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 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 cmPR = 4 cmand 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.
Time (minutes) / 63 / 55 / 51 / 40 / 38 / 30 / 25 / 19 / 12
(a)Plot this information as points on a scatter diagram.
(1 mark)
(b)Describe the relationship between the room temperature and the time it takes an ice cube to melt.
The hotter the room, the less time it takes an ice-cream to melt
......
......
(1 mark)
(c)Draw a line of best fit on the scatter diagram.
(1 mark)
(d)Use your line of best fit to estimate the time it will take for an ice cube to melt when the room temperature is 15 C.
...... minutes
(1 mark)
(e)Use your line of best fit to estimate the room temperature when an ice cube took 19 minutes to melt.
...... C
(1 mark)
(f)Explain why it would be silly to use the line of best fit to estimate the time it would take for an ice cube to melt when the room temperature is 35 C.
Can’t assume the same linear relationship holds at higher temperatures
......
......
(1 mark)
10.Work out an estimate for the value of
100
......
(2 marks)
11.Solve the equation
(a)4y = 12
3
y = ......
(1 mark)
(b)p – 2 = 6
8
p = ......
(1 mark)
(c)5x – 2 = 18
4
x = ......
(2 marks)
(d)5n – 3 = 7 + 2n
3
n = ......
(2 marks)
(e)7(t – 2) = 5 – 4t
1
t = ......
(3 marks)
(f)7 – = 12
–3
m = ......
(2 marks)
(g) + 3 = 11
–
s = ......
(3 marks)
12.The graph can be used for converting between pounds sterling (£) andKenyan shillings (K).
K3000
2000
1000
O
5 / 10 / £Use the graph to
(i)convert £5 to Kenyan shillings,
1000
...... Kenyan shillings
(ii)convert 2000 Kenyan shillings to pounds,
10
£......
(iii)convert £340 to Kenyan shillings,
68 000
...... Kenyan shillings
13.James went for a ride on his bicycle.
He rode from his home to the river.
The travel graph below shows part of his journey.
km16
14
12
10
8
6
4
2
1400 / 1500 / 1600 / 1700 / 1800 / 1900 / 2000
(a)Write down the time at which James arrived at the river.
1500
......
(1 mark)
James left the river at 1800
He rode home at a steady speed of 8 km/h.
(b)Complete the travel graph.
(2 marks)
14.The diagram represents a biased spinner.
When the spinner is spun once information about the probabilities of it stopping on the various sections is given below.
Section / A / B / C / D / EProbability / 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
AB
(2 marks)
18.(a)Write the number 1500 as the product of its prime factors.
3
15
5
15002
10
1005
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.
(a)Write down the scale factor of the enlargement.
2
......
(1 mark)
(b)On the grid, complete triangle B.
(2 marks)
Triangle A is enlarged by scale factor , centre (8, 9) to give triangle C.
(c)On the grid, draw triangle C.
(2 marks)
20.(a)Solve the inequality
3x – 2 < 17
x < 6
......
(2 marks)
(b)Solve the inequality
5t + 1 2t – 11
t –4
......
(2 marks)
21.
The diagram represents a solid cube.
Draw a plane of symmetry on the diagram.
(2 marks)
22.
The triangle labelled T is reflected in the mirror line y = x to create a triangle S.
Draw the triangle S
(2 marks)
23.
The shape labelled A is transformed to create the shape labelled B.
Describe this transformation as fully as possible.
......
90 rotation clockwise about (0, 0)
......
......
(3 marks)
24.Solve the simultaneous equations
5x – 3y = 21
2x + y = 4
3–2
x = ...... , y = ......
(4 marks)
25.Solve the simultaneous equations
6p + 2q = 21
4p + 3q = 19
23
p = ...... , q = ......
(4 marks)
26.Evaluate 56 53
125
......
(2 marks)
27.Here are some expressions:
ab2 / abc / ab + c / /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 HardingeHigh School.
The table below provides information about the normal means by which these students travel to school.
Means of travel / Frequency / AngleWalk / 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 / Frequency0 < 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 Frequencyup 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.
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.
10 / 20 / 30 / 40 / 50 / 60Mark
(3)
32.Work out the value of .
Give your answer correct to 3 significant figures.
6.62
......
(3 marks)
33.(a)Simplify
(i)5n + 3n – 4n
4n
......
(ii)4(x + 3y) – (x – y)
3x + 13y
......
(3 marks)
(b)Find the value of
(i)4x + 3y when x = 4 and y = 5
31
......
(ii)3t – 5s when t = 2 and s = –5
25
......
(4 marks)
34.In the sales, a shop reduces all its prices by 20%.
The price of a coat before the sales was £90
(a)Work out the price of the cost in the sales.
72
£......
(2 marks)
Helena bought a pair of shoes in the sale for £44.
(b)Work out the price of these shoes before the sales.
55
£......
(2 marks)
35.Jacqui has a part-time job.
This week she is paid £70
Next week she will receive a rise of 8%
Work out how much she will be paid next week.
75.60
£......
(2 marks)
36.The selling price of a video is the list price plus VAT at 17%.
The list price of a video is £240
(a)Work out the selling price of this video.
282
£......
(2 marks)
The selling price of a second video is £411.25
(b)Work out the list price of this second video.
350
£......
(2 marks)
37.Mrs Aziz bought a new car for £12 000
The value of the car depreciated by 15% per year.
Work out the values of Mrs Aziz’s car after 3 years.
7369.50
£......
(3 marks)
38.£300 is invested for 4 years at 5% per annum compound interest.
Work out the total interest earned over the 4 years.
64.65
£......
(3 marks)
39.Mark and Jenny bought a new flat for £60 000
For the first two years the value of the flat increased by 8% per annum.
In the third year the value of the flat depreciated by 6%.
Work out the value of the flat at the end of three years after it was bought by Mark and Jenny.
65 784.96
£......
(4 marks)
40.Work out the simple interest on £500 when it is invested for 6 years at a rate of 4% per year.
120
£......
(2 marks)
41.ABC is a right-angled triangle.
AB = 7 cm, BC = 15 cm and angle ABC = 90
Work out the length of AC.
16.55
...... cm
(3 marks)
42.The diagram shows the relative positions of the three towns Prestown, Queensville and Roywell.
Prestown is due West of Queensville.
Roywell is 32 km due South of Queensville.
The straight line distance from Prestwon to Roywell is 57 km.
Work out the distance from Queensville to Prestown.
47.17
...... km
(3 marks)
43.ABCD is a rectangle.
AB = DC = 8 cm.
The area of ABCD = 120 cm2.
(a)Work out the length of each of the diagnonals AC and BD of the rectangle.
17
...... cm
(5 marks)
(b)Work out the area of the smallest circle in which the rectangle ABCD can be fully enclosed.
226.98
...... cm2
(4 marks)
44.The diagram represents a semi-circle of radius 5 cm.
Work out the perimeter of this semi-circle.
15.71
...... cm
(3 marks)
45.
The diagram represents the face of a church door.
The door consists of a rectangle with a semi-circular top.
The height of the door is 2.9 m.
The width of the door is 1.4 m.
(a)Work out the area of the face of the door.
Give your answer is square metres and correct to two decimal places.
4.62
...... m2
(6 marks)
The door has a uniform thickness of 6 cm.
(b)Work out the volume of the door.
Give your answer in cubic metres.
0.2772
...... m2
(2 marks)
The door is made of metal of density 7500 kg/m3
(c)Work out the mass of the door.
Give your answer correct to the nearest kg.
2079
...... kg
(2 marks)
46.The diagram represents a semi-circle with a radius 4 cm.
Work out the area of the semi-circle.
Leave your answers in terms of .
8
...... cm2
(2 marks)
47.The diagram represents a cylinder.
The cylinder has a length of 53 cm and a radius of 24 cm.
Work out the volume of the cylinder.
Give your answer in cm3 and correct to 3 significant figures.
95 900
...... cm3
(2 marks)
48.Rearrange the formula
y = 3x – 7
to make x the subject.
x = ......
(2 marks)
49.Rearrange the formula
y = 3x² – 7
to make x the subject.
x = ......
(2 marks)
50.
Use the method of trial and improvement to find the positive solution of
x3 + x = 37
Give your answer correct to 1 decimal place. (3 marks)
x / x³ + x2 / 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) / Frequency0 < 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
On the grid below, draw a front elevation of the prism.
(Total 3 marks)
57. Triangle ABC is similar to triangle PQR.
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
1