1

Auchinleck Academy Maths Department

S3 Homework

Units 1 - 3 & Revision

Level 3/4

2

Auchinleck Academy

Mathematics

Homework 1.1

Rounding Numbers and Scientific Notation

1 Round to 1 decimal place:

a) 16.54 b) 34.88 c) 134.92 d) 5.876 e) 42.108

2 Round to 2 decimal places:

a) 89.174 b) 567.812 c) 912.675 d) 21.342 e) 67.899

3 Round to 1 significant figure:

a) 25.2 b) 324 c) 453.9 d) 67.1 e) 0.32

4 Round to 2 significant figures:

a) 678 b) 78.94 c) 5043 d) 0.0735 e) 1542.7

5 Write in standard form:

a) 32.6 b) 456000 c) 67540 d) 0.0641 e) 0.000034

6 Write in normal “floating point” form:

a) 4.5 x 103 b) 7.92 x 105 c) 8.245 x 107 d) 8.65 x 10-4 e)

6.4 x 10-3

7 Light travels one metre in 3 x 10-9 seconds. How long does it take

light to travel from the Sun to the Earth, an approximate distance

of 1.5 x 1011 metres?

3

Auchinleck Academy

Mathematics

Homework 1.2

Number and number processes (BODMAS)

Integers

1 Calculate:

a) 4 + (-3) b) -65 + 32 c) 27 + (-8) d) -12 + 5 + (-4) e) 59 – 13 –

(-3)

2 Work out:

a) 8 – 16 b) -76 - 6 c) 56 – (-4) d) 43 + 73 - 88 e) 32 – 64 –

(-2)

3 Calculate:

a) 4 x (-6) b) (-3) x 7 c) (-5) x 9 x (-2) d) 8 x 4 x (-2) e) (-1) x 12

x (-3)

4 What is the answer to:

a) 35 (-7) b) -100 10 c) 32 d) (-63) (-9) e) (-72)

(-4) (-8)

5 Find the value of:

a) 4 + 5 x (-2) b) -6 + 8 x 2 - 4 c) 16 – 4 x (-3) d) 6 + 20 ((-4)

+ 9)

6 Use each formula to calculate the value of the missing value:

a) D = S x T Find D when S = 30 and T = 16

b) Q = vR – W Find Q when v = (-5) , R = 20 and W = (-4)

c) B = A + EG Find B when A = -7, E = 9, G = (-4) and H = 6

H

4

Auchinleck Academy

Mathematics

Homework 1.3

Factors, Primes, Squares and Square Roots

1 Calculate :

a) 25 b) 34 c) 53 d) 62 e) 164

2 Find the following. If required round your answer to 2 d.p.

a) 81 b) 676 c) 128. d) 5 1024 e) 7 128

3

The square shown has an area of 289 m2

Calculate the length of one of its sides.

4 Calculate the following :

a) 63 + 54 b) 163 - 37 c) 28 ÷ 16 d) 6241 -

3969

5 Find the L.C.M. of :

a) 3, 6 and 15 b) 5, 10 and 12 c) 3, 5 and 10 d) 2, 3

and 9

6 Find the H.C.F. of :

a) 8 and 12 b) 14 and 56 c) 16, 32 and 72 d) 12, 18

and 48

7 Find the prime factors of the following :

a) 16 b) 48 c) 162 d) 1700 e) 684

Area =

289 m2

5

Auchinleck Academy

Mathematics

Homework 1.4 Areas of quadrilaterals

1. Calculate the area of each shape. Write down the Area formula for

each shape and show all your working.

a) b)

2.

c) d)

Calculate the shaded area of the given shapes. Show all working.

a) b)

6 cm

15cm 9 cm

7 cm

10 cm

12 cm

6 cm

14 cm

8 cm

14 cm

6 cm 8 cm

2 cm

12 cm

8 cm

6

Auchinleck Academy

Mathematics

Homework 1.5a

Probability

1 A die is rolled. What is the probability of getting :

a) a number less than 3.

b) a prime factor of 40.

2 A golfer has a box of coloured golf balls. It contains 8 white balls, 5

orange balls and 7 yellow balls.

a) What is the probability that the first ball he picks is an orange golf

ball?

b) If he then lost his orange ball, what is the probability the next ball

he picks from the box is also an orange golf ball?

3 Three out of eight people drive a silver car. If 400 drivers were asked,

how many of them would you expect to drive a silver car?

4 How many girls from a school roll of 420 would you expect to have been

born in the month of November?

5 A card is drawn from a standard pack of 52 playing cards.

a) What is the probability that the card picked was a black King?

b) If a black King was drawn and not replaced and a second card drawn,

what would be the probability of drawing a Diamond?

6 Mr. Dimple buys a punnet containing 36 strawberries. When he got home

he discovered that 8 strawberries were damaged.

a) What is the probability of getting a damaged strawberry?

b) Assuming the probability remains the same, how many damaged

strawberries would you expect to get in a larger punnet containing

63 strawberries?

7

Auchinleck Academy

Mathematics

Homework 1.5b

Data Analysis

1 These are the shoe sizes of eight pupils in year 7:

4, 6, 5, 3, 5, 2, 4, 7

Calculate the mean, median, mode and range for this data.

2 Johnny wants to find out how many brothers and sisters other pupils in

his class have. These are the results of his survey:

Number of

children in

family

Number of

pupils

Total number of

children

0 3 0 x 3 = 0

1 8 1 x 8 = 8

2 6

3 4

4 3

5 1

Total

a) Copy and complete the table, then calculate the mean number of

children in a family.

b) Work out the modal number of children and the range.

3 The table below shows the cost of a new car last year and the number

of purchases made.

Cost £7000 £8000 £10000 £12000 £55000

frequency 12 8 12 14 4

(a) Find the mean amount spent on a new car.

(b) Find the median amount spent on a new car.

(c) Find the modal value

(d) Which of the 3 averages is best? Justify your answer.

8

Auchinleck Academy

Mathematics

Homework 1.6

Equations and Inequalities

1.

2.

Simplify the following expressions:

a) 3x + 5 – 2x + 6 b) 3g - 5h + 6g – 2h

c) 12y – 4x – 8y + 6x d) 10a + 5 – 6b – 3a + 5b

e) 3x – 4y + 13 - 5y - 5x f) 3x2 – 4x2 + 7x2

Solve the following equations

a) 2x + 3 = 17 b) 5h – 9 = 11 c) 4 = 3y – 8

d) 8r = 72 e) 0 = 35 – 7y f) 3x + 7 = 4x

3.

4.

Solve these equations.

a) 4r = 2r + 16 b) 8t = 21 + t

c) 6y – 2 = 2y + 18 d) 3m + 4 = m + 6

Solve these inequalities where the solutions are whole numbers.

a) K + 5 › 7 b) 4y – 5 ≤ 23

c)3x – 7 ≥ = x + 11 d) 5b – 4 ‹ 17 + 2b

9

Auchinleck Academy

Mathematics

UNIT 1

MIXED Homework 1A

1 A lottery win of £9,433,914 was shared equally among 6 people.

Calculate each person’s winnings correct to 2 decimal places.

2 Calculate the following:

a) 5 + 4 ÷ 2 b) (5+4) ÷ 2 c) 4 + ( 2 + 3) x 7

3 The diameter of a brake disc manufactured should have a certain

value in order for it to fit a car wheel:

Diameter = (180 ± 25) mm

Which of the following are acceptable diameters:

(a) 149mm (b) 203mm (c) 17.56cm (d) 20.6cm ?

4 The temperature in Ayr at 6.00am was -3˚C. By mid-day the

temperature had risen by 9˚C. What was the temperature at mid –

day?

5 Calculate the following:

a) (-6) + 3 (b) 25 - (-5) (c) 9 + (-7)

6 Write the following numbers in scientific notation:

(a) 43,000,000 (b) 0.00000038 (c) ½

million

7 Write the following numbers in full:

(a) 1.7 x 107 (b) 2.03 x 105 (c) 9.12 x 10-8

(d) 5.102 x 10-4

10

Auchinleck Academy

Mathematics

UNIT 1

MIXED Homework 1B

1 Mr Cameron is building an extension onto his house. The building

materials cost £9763.42 plus VAT at 17.5%. What is the total

cost rounded to 2 decimal places?

2 Mr Golden buys 15 apples and discovers that 6 are bruised.

a) What is the probability of getting a bruised apple?

b) How many bruised apples can we expect to get in a further 40

apples?

3 List all the prime numbers between 20 and 50.

4 Find:

a) The L.C.M. of 3, 6 and 8 b) Find the H.C.F. of 12, 18 and 30

5 Find the following:

a) 23 b) 152 c) d)

6 A square has an area of 320cm2.

Calculate the length of one of its sides.

Round your answer to 2 decimal places

7 If a = 4, b = – 3 and c = 2, evaluate the following and remember

to show appropriate working.

(a) 2a – b (b) c + b (c) c3 (d) 2a2

(e) 3ac

3 27

11

Auchinleck Academy

Mathematics

UNIT 1

MIXED Homework 1C

1 Calculate :

(a) 5% of £24 (b) 8% of £200 (c) 15% of £6.40

2 a) What is the probability of being born on a Friday

b) How many pupils in a class of 28 would you expect to have been

born on a Friday?

3 a) ½ of 30 + 12 b) 24 – 10 x 2 c) 3 + (5 + 6) x 2

4 The table shows the number of sick days of all the staff in a

factory. Calculate the mean number of sick days.

Sick Days Frequency Sick days x

frequency

0 23

1 11

2 9

3 1

4 0

5 6

Total

5 The judges in a dancing competition give Gavin & Katya the

following scores:

5.6 5.4 6.0 5.8 5.6 6.0 5.4 5.9 5.8 6.0

a) i) Find the mode ii) Calculate the mean.

b) Which of these averages gives a fairer picture of their

performance?

12

Auchinleck Academy

Mathematics

UNIT 1

MIXED Homework 1D

1 If a = 4, b = – 3 and c = 2, evaluate the following and remember

to show appropriate working.

(a) 2a – b (b) c + b (c) c3 (d) 2a2 (e) 3ac

2 Do not use a calculator and show all working:

(a) 239.4 + 87.12 + 17 (b) 98.32 – 14.28 + 5.9

(c) 23.6 x 40

3 Solve the following:

(a) 7x – 2 = 40 (b) 5x + 7 = 32 (c) 42 = 3g - 3

4 If you rolled a dice 300 times, how many times would you expect to

roll a 4?

5 Find the range, mean, mode and median for the following :

(a) 14 5 7 11 3 1 14 9

(b) £11 £15 £3 £6 £2 £14 £7 £13 £11 £10 £7

13

Auchinleck Academy

Mathematics

UNIT 1

MIXED Homework 1E

1 This table shows the results of a survey into the number of people

in the families of a group of children.

No. in family (x) Frequency (f) f x x

3 5 3 x 5

4 9

5 4

6 1

7 1

Totals

a) Copy and complete the table.

b) Calculate the mean number of people per family.

c) What is the modal number of people in a family?

2 In a box of mixed crisps there are 8 plain, 3 bacon, 4 prawn, and 9

vinegar.

a) If I put my hand in without looking what is the probability of

choosing a packet of bacon crisps?

b) I pull out a packet of vinegar crisps and eat them.

What is the probability of choosing another packet of vinegar

crisps?

3 Write the following numbers in scientific notation :-

a) 195 000 b) 749 c) 7.4 million

4 Write out the following numbers in full:-

a) 2.7 x 106 b) 3 x 104 c) 5.3 x 10-5

14

Auchinleck Academy

Mathematics

Homework 2.1 Area and Circumference of a circle.

1. For each shape, calculate;

a) The circumference b) The area

i) ii) iii)

2.

3.

For the circular smiley face shown in the diagram below.

Calculate: a) the Circumference

b) the Area

The Diameter of the face is 12cm.

A circular path is built to around a pond in a local park as shown:

7 cm

12 cm

10 cm

8 cm

a) Calculate the area of the path to

the nearest m2.

b) The bricks are sold in packs which

contain 4 m2 each. How many packs

of bricks will be required to

complete the job?

7.6 m

10 m

15

Auchinleck Academy

Mathematics

Homework 2.2

Patterns and relationships.

1.

Pattern No.1 Pattern No.2 Pattern No.3

a) Draw pattern No.4

b) Copy and complete the following table.

Pattern No. (P) 1 2 3 4 5 6

No. of Straws (S) 4 7

c) For every extra pattern, how many extra straws are needed?

d) Write down the formula using symbols for calculating how many straws

are needed if you know the pattern number. S = ? x P + ?

e) Use your formula to decide how many straws are needed for

Pattern No. 15.

2.

Shape No. 1 Shape No. 2 Shape No. 3

6 Rods 11 Rods 16 Rods

a) Copy and complete the following table.

Shape No. (S) 1 2 3 4 5 6

No. of Rods (R)

b) Write down a formula using symbols for calculating how many rods are

needed if you know the shape number. R =

c) Use your formula to decide how many rods are needed for shape No. 60.

16

Auchinleck Academy

Mathematics

Homework 2.3

Time, Distance and Speed

1 Calculate the distances travelled by the following :

a) a car travelling at an average speed of 60 m.p.h. for 3hours ?

b) an athlete running at 6 km/h for 1½ hours ?

c) a plane journey of 4hours 15 minutes, at an average speed of 280

m.p.h. ?

2 Andrew left his house at 07:20. He travelled by car at an average

speed of 90 km/h and arrived at his destination at 11:50. How far

did he travel?

3 Find the average speed of these journeys:

a) a bus which travels 180km in 4 hours.

b) a ship sails 130 miles in 6½ hours.

c) a motor cyclist covers 375 km in 3hours 45 minutes.

4 Deborah flew from Glasgow to London a distance of 552 km. She

left Glasgow at 7.40 am and landed in London at 9.10am.

What was the plane’s average speed?

5

6

Calculate the time taken for each of the following:

a) a car travelling 320 km at an average speed of 64 km/h.

b) a bicycle travelling at an average speed of 24 km/h for 72 km.

c) a person walking 1700 metres at an average speed of 50m/min

Louise travelled by train from Kilmarnock to Manchester a distance

of 180 miles. If the train went at an average speed of 72 m.p.h.

calculate:

a) the time taken for the journey. (in hours and minutes)

b) If the train left Kilmarnock at 09:37. when would it arrive at

Manchester?

17

Auchinleck Academy

Mathematics

Homework 2.4 Rotational Symmetry

1.

Which of the following shapes have (i) half-turn /order 2 symmetry ?

(ii) quarter-turn/order 4 symmetry ?

a) b) c)

2.

3.

d) e) f)

Copy and complete each diagram. Rotate each shape 180˚ about the

fixed point to show half-turn symmetry.

Copy and complete each diagram. Rotate each shape about the

fixed point to show quarter-turn symmetry.

18

Auchinleck Academy

Mathematics

Homework 2.5

Data and Analysis

1 Shown is a set of results from a class test.

a) Construct an ordered stem-and-leaf diagram to represent this set

of results.

b) What is the median?

16 20 33 31 25

56 36 40 16 23

29 22 40 17 23

47 19 42 45 59

60 51 56 39 56

2 Florence spent a week at her local vet’s surgery for work experience. In

her report she decided to illustrate the types of animals which visited

the surgery. She counted 20 cats, 30 dogs, 3 rabbits, 5 birds and 2

reptiles. Copy and complete the table and then construct a pie chart. (You’ll

need a protractor.)

Animal Frequency Angle

Cat

Dog

Rabbit

Bird

Reptile

Total 360

3 At a road-safety test centre young drivers were asked to do an

emergency stop . Their instructor noted their speeds and stopping times.

Alf Bob Jim Dean Elkie Fran Gina Hugh Irene Janis

Speed

(mph)

25 39 30 27 32 34 26 35 37 28

Stopping

time(s)

2.5 3.4 2.8 2.8 2.8 3 2.7 3.1 3 2.5

a) Draw a scatter graph using the information in the table.

b) From the scatter graph write a sentence describing the

relationship between the speed and stopping time for this

group.

19

Auchinleck Academy

Mathematics

Homework 2.6

Expressions

1 Expand these brackets:

Simplify;

a) 3(a + 5) b) 7(y – 6) c) –4(3 + x) d) -9(x - y)

e) -6(3p - 2) f) x(x + 4) g) y(2y – 5) h) –a(3 – 4a)

2 Solve each equation by first removing the brackets.

a) 6(n – 3) = 12 b) 5(r + 2) = 40

c) 9 = 3(x – 8) d) 7(g + 2) = 70

e) 7(m – 1) = 2m + 3 f) 4(2t + 3) = 11x

3 Factorise these expressions;

a) 4a + 8 b) 5x - 30 c) 12 - 6y d) -3p - 15 e) -6p + 18r

4 James gets paid £x a week for his paper round. He also gets £3 a week

pocket money.

a) Write an expression that shows how much money James is given per

week.

b) Write an expression that shows how much he will be paid over 4 weeks.

Write the expression in 2 different ways (Hint; one will have a bracket)

5 Expand and simplify where possible:

a) 3(x + y + z) b) x( 2x + 3 + y) c) 6(2x – 4) + 5x c) 2(5x + 1) + 3(x +

6)

6 Factorise fully;

a) 4a + 6b + 12c b) -2x - 8y – 4z c) x2 – 3x d) 4a2 – 12a

20

Auchinleck Academy

Mathematics

UNIT 2

MIXED Homework 2A

Marks

1 Superbuy stores have a Friendly card which allows the shopper to

collect points for money spent.

One point is given for each whole £1 spent.

a) Kayleigh spends £27.26 in a Superbuy Store.

Calculate the points for this sale, and her total points.

b) When you buy petrol from Superbuy, you get 3 points for

every £5 you spend.

Points may be exchanged for goods.

c) How much must be spent on petrol to obtain an MP3 player

worth 576points?

2

A wedding invitation made up of a square and four semi-circles is to

have gold ribbon around the outside.

3 Factorise the following:

a) 4x + 12y b) 12x – 18 c) 3p + 15 d) 15a – 20ab

Previous Points 1367 Points this sale Total Points

12cm

12cm

a) How much ribbon will be required for 80

invitations?

b) The ribbon costs £0.78 per metre. What is the

total cost of the ribbon for the 80 invitations?

21

Auchinleck Academy

Mathematics

UNIT 2

MIXED Homework 2B

Marks

1 Find the area of the shapes below:

a) b)

2

Calculate the area of the following shapes:

a) b) c)

3 The area of a triangle is 84cm2. Its altitude (height) is 12cm.

Find the length of the base.

4 Find the areas of the shapes below.

a) b)

4m

1.5m

0.3m 3.4m

2.3m

5cm

20cm

15cm

4cm 16cm

12.8m

35cm

15cm

22

Auchinleck Academy

Mathematics

UNIT 2

MIXED Homework 2C

1 A tolerance is given as (… 0.6) mm.

The maximum value allowed is 32.4mm.

What must the minimum value be?

2

Given x = 6, y = 3, z = 2, evaluate the following:

a) xy + z b) x – z2 c) 3y2 – z

d) zx 3 e) x

yz f) z(2y – 2x)

3 Two out of five car owners have a diesel car. If 300 car owners are

asked, how many of them are expected to own a diesel car?

4 The play park is made up of a rectangle and triangle.

Calculate the cost of surfacing the children’s play park if the special

surface area costs £44.99 per square metre.

12m

5m

8.4m

23

Auchinleck Academy

Mathematics

UNIT 2

MIXED Homework 2D

1 The doormat below is made up from a rectangle and two semi-circles.

a) A coloured border is to be put round the edge of the mat.

Calculate the length of the border.

b) Calculate the area of the mat.

2

The strip for fastening babies’ nappies is printed with colourful animals. It is

manufactured in one long piece and then cut to size. Part of one of the strips

is shown below.

a) Copy and complete the table.

b) Write down a formula for the number of birds, B, when you know the

number of fish, F.

c) How many birds would there be if there were 20 fish?

d) How many fish would there be for 30 birds ?

3 Make a list of all the capital letters of the alphabet that have rotational

symmetry and state the order of symmetry for each.

24

Auchinleck Academy

Mathematics

UNIT 2

MIXED Homework 2E

1 Use an appropriate formula to calculate the following:

a) Kyle cycled at an average speed of 15 km/hr for 4 hours. How far

did he cycle?

b) Denise drove her van for 4 hrs 30 mins and travelled a distance

of 252 miles. What was Denise’s average speed?

c) Fiona piloted a jet at a speed of 300 km/hr and travelled 450 km.

How long did the flight take?

2

Karen was driving home to Ayr from Newcastle, a distance of 160

miles. She stopped halfway to phone her husband saying she would

be home in 1 hour 30 minutes.

If she drove at an average speed of 52 mph would she be home on

time? Show working to explain your answer.

3 Calculate the length of the diagonal of the rhombus below.

Area = 36cm2 6cm

25

Auchinleck Academy

Mathematics

UNIT 2

MIXED Homework 2F

1 Some sums just for the fun of it……

Remember: NO CALCULATORS. NO WORKING NO MARKS!!!!!!

a) 1.376 – 2.93 + 3.007 b) 39.1 5

c) 83 x 25 d) 40% of 72kg

e) 35 + 10 x 4 - 32 f) 785 500

g) 2.35 x 2000 h) 5% of £4.80

2

Solve these equations:

a) 5x + 7 = 22 b) 6x – 7 = 29

c) ½x = 18 d) x 7 = 8

e) 7x – 12 = 3x + 20 f) 4(3x + 7) = 10x + 26

3 Calculate the mean, median, mode and range for the data sets below.

a) 2,3,3,3,5,9,17 b) 65, 65, 63, 64, 67, 66, 67, 67

4 Round the following numbers to 2 significant figures

a) 2527 b) 0.0189 c) 709 d) 0.69 e) 127500

5

This shape consists of a rectangle

joined to a semi-circle.

Calculate the area of this shape. 8 cm

7 cm

26

Auchinleck Academy

Mathematics

Pythagoras

Homework 3.1

1. Calculate the value of ‘x’ in each right angled triangle.

a) b) c)

d) e)

2.

3.

In each diagram, calculate the length of L.

Calculate the perimeter of the isosceles triangle.

x cm

8 cm

6 cm

x cm

5 cm

12 cm

13 m

x m 5 m

x cm

27 cm

36 cm

L m

82 m

56 m

L m

2·8 m 3·2 m

12 cm

8 cm

x m

14 m

11 m

3.0 m

27

Auchinleck Academy

Mathematics

Angles

Homework 3.2

1 Copy the diagrams and Fill in the missing angles

2 Copy the diagrams and Fill in the missing angles

3

Find the missing angles

72 a

b c

112

d

e 135 f

g h

k

m

n

152 52

85

p

q

n

139 r 133

75

98 93

e

f

38

25

a

b

c

d

28

Auchinleck Academy

Mathematics

Fractions, Decimals and Percentages

Homework 3.5

1 Copy and complete the following table

Fraction Decimal Percentage

0•2

30%

0•75

85%

2 Calculate:

1) 10% of £70 2) 10% of £59 3) 1 % of £900 4) 1% of £520

5) 70% of £49 6) 80% of £86 7) 3% of £400 8) 7% of £580

9) 5% of £60 10) 5% of £20 11) 5% of £58 12) 5% of £65

13) 15% of £10 14) 15% of £64 15) 35% of £82 16) 65% of £75

3 A jacket that costs £140 is on sale for the price of £105.

Calculate the percentage decrease.

4 A house was valued at £98,000 in 2005. In 2013 it was worth £110,000.

Calculate the percentage increase.

29

Auchinleck Academy

Mathematics

Ratio and Proportion

Homework 3.6

1 Share the following sums of money in the given ratio:

a) £72000 in the ratio of 5:1

b) £112000 in the ratio of 4:3

c) £45000 in the ratio of 6:4:5

2 Auchinleck Academy’s Christmas concert was a sell out with an audience

of 300. A survey of the audience showed that:

2 out of 5 people were male.

7 out of 10 were under 50 years old.

a) How many males and females were in the audience

b) How many people were over 50?

3

A box of 50 apples costs £6.50. How much would you expect to pay for

12 apples?

4 An 80 g packet of crisps contains 520 Kilojoules of energy.

a) How much energy would you expect in a 200g Family

bag of crisps?

b) If a bag of crisps has 325 Kilojoules of energy, what

weight would you expect it to be?

5 In 24 hours the Earth turns about its axis through an angle

of 360o. What angle has it turned through after 15 hours?

6 a) It takes 3 workmen 12 hours to build a wall. How long will it take 5

workmen to build the same wall?

b) A farmer has enough food to feed 300 cows for 20 days. If he

buys 100 more cows, how long would the same amount of feed last?

30

Auchinleck Academy

Mathematics

UNIT 3

MIXED Homework 3A

1 Find the area of the following shapes

a) b)

2 a) Find the mean of 9, 6, 4, 8

b) Round this number to 3 significant figures: 22,659

3 a) 5% of £80 b) 15% of £84 c) 35% of £62

d) 65% of £86 e) 33�

� % of £12 f) 33�

� % of £39

g) 66�

� % of £12 h) 66�

� % of £39 i) 66�

� % of £240

4 A car was valued at £2400 in 2012. In 2012 it was worth £2160.

Calculate the percentage decrease.

5 Find the length of the side marked x.

12m

3m

8m

11m

10m

12m

5 m x

31

Auchinleck Academy

Mathematics

UNIT 3

MIXED Homework 3B

1 The cost of a food item divided by the number of grams it weighs

gives the cost per gram.

Find the cost per gram for each of these:

a) 450g of Muesli costs £1.99

b) 2kg of Basmati Rice costs £2.99

c) 350g of Cheddar Cheese costs £3.00

d) 250g of Bacon costs £2.79

2 David and Jenny helped clean their gran’s garage. Jenny did 4 hours

cleaning and David did 3 hours cleaning.

Their Gran gave them £28 for doing this but told them to split the

money in a fair ratio of the hours they worked.

Calculate how much money they should each get.

3 Change the following test scores to percentages (WITHOUT A

CALCULATOR)

a) Maths score 1216

b) Music score 1220

c) History score 2840

4 Calculate the value of x

x 20

16

32

Auchinleck Academy

Mathematics

UNIT 3

MIXED Homework 3C

1 Simplify the following

a) 2x + 4y + 5x + 9y b) 3x + 4y + 11x – 3y

c) 6x – 4y – 2x + 6y d) f2 – 5f + 2f2 – 3f

2 Solve the following:

a) 3(2x + 5) = 39 b) 5x – 2 = 3x + 28

c) 7x + 8 = 3x + 48 d) 3(x – 2) > 2x + 1

3 Calculate the following, showing all working

a) 9•87 × 80 b) 92•4 ÷ 60 c) 12•07 – 14•91 + 7•32

d) 3 × 22 e) 5 + 3 x 2 f) 4/5 of £780

4 Find the volume of the following shapes put your answer in litres

5 A new computer costs £650. It can be paid up on a Hire Purchase

deal of a £100 initial payment and 12 payments of £50 per month.

How much more expensive is it to pay on hire purchase?

30cm

20cm

40cm

30cm

33

Auchinleck Academy

Mathematics

UNIT 3

MIXED Homework 3D

Marks

1 The distance from the earth to the sun is 93 million miles.

Write 93 million in scientific notation.

2 One day last March, Bob compared the temperature

in Glasgow with the temperature in Toronto.

The temperature in Glasgow was 11º C.

The temperature in Toronto was - 14ºC.

Find the difference between these temperatures.

3 a) 5 bottles of juice cost £1.50, how much will 2 bottles cost?

b) If 6 rolls cost £1.32, how much would 8 rolls cost?

4 Calculate the length of AB.

8 cm

7 cm

13 cm B

A