |3740 |

|60 < t ( 70 | 79 |65 |5135 |

|70 < t ( 80 | 31 |75 |2325 |

Work out an estimate of the mean number of hours worked by the headteachers

that week.

.................... hours

53. Diagrams NOT

accurately drawn

T and S are points on the circumference of a circle.

PT and PS are tangents to the circle.

Angle STP = 52(.

Angle TPS = x(.

(i) Work out the value of x.

x = ................................

(ii) Give reasons for your answer.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................

(Total 2 marks)

54. ABCDE is a regular pentagon.

AEF and CDF are straight lines.

A Diagram NOT

Accurately drawn

Work out the size of angle DFE.

Give your reason for your answer.

Angles FDE and FED are both exterior angles.

So each exterior angle = 360 ( 5 = 72º

Shape FED is an isosceles triangle so

Angle DFE 180 – 72 – 72 = 36º

(

……………

(3)

55.

P, Q and R are points on a circle, centre O.

POQ is a straight line.

TQ and TR are tangents to the circle.

Angle TQR = 56°.

(a) Explain why angle PQR = 24°.

If QT is a tangent then OQT is a right angle.

So PQR = 90 – 56 = 24º

(b) Calculate the size of angle PRT.

Give reasons for your answer.

PRQ is a right angle (90º)

If QT and QR are tangents they must be equal, which means that QRT is an isosceles triangle.

Therefore QRT = 56º as well.

So angle PRT = 90 + 56 = 146º

(3)

(Total 4 marks)

7. Here are the plan and side elevation of a prism.

The side elevation shows the cross section of the prism

| | | | | | | | | | |

| | | | | | | | | | | |

| | | | | | | | | | |

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| | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | |

On the grid below, draw a front elevation of the prism.

| | | | | | | | | | |

| | | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | | |

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| | | | | | | | | | |

| | | | | | | | | | |

| | | | | | | | | |

(Total 3 marks)

57. Triangle ABC is similar to triangle PQR.

[pic]

Angle ABC = angle PQR.

Angle ACB = angle PRQ.

Calculate the length of:

i) PQ

ii) AC

Scale factor = 5 ( 4 = 1.25

PQ = 3 × 1.25 = 3.75cm

AC = 6.5 ( 1.25 = 5.2cm

-----------------------

12 m

4 m

C

B

D

E

A

40cm

40cm

60cm

B

A

A

B

15 cm

A

C

B

7 cm

Queensville

57 km

32 km

Prestown

Roywell

A

B

C

D

8 cm

5 cm

1.4 m

2.9 m

4 cm

53 cm

24 cm

11m

5 m

[pic]

D

D

D

E

D

D

D

D

D

D

C

D

D

E

E

D

D

C

B

B

E

D

D

D

D

C

C

B

C

B

C

C

D

D

D

B

B

D

B

D

D

B

T

D

D

C

D

C

D

D

C

B

C

C

B

D

C

C

C

C

C

C

B

C

B

C

B

B

27 × 238 = 6426

774 ( 43 = 18

16, 19

0th term = -2 d = 3 T(n) = 3n – 2

T(50) = 3 × 50 – 2 = 148

10% = 2.5p 20% = 5p 30p each 20 × 30 = £6

4 pens for £1 4 × 160 = 640 pens

160 ( 4 × 3 = £120

1/20

6/20 = 3/10

13/20

12/20 = 3/5

0

C = 12x + 25y

246 = 12x + 150 x = 8

Negative Correlation

(200 × 4) ( "64 = 100

y = 3

p = 8

x = 4

3n = 10 n = 10/3 3

1/20

6/20 = 3/10

13/20

12/20 = 3/5

0

C = 12x + 25y

246 = 12x + 150 x = 8

Negative Correlation

(200 × 4) ( √64 = 100

y = 3

p = 8

x = 4

3n = 10 n = 10/3 3 1/3

11t = 19 t = 19/11 = 1 8/11

3n = -10 n = -3 1/3

s = -0.5

£12.50

500K

£3

1500

0.23 × 1000 = 230

0.16

12 + 11 + 5 + 7 + 7 + 4 = 56m

(12 × 4) + (5 × 7) = 83m²

40 × 60 × 40 = 96000cm³

x < 19/3 x < 6 1/3

3t ≥ -12 t ≥ -4

2

Rotation 90º about (0, 0)

x = 3 y = -2

p = 2.5 q = 3

5³ = 125

65/120 = 13/24

240 ( 100 × 45 = £108

6.62

4n

3x + 13y

31

31

20% = £18 90 – 18 = £72

(OR: 90 × 0.8 = £72)

Original Price × 0.8 = 44

Original price = 44 ( 0.8 = £55

70 × 1.08 = £75.60

240 ( 100 × 17.5 = 42 240 + 42 = £282

List Price × 1.175 = 411.25

List price = 411.25 ( 1.175 = £350

1200 × 0.85³ = £736.95

300 × 1.054 = £364.65

Interset = 364.65 – 300 = 64.65

60000 × 1.08² × 0.94 = £65784.96

4% = 500 ( 100 × 4 = 20

Simple interest over 6 years = 6 × 20 = £120

7² + 15² = 274 √274 = 16.6

57² - 32² = 2225 √2225 = 47.2km

120 ( 8 = 15

8² + 15² = 289 √289 = 17cm

AC or BD will be diameter = 17

Radius = 8.5

Area = π × 8.5² = 226.98

(π × 10) ( 2 = 15.71

15.71 + 10 – 25.71

(π × 0.7²) ( 2 = 0.76969020 (Semicircle)

1.4 × 1.5 = 2.1 (Rectangle)

Total = 2.1 + 0.76969020 = 2.87m²

2.87 × 6 = 17.2181412m³

Mass = density × Volume

= 17.2181412 × 7500 = 129136kg

π × 4² ( 2 = 8π

Area = π × 24² = 1809.55736

Volume = 1809.55736 × 53 = 95906.540528

= 95900

x = y + 7

3

x = √(y + 7)

3

12150 ( 200 = 60.75

5/12 × 5/12 = 25/144

(5/12 × 7/12) × 2 = 70/144

S

x(

52(

P

Exterior angles of any polygon always add up to 360º

F

D

E

C

A

B

Diagram NOT accurately drawn

Q

T

R

P

O

56(

................
................

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