MEP Y8 Practice Book A
7 Ratio and Proportion
7.1 Equivalent Ratios
Orange squash is to be mixed with
water in a ratio of 1 : 6; this means
that for every unit of orange squash,
6 units of water will be used. The
table gives some examples:
Amount of
Orange Squash
Amount of
Water
(cm )
(cm )
3
3
1
6
20
120
5
30
The ratios 1 : 6 and 20 : 120 and 5 : 30 are all equivalent ratios, but 1 : 6 is the
simplest form.
Ratios can be simplified by dividing both sides by the same number: note the
similarity to fractions. An alternative method for some purposes, is to reduce to the
form 1 : n or n : 1 by dividing both numbers by either the left-hand-side (LHS) or
the right-hand-side (RHS). For example:
4 10
the ratio 4 :10 may be simplified to
⇒ 1 : 2.5
:
4 4
the ratio 8 : 5 may be simplified to
8 5
:
5 5
⇒ 1.6 : 1
Example 1
Write each of these ratios in its simplest form:
(a)
7 : 14
(b)
15 : 25
Solution
(a)
Divide both sides by 7, giving
7 14
:
7 : 14 =
7 7
= 1:2
(b)
Divide both sides by 5, giving
15 25
15 : 25 =
:
5 5
= 3 :5
(c)
Divide both sides by 2, giving
10 4
10 : 4 =
:
2 2
= 5 :2
114
(c)
10 : 4
MEP Y8 Practice Book A
Example 2
Write these ratios in the form 1 : n.
(a)
3 : 12
(b)
5:6
(c)
10 : 42
Solution
(a)
Divide both sides by 3, giving
3 : 12 = 1 : 4
(b)
Divide both sides by 5, giving
6
5
= 1 : 1.2
5:6 = 1:
(c)
Divide both sides by 10, giving
42
10
= 1 : 4.2
10 : 42 = 1 :
Example 3
The scale on a map is 1 : 20 000. What actual distance does a length of 8 cm on the
map represent?
Solution
Actual distance = 8 × 20 000
= 160 000 cm
= 1600 m
= 1.6 km
Exercises
1.
2.
Write each of these ratios in its simplest form:
(a)
2:6
(b)
4 : 20
(c)
3 : 15
(d)
6:2
(e)
24 : 4
(f)
30 : 25
(g)
14 : 21
(h)
15 : 60
(i)
20 : 100
(j)
80 : 100
(k)
18 : 24
(l)
22 : 77
Write in the form 1 : n, each of the following ratios:
(a)
2:5
(b)
5:3
(c)
10 : 35
(d)
2 : 17
(e)
4 : 10
(f)
8 : 20
(g)
6:9
(h)
15 : 12
(i)
5 : 12
115
MEP Y8 Practice Book A
7.1
3.
Write in the form n : 1, each of the following ratios:
(a)
24 : 3
(b)
4:5
(c)
7 : 10
(d)
15 : 2
(e)
18 : 5
(f)
6:5
4.
Jennifer mixes 600 ml of orange juice with 900 ml of apple juice to make a
fruit drink. Write the ratio of orange juice to apple juice in its simplest
form.
5.
A builder mixes 10 shovels of cement with 25 shovels of sand. Write the
ratio of cement to sand:
6.
(a)
in its simplest form,
(b)
in the form 1 : n,
(c)
in the form n : 1,
In a cake recipe, 300 grams of butter are mixed with 800 grams of flour.
Write the ratio of butter to flour:
(a) in its simplest form,
(b)
in the form 1 : n,
(c)
in the form n : 1.
7.
In a school there are 850 pupils and 40 teachers. Write the ratio of teachers
to pupils:
(a) in its simplest form,
(b) in the form 1 : n.
8.
A map is drawn with a scale of 1 : 50 000. Calculate the actual distances,
in km, that the following lengths on the map represent:
(a)
2 cm
(b)
9 cm
(c)
30 cm.
9.
A map has a scale of 1 : 200 000. The distance between two towns is
60 km. How far apart are the towns on the map?
10.
On a map, a distance of 5 cm represents an actual distance of 15 km. Write
the scale of the map in the form 1 : n.
7.2 Direct Proportion
Direct proportion can be used to carry out calculations like the one below:
If 10 calculators cost £120,
then 1 calculator
costs £12,
and 8 calculators cost £96.
116
MEP Y8 Practice Book A
Example 1
If 6 copies of a book cost £9, calculate the cost of 8 books.
Solution
If 6 copies cost £9,
then 1 copy costs
£
9
6
= £1.50
£1.50 × 8
and 8 copies cost
= £12
Example 2
If 25 floppy discs cost £5.50, calculate the cost of 11 floppy discs.
Solution
If 25 discs cost
£5.50 = 550p
then 1 disc costs
550
25
so 11 discs cost
= 22p
11 × 22 p = 242p
= £2.42
Exercises
1.
If 5 tickets for a play cost £40, calculate the cost of:
(a)
6 tickets
(b)
9 tickets
(c)
20 tickets.
2.
To make 3 glasses of orange squash you need 600 ml of water. How much
water do you need to make:
(a) 5 glasses of orange squash,
(b) 7 glasses of orange squash?
3.
If 10 litres of petrol cost £8.20, calculate the cost of:
(a)
4.
4 litres
(b)
12 litres
(c)
30 litres.
A baker uses 1800 grams of flour to make 3 loaves of bread. How much
flour will he need to make:
(a)
2 loaves
(b)
7 loaves
117
(c)
24 loaves?
7.2
MEP Y8 Practice Book A
5.
Ben buys 21 football stickers for 84p. Calculate the cost of:
(a)
6.
7.
7 stickers
(b)
12 stickers
(c)
50 stickers.
A 20 m length of rope costs £14.40.
(a)
Calculate the cost of 12 m of rope.
(b)
What is the cost of the rope, per metre?
A window cleaner charges n pence to clean each window, and for a house
with 9 windows he charges £4.95.
(a)
What is n ?
(b)
Calculate the window cleaner's charge for a house with 13 windows.
8.
16 teams, each with the same number of people, enter a quiz. At the
semifinal stage there are 12 people left in the competition.
How many people entered the quiz?
9.
Three identical coaches can carry a total of 162 passengers. How many
passengers in total can be carried on seven of these coaches?
10.
The total mass of 200 concrete blocks is 1460 kg. Calculate the mass of
900 concrete blocks.
7.3 Proportional Division
Sometimes we need to divide something in a given ratio. Malcolm and Alison
share the profits from their business in the ratio 2 : 3. This means that, out of
every £5 profit, Malcolm gets £2 and Alison gets £3.
Example 1
Julie and Jack run a stall at a car boot sale and take a total of £90. They share the
money in the ratio 4 : 5. How much money does each receive?
Solution
As the ratio is 4 : 5, first add these numbers together to see by how many parts
the £90 is to be divided.
4 + 5 = 9 , so 9 parts are needed.
Now divide the total by 9.
90
= 10 , so each part is £10.
9
118
MEP Y8 Practice Book A
Julie gets 4 parts at £10, giving 4 × £10 = £40,
Jack gets 5 parts at £10, giving 5 × £10 = £50.
Example 2
Rachel, Ben and Emma are given £52. They decide to divide the money in the
ratio of their ages, 10 : 9 : 7. How much does each receive?
Solution
10 + 9 + 7 = 26 so 26 parts are needed.
Now divide the total by 26.
52
= 2, so each part is £2.
26
Rachel gets 10 parts at £2, giving 10 × £2 = £20
gets 9 parts at £2, giving 9 × £2
= £18
Emma gets 7 parts at £2, giving 7 × £2
= £14
Ben
Exercises
1.
2.
(a)
Divide £50 in the ratio 2 : 3.
(b)
Divide £100 in the ratio 1 : 4.
(c)
Divide £60 in the ratio 11 : 4.
(d)
Divide 80 kg in the ratio 1 : 3.
(a)
Divide £60 in the ratio 6 : 5 : 1.
(b)
Divide £108 in the ratio 3 : 4 : 5.
(c)
Divide 30 kg in the ratio 1 : 2 : 3.
(d)
Divide 75 litres in the ratio 12 : 8 : 5.
3.
Heidi and Briony get £80 by selling their old toys at a car boot sale. They
divide the money in the ratio 2 : 3. How much money do they each receive?
4.
In a chemistry lab, acid and water are mixed in the ratio 1 : 5. A bottle
contains 216 ml of the mixture. How much acid and how much water were
needed to make this amount of the mixture?
5.
Blue and yellow paints are mixed in the ratio 3 : 5 to produce green. How
much of each of the two colours are needed to produce 40 ml of green paint?
119
MEP Y8 Practice Book A
7.3
6.
Simon, Sarah and Matthew are given a total of £300. They share it in the
ratio 10 : 11 : 9. How much does each receive?
7.
In a fruit cocktail drink, pineapple juice, orange juice and apple juice are
mixed in the ratio 7 : 5 : 4. How much of each type of juice is needed to
make:
(a) 80 ml of the cocktail,
(b) 1 litre of the cocktail?
8.
Blue, red and yellow paints are mixed to produce 200 ml of another colour.
How much of each colour is needed if they are mixed in the ratio:
(a)
1 : 1 : 2,
(b)
3 : 3 : 2,
(c)
9:4:3?
9.
To start up a small business, it is necessary to spend £800. Paul, Margaret
and Denise agree to contribute in the ratio 8 : 1 : 7. How much does each
need to spend?
10.
Hannah, Grace and Jordan share out 10 biscuits so that Hannah has 2, Grace
has 6 and Jordan has the remainder. Later they share out 25 biscuits in the
same ratio. How many does each have this time?
7.4 Linear Conversion
The ideas used in this unit can be used for converting masses, lengths and
currencies.
Example 1
If £1 is worth 9 French francs, convert:
(a)
£22 to Ff,
(b)
45 Ff to £,
Solution
(a)
£22 = 22 × 9
= 198 Ff
(b)
1 Ff = £
so
1
9
45 Ff = 45 ×
=
1
9
45
9
= £5
120
(c)
100 Ff to £.
MEP Y8 Practice Book A
(c)
100 Ff = 100 ×
=
1
9
100
9
= £11
1
9
= £11.11 to the nearest pence
Example 2
Use the fact that 1 foot is approximately 30 cm to convert:
(a)
8 feet to cm,
(b)
50 cm to feet,
(c)
195 cm to feet.
Solution
(a)
8 feet = 8 × 30
= 240 cm
(b)
1 cm =
1
feet
30
so 50 cm = 50 ×
=
5
3
= 1
(c)
1
30
2
feet
3
195 cm = 195 ×
1
30
195
30
13
=
2
1
= 6 feet
2
=
Example 3
If £1 is worth $1.60, convert:
(a)
£15 to dollars
(b)
121
$8 to pounds.
MEP Y8 Practice Book A
7.4
Solution
(a)
£15 = 15 × 1.60
= $24
(b)
$1 = £
= £
1
1.60
10
16
$8 = 8 ×
10
16
80
16
= £5
=
Exercises
1.
2.
3.
4.
5.
If £1 is worth 9 Ff, convert:
(a)
£6 to Fr,
(b)
£100 to Ff,
(c)
54 Ff to £,
(d)
28 Ff to £.
Use the fact that 1 inch is approximately 25 mm to convert:
(a)
6 inches to mm,
(b)
80 inches to mm,
(c)
50 mm to inches,
(d)
1000 mm to inches.
Before 1971, Britain used a system of money where there were 12 pennies
in a shilling and 20 shillings in a pound. Use this information to convert:
(a)
100 shillings into pounds,
(b)
8 shillings into pennies,
(c)
132 pennies into shillings,
(d)
180 pennies into shillings.
Given that a weight of 1 lb is approximately equivalent to 450 grams,
convert:
(a)
5 lbs to grams,
(b)
9 lb into grams,
(c)
1800 grams to lb,
(d)
3150 grams to lb.
Use the fact that 1 mile is approximately the same distance as 1.6 km to
convert:
(a)
30 miles to km,
(b)
21 miles to km,
(c)
80 km to miles,
(d)
200 km to miles
122
MEP Y8 Practice Book A
6.
On a certain day, the exchange rate was such that £1 was worth $1.63. Use
a calculator to convert the following amounts to £, giving each answer
correct to the nearest pence.
(a)
7.
9.
$250
(c)
$75.
1000 Y
(b)
200 Y
(c)
50 000 Y.
A weight of 1 lb is approximately equivalent to 450 grams. There are
16 ounces in 1 lb. Give answers to the following questions correct to
1 decimal place.
(a)
Convert 14 oz to lb.
(b)
Convert 200 grams to lb.
(c)
Convert 300 grams to ounces.
If £1 is worth 2.8 German Marks (DM), and 1 DM is worth 2800 Italian
Lira (L), use a calculator to convert:
(a)
10.
(b)
The Japanese currency is the Yen (Y). The exchange rate gives 197 Yen for
every £1. Using a calculator, convert the following amounts to pounds,
giving each answer correct to the nearest pence.
(a)
8.
$100
800 DM to £,
(b)
10 000 L to DM,
(c)
50 000 L to £.
There are 8 pints in one gallon. One gallon is equivalent to approximately
4.55 litres. Use a calculator to convert:
(a)
12 pints to litres,
(b)
20 litres to pints.
Give your answers correct to 1 decimal place.
7.5 Inverse Proportion
Inverse proportion is when an increase in one quantity causes a decrease in
another.
The relationship between speed and time is an example of inverse proportionality:
as the speed increases, the journey time decreases, so the time for a journey can
be found by dividing the distance by the speed.
Example 1
(a)
Ben rides his bike at a speed of 10 mph. How long does it take him to cycle
40 miles?
(b)
On another day he cycles the same route at a speed of 16 mph. How much
time does this journey take?
123
MEP Y8 Practice Book A
7.5
Solution
(a)
Time =
40
10
(b)
= 4 hours
1
40
= 2
2
16
1
= 2 hours
2
Time =
Note: Faster speed ⇒ shorter time.
Example 2
Jai has to travel 280 miles. How long does it take if he travels at:
(a)
50 mph,
(b)
60 mph ?
(c)
How much time does he save when he travels at the faster speed?
Solution
(a)
Time =
280
50
= 5.6 hours
= 5 hours 36 minutes
(b)
Time =
280
60
= 4
2
hours
3
= 4 hours 40 minutes
(c)
Time saved = 5 hours 36 mins – 4 hours 40 mins
= 56 minutes
Example 3
In a factory, each employee can make 40 chicken pies in one hour. How long will
it take:
(a)
6 people to make 40 pies,
(b)
3 people to make 240 pies,
(c)
10 people to make 600 pies?
124
MEP Y8 Practice Book A
Solution
(a)
1 person makes 40 pies in 1 hour.
1
6 people make 40 pies in
hour (or 10 minutes).
6
(b)
1 person makes 40 pies in 1 hour.
240
1 person makes 240 pies in
= 6 hours.
40
3 people make 240 pies in
(a)
6
3
= 2 hours.
1 person makes 40 pies in
1 hour.
1 person makes 600 pies in
600
= 15 hours.
40
10 people make 600 pies in
15
10
= 1
1
hours.
2
Exercises
1.
How long does it take to complete a journey of 300 miles travelling at:
(a) 60 mph,
(b) 50 mph,
(c) 40 mph ?
2.
Alec has to travel 420 miles. How much time does he save if he travels at
70 mph rather than 50 mph?.
3.
Sarah has to travel 60 miles to see her boyfriend. Her dad drives at
30 mph and her uncle drives at 40 mph. How much time does she save if
she travels with her uncle rather than with her dad?
4.
Tony usually walks to school at 3 mph. When Jennifer walks with him he
walks at 4 mph. He walks 1 mile to school. How much quicker is his
journey when he walks with Jennifer?
5.
One person can put 200 letters into envelopes in 1 hour. How long would it
take for 200 letters to be put into envelopes by:
(a) 4 people,
(b)
6 people,
(c)
10 people?
125
7.5
MEP Y8 Practice Book A
6.
A person can make 20 badges in one hour using a machine. How long
would it take:
(a)
4 people with machines to make 20 badges,
(b)
10 people with machines to make 300 badges,
(c)
12 people with machines to make 400 badges?
1
hours. How much
2
faster would it have to travel to complete the journey in 4 hours?
7.
A train normally complete a 270-mile journey in 4
8.
On Monday Tom takes 15 minutes to walk one mile to school. On Tuesday
he takes 20 minutes to walk the same distance. Calculate his speed in mph
for each day's walk.
9.
Joshua shares a 2 kg tin of sweets between himself and three friends.
10.
(a)
How many kg of sweets do they each receive?
(b)
How much less would they each have received if there were four
friends instead of three?
Nadina and her friends can each make 15 Christmas cards in one hour.
How long would it take Nadina and four friends to make:
(a)
300 cards,
(b)
1000 cards?
126
MEP: Demonstration Project
UNIT 7
1.
2.
3.
4.
Teacher Support Y8A
Ratio and Proportion
Extra Exercises 7.1
Write each of these ratios in its simplest form:
(a)
3 : 12
(b)
4 : 30
(c)
7 : 21
(d)
9 : 21
(e)
8 : 64
(f)
12 : 15
(g)
6 : 22
(h)
11 : 99
(i)
15 : 27
Write in the form 1 : n, each of the following ratios:
(a)
2:5
(b)
8 : 40
(c)
5:7
(d)
5:2
(e)
10 : 37
(f)
20 : 50
In a class there are 18 girls and 12 boys. Write the ratio of boys to girls:
(a)
in its simplest form,
(b)
in the form 1 : n.
In a drink, 80 cm 3 of pineapple juice is mixed with 20 cm 3 of orange juice. Write the
ratio of pineapple juice to orange juice:
(a)
in its simplest form,
(b)
in the form 1 : n.
© The Gatsby Charitable Foundation
MEP: Demonstration Project
UNIT 7
1.
Ratio and Proportion
Teacher Support Y8A
Extra Exercises 7.2
If 10 m of chain costs £6, calculate the cost of:
(a)
1 m,
(b)
7 m,
(c)
22 m.
2.
If the mass of 20 wooden blocks is 3000 grams, calculate the mass of 16 wooden blocks.
3.
To make 8 glasses of squash, you need 1280 cm 3 of water. How much water would you
need to make:
4.
5.
(a)
4 glasses of squash,
(b)
1 glass of squash,
(c)
7 glasses of squash?
A car uses 22 litres of petrol to travel 176 miles. How far would the car travel using:
(a)
10 litres of petrol,
(b)
35 litres of petrol?
Four identical minibuses carry a total of 64 passengers. How many passengers can be
carried in 6 of these minibuses?
© The Gatsby Charitable Foundation
MEP: Demonstration Project
UNIT 7
Ratio and Proportion
Teacher Support Y8A
Extra Exercises 7.3
1.
Divide £60 in the ratio 2 : 3.
2.
Divide £170 in the ratio 9 : 8.
3.
Divide 240 kg in the ratio 1 : 2 : 5.
4.
Divide 320 kg in the ratio 1 : 5 : 10.
5.
John and Steve have earned £150 by doing extra work. They divide the money in the
ratio 2 : 3. How much do they each receive?
6.
Red, blue and yellow paint are mixed in the ratio 4 : 7 : 3 to produce 308 cm 3 of
another colour. How much of each colour paint is used?
© The Gatsby Charitable Foundation
MEP: Demonstration Project
UNIT 7
1.
2.
3.
Ratio and Proportion
Teacher Support Y8A
Extra Exercises 7.4
If 1 pound sterling (£) is worth 300 Portuguese Escudos (Esc), convert:
(a)
£5 to Esc,
(b)
£7 to Esc,
(c)
3600 Esc to £,
(d)
1740 Esc to £.
If one pound sterling (£) is worth 60 Belgian Francs (BFr), convert:
(a)
£45 to BFr,
(b)
£8.60 to BFr,
(c)
1140 BFr to £,
(d)
495 BFr to £.
If there are 4.55 litres in one gallon, convert:
(a)
20 gallons to litres,
(b)
42 gallons to litres,
(c)
37 gallons to litres,
(d)
45.5 litres to gallons,
(e)
182 litres to gallons,
(f)
236.6 litres to gallons.
© The Gatsby Charitable Foundation
MEP: Demonstration Project
UNIT 7
1.
2.
Ratio and Proportion
Teacher Support Y8A
Extra Exercises 7.5
If Ernie drives at 60 mph, how long will it take him to travel:
(a)
240 miles,
(b)
75 miles,
(c)
165 miles,
(d)
140 miles?
Jane has to drive 60 miles to visit her parents. How long will the journey take if she
drives at:
(a)
40 mph,
(b)
50 mph,
(c)
60 mph?
3.
Amy has to drive 350 miles. How much time does she save if she drives at 70 mph
rather than at 50 mph?
4.
One person can address 50 envelopes in 1 hour. How long will it take:
(a)
3 people to address 300 envelopes,
(b)
2 people to address 500 envelopes,
(c)
5 people to address 1000 envelopes?
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Teacher Support Y8A
Extra Exercises 7.1 Answers
1.
(a)
1:4
(b)
2 : 15
(c)
1:3
(d)
3:7
(e)
1:8
(f)
4:5
(g)
3 : 11
(h)
1:9
(i)
5:9
(a)
1 : 2:5
(b)
1:5
(c)
1 : 1.4 (2 s.f.)
(d)
1 : 0.4
(e)
1 : 3.7
(f)
1 : 2.5
3.
(a)
2:3
(b)
1 : 1.5
4.
(a)
4:1
(b)
1 : 0.25
2.
Extra Exercises 7.2 Answers
1.
(a)
60p
(b)
£4.20
(c)
£13.20
2.
2400 grams
3.
(a)
640 cm 3
(b)
160 cm 3
(c)
1120 cm 3
4.
(a)
80 miles
(b)
280 miles
5.
96 passengers
Extra Exercises 7.3 Answers
1.
£24, £36
2.
£90, £80
3.
30 kg, 60 kg, 150 kg
4.
20 kg, 100 kg, 200 kg
5.
£60, £90
6.
88 cm 3 , 154 cm 3 , 66 cm 3
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Teacher Support Y8A
Extra Exercises 7.4 Answers
1.
(a)
1500 Esc
(b)
2100 Esc
(c)
£12
(d)
£5.80
2.
(a)
2700 BFr
(b)
516 BFr
(c)
£19
(d)
£8.25
3.
(a)
91 litres
(b)
191.1 litres
(c)
168.35 litres
(d)
10 gallons
(e)
40 gallons
(f)
52 gallons
Extra Exercises 7.5 Answers
1.
(a)
(c)
1
hours (1 hour 15 mins)
4
3
1
(d)
2 hours (2 hours 45 mins)
2 hours (2 hours 20 mins)
4
3
4 hours
1
2.
(a)
3.
2 hours
4.
(a)
(b)
1
1
hours (1 hour 30 mins)
2
2 hours
(b)
© The Gatsby Charitable Foundation
5 hours
1
hours (1 hour 12 mins)
5
(b)
1
(c)
4 hours
(c)
1 hour
MEP: Demonstration Project
UNIT 7
Y8ATeacher Support M7
Ratio and Proportion
M 7.1 Standard Route
Mental Tests
(no calculator)
1.
Simplify the ratio 3 : 6.
(1 : 2)
2.
Simplify the ratio 4 : 20.
(1 : 5)
3.
Simplify the ratio 5 : 40.
(1 : 8)
4.
Simplify the ratio 6 : 8.
(3 : 4)
5.
If 10 bars of chocolate cost £3, how much does 1 bar cost?
(30p)
6.
If 2 tickets for a swimming session cost £5, how much do 6 tickets cost?
(£15)
7.
If 5 packets of sweets cost £1, how much do 2 packets cost?
(40p)
8.
If £1 is worth 3 German Marks, convert:
(a)
£20 to German Marks,
(60 DM)
(b)
£2.50 to German Marks,
(7.5 DM)
(c)
45 German Marks to pounds.
M 7.2 Academic Route
(£15)
(no calculator)
1.
Simplify the ratio 4 : 20.
(1 : 5)
2.
Simplify the ratio 6 : 15.
(2 : 5)
3.
Simplify the ratio 14 : 24.
(7 : 12)
4.
If 8 bars of chocolate cost £2.40, how much do 3 bars cost?
5.
If 5 tickets for a swimming session cost £6, how much do 3 tickets cost?
6.
Share £12 in the ratio 1 : 2.
7.
Share £18 in the ratio 1 : 2 : 3.
8.
If £1 is worth 3 German Marks, convert:
(a)
£22 to German Marks,
(b)
£7.50 to German Marks,
(c)
57 German Marks to pounds.
© The Gatsby Charitable Foundation
(90p)
(£3.60)
(£4, £8)
(£3, £6, £9)
(66 DM)
(22.5 DM)
(£19)
MEP: Demonstration Project
UNIT 7
Y8ATeacher Support M7
Ratio and Proportion
M 7.3 Express Route
Mental Tests
(no calculator)
1.
Simplify the ratio 6 : 42.
(1 : 7)
2.
Simplify the ratio 20 : 45.
(4 : 9)
3.
Simplify the ratio 63 : 81.
(7 : 9)
4.
If 7 packets of sweets cost £2.80, how much do 5 packets cost?.
5.
If you travel 100 miles at 60 mph, how long does your journey take?
6.
Share £49 in the ratio 1 : 2 : 4.
(£7, £14, £28)
7.
Share £56 in the ratio 5 : 2 : 7.
(£20, £8, £28)
8.
If £1 is worth 11 Danish Krone, convert:
(£2)
(1 hr 40 mins)
(a)
£3.50 to Danish Krone,
(b)
275 Danish Krone to pounds,
(£25)
(c)
209 Danish Krone to pounds.
(£19)
© The Gatsby Charitable Foundation
(38.5 Dkr)
𝑆𝐻𝐴𝑃𝐸
𝐴𝑟𝑒𝑎 𝑎𝑛𝑑 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝐶𝑖𝑟𝑐𝑙𝑒
𝑀𝐴𝑇𝐻𝑆
𝑆𝐻𝐴𝑃𝐸
𝐴𝑟𝑒𝑎 𝑎𝑛𝑑 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝐶𝑖𝑟𝑐𝑙𝑒
𝑀𝐴𝑇𝐻𝑆
𝑆𝐻𝐴𝑃𝐸
𝐴𝑟𝑒𝑎 𝑎𝑛𝑑 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝐶𝑖𝑟𝑐𝑙𝑒
𝑀𝐴𝑇𝐻𝑆
𝑆𝐻𝐴𝑃𝐸
𝐴𝑟𝑒𝑎 𝑎𝑛𝑑 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝐶𝑖𝑟𝑐𝑙𝑒
𝑀𝐴𝑇𝐻𝑆
MEP: Demonstration Project
UNIT 7
1.
Teacher Support Y8A
Ratio and Proportion
Revision Test 7.1
(Standard)
Write each of the following ratios in its simplest form:
(a)
5 : 15
(b)
6 : 14
(c)
3 : 12
(6 marks)
2.
Write in the form of 1 : n, each of the following ratios:
(a)
2 : 10
(b)
2:5
(c)
10 : 22
(6 marks)
3.
Given that one pound sterling (£) is worth 200 Japanese Yen (Y), convert:
(a)
£60 to Y ,
(b)
£2.50 to Y,
(c)
1600 Y to £ .
(6 marks)
4.
Share £99 in the ratio 4 : 7.
(4 marks)
5.
If 7 books cost £35, calculate the cost of:
(a)
1 book,
(b)
4 books,
(c)
20 books.
(6 marks)
6.
Sugar and flour are mixed in the ratio 1 : 3 in a recipe.
How much sugar should be mixed with 900 grams of flour?
(2 marks)
© The Gatsby Charitable Foundation
MEP: Demonstration Project
UNIT 7
1.
Teacher Support Y8A
Ratio and Proportion
Revision Test 7.2
(Academic)
Write each of the following ratios in its simplest form:
(a)
21 : 35
(b)
42 : 49
(c)
24 : 40
(6 marks)
2.
Write in the form of 1 : n, each of the following ratios:
(a)
10 : 45
(b)
5:8
(c)
2 : 17
(6 marks)
3.
Given that one pound sterling (£) is worth 240 Spanish Pesetas (Pta), convert:
(a)
£8 to Pta,
(b)
£3.50 to Pta,
(c)
2640 Pta to £ .
(6 marks)
4.
Share £90 in the ratio 7 : 6 : 5.
(4 marks)
5.
If 9 hockey sticks cost £126, calculate the cost of:
(a)
1 stick,
(b)
7 sticks.
(4 marks)
6.
If Debbie drives 150 miles at 60 mph, how long does her journey take?
(2 marks)
7.
A map uses a scale of 1 : 20 000. What distance on the map would
represent an actual distance of 2 km?
(2 marks)
© The Gatsby Charitable Foundation
MEP: Demonstration Project
UNIT 7
1.
Teacher Support Y8A
Ratio and Proportion
Revision Test 7.3
(Express)
Write each of the following ratios in its simplest form:
(a)
42 : 49
(b)
60 : 150
(c)
45 : 63
(6 marks)
2.
Write in the form of 1 : n, each of the following ratios:
(a)
10 : 4.7
(b)
5 : 22
(4 marks)
3.
Given that one pound sterling (£) is worth 2.4 Swiss Francs (SFr), convert:
(a)
£40 to SFr,
(b)
480 SFr to £,
(c)
4.2 SFr to £ .
(6 marks)
4.
Share £198 in the ratio 3 : 6 : 9.
(4 marks)
5.
If 12 footballs cost £168, calculate the cost of:
(a)
4 footballs,
(b)
9 footballs
(4 marks)
6.
Debbie and Karen each drive 60 miles. Debbie drives at 40 mph and
Karen at 50 mph. How long does each journey take?
(4 marks)
7.
A map uses a scale of 1 : 25 000. What distance on the map would
represent an actual distance of 4.5 km?
(2 marks)
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Teacher Support Y8A
Revision Test 7.1 (Standard)
1.
2.
3.
4.
5.
6.
Answers
(a)
1:3
B2
(b)
3:7
B2
(c)
1:4
B2
(a)
1:5
B2
(b)
1 : 2.5
B2
(c)
1 : 2.2
B2
(a)
60 × 200 = 12 000 Y
M1 A1
(b)
2.5 × 200 = 500 Y
M1 A1
(c)
1600 ÷ 200 = £8
M1 A1
4 + 7 = 11
M1
99 ÷ 11 = 9
M1
4 × 9 = £36
B1
7 × 9 = £63
B1
(6 marks)
(6 marks)
(6 marks)
(4 marks)
(a)
35 ÷ 7 = £5
(b)
4 × 5 = £20
M1 A1
(c)
20 × 5 = £100
M1 A1
(6 marks)
900 ÷ 3 = 300 grams
M1 A1
(2 marks)
-
M1 A1
(TOTAL MARKS 30)
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Teacher Support Y8A
Revision Test 7.2 (Academic)
1.
2.
3.
4.
(a)
3:5
B2
(b)
6:7
B2
(c)
3:5
B2
(a)
1 : 4.5
B2
(b)
1 : 1.6
B2
(c)
1 : 8.5
B2
(a)
8 × 240 = 1920 Pta
M1 A1
(b)
3.5 × 240 = 840 Pta
M1 A1
(c)
2640 ÷ 240 = £11
M1 A1
7 + 6 + 5 = 18
M1
90 ÷ 18 = 5
A1
7 × 5 = £35
6 × 5 = £30
5 × 5 = £25
5.
Answers







M1 A1
(6 marks)
(6 marks)
(6 marks)
(4 marks)
(a)
126 ÷ 9 = £14
M1 A1
(b)
7 × 14 = £98
M1 A1
(4 marks)
6.
150
1
= 2 hours
60
2
M1 A1
(2 marks)
7.
2000 × 100
= 10 cm
20 000
M1 A1
(2 marks)
(TOTAL MARKS 30)
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Teacher Support Y8A
Revision Test 7.3 (Express)
1.
2.
3.
4.
5.
6.
7.
Answers
(a)
6:7
B2
(b)
2:5
B2
(c)
5:7
B2
(a)
1 : 0.47
B2
(b)
1 : 4.4
B2
(a)
40 × 2.4 = 96 SFr
M1 A1
(b)
480 ÷ 2.4 = £200
M1 A1
(c)
4.2 ÷ 2.4 = £1.75
M1 A1
4 + 6 + 9 = 18
M1
198 ÷ 18 = 11
A1
3 × 11 = 33 


6 × 11 = 66 

9 × 11 = 99 

M1 A1
(a)
168
× 4 = £56
12
M1 A1
(b)
168
× 9 = £126
12
M1 A1
(6 marks)
(4 marks)
(6 marks)
(4 marks)
(4 marks)
60
1
= 1 hours
40
2
M1 A1
60
1
= 1 hours
50
5
M1 A1
(4 marks)
4500 × 100 450
=
= 18 cm
25000
25
M1 A1
(2 marks)
(TOTAL MARKS 30)
© The Gatsby Charitable Foundation
Converting between units of area and volume
1cm
1cm
1cm
1)
2)
3)
4)
5)
𝑐𝑐𝑐𝑐2 𝑡𝑡𝑡𝑡 𝑚𝑚2
11)
12)
13)
14)
15)
2𝑐𝑐𝑐𝑐2 =
36𝑐𝑐𝑐𝑐2 =
17𝑐𝑐𝑐𝑐2 =
2468𝑐𝑐𝑐𝑐2 =
0.5𝑐𝑐𝑐𝑐2 =
=
𝟏𝟏𝟏𝟏𝟏𝟏𝟑𝟑
5𝑐𝑐𝑐𝑐3 =
89𝑐𝑐𝑐𝑐3 =
20𝑐𝑐𝑐𝑐3 =
0.7𝑐𝑐𝑐𝑐3 =
0.9𝑐𝑐𝑐𝑐3=
𝑚𝑚2 𝑡𝑡𝑡𝑡 𝑐𝑐𝑚𝑚2
9𝑚𝑚2 =
87𝑚𝑚2 =
253𝑚𝑚2 =
0.6𝑚𝑚2 =
4.6𝑚𝑚2 =
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟑𝟑
Extensions
21)
22)
23)
24)
25)
𝟏𝟏𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟐𝟐
100cm
6)
7)
8)
9)
10)
𝑚𝑚𝑚𝑚2 𝑡𝑡𝑡𝑡 𝑐𝑐𝑚𝑚2
700𝑚𝑚𝑚𝑚2 =
2300𝑚𝑚𝑚𝑚2 =
540𝑚𝑚𝑚𝑚2 =
0.2𝑚𝑚𝑚𝑚2 =
0.09𝑚𝑚𝑚𝑚2 =
=
𝟏𝟏𝟏𝟏𝟑𝟑
=
1m
100cm
𝑚𝑚𝑚𝑚3 𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐3
9000𝑚𝑚𝑚𝑚3 =
64000𝑚𝑚𝑚𝑚3 =
500𝑚𝑚𝑚𝑚3 =
30𝑚𝑚𝑚𝑚3 =
28.8𝑚𝑚𝑚𝑚3 =
Find the volume of this cylinder in 𝑐𝑐𝑐𝑐3 .
Then convert your answer to 𝑚𝑚𝑚𝑚3 .
16)
17)
18)
19)
20)
𝑚𝑚3 𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐3
8𝑚𝑚3 =
4𝑚𝑚3 =
0.5𝑚𝑚3 =
1.2𝑚𝑚3 =
0.00007𝑚𝑚3=
Find the area of this trapezium in 𝑐𝑐𝑐𝑐3 .
Then convert your answer to 𝑚𝑚3 .
30cm
7cm
3cm
100cm
1m
10mm
𝑐𝑐𝑐𝑐3 𝑡𝑡𝑡𝑡 𝑚𝑚𝑚𝑚3
=
𝟏𝟏𝟏𝟏𝟐𝟐
1m
10mm
1cm
26)
27)
28)
29)
30)
10mm
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟐𝟐
100cm
=
𝟏𝟏𝟏𝟏𝟏𝟏𝟐𝟐
60cm
10.1. Distance-Time Graphs
(1) Paul was travelling in his car to a meeting. This distance-time graph illustrates
his journey.
a. How long after he set off did he:
i)
Stop for his break
ii)
iii)
Set off after this break
Get to his meeting place?
b. At what average speed was he
travelling:
i)
Over the first hour
ii)
Over the second hour
iii)
For the last part of his journey?
c. The meeting was scheduled to start at
10.30am. What is the latest time he should have left home?
(2) James was travelling to Cornwall on his holiday. This distance-time graph
illustrates his journey.
a. His greatest speed was on the
motorway.
i)
How far did he travel on the
ii)
motorway?
What was his average speed on
the motorway?
b.
i)
When did he travel the most
slowly?
ii)
What was his lowest average
speed?
10.1. Distance-Time Graphs
(3) A small bus set off from Leeds to pick up Mike and his family. It then went on
to pick up Mike’s parents and grandparents. It then travelled further, dropping
them all off at a hotel. The bus then went on a further 10km to pick up another
party and it took them back to Leeds. This distance-time graph illustrates the
journey.
a. How far from Leeds did Mike’s parents and grandparents live?
b. How far from Leeds is the hotel at which they all stayed?
c. What was the average speed of the bus on its way back to Leeds?
(4) Three friends, Patrick, Araf and Sean, ran a 1000m race. The race is illustrated
on the distance-time graph shown here:
a. Describe how each of them completed the race.
b.
i)
ii)
What is Araf’s average speed in m/s?
What is this speed in km/h?
10.1. Distance-Time Graphs
(5) Richard and Paul took part in a 5000m race. It is illustrated in this graph.
a. Paul ran a steady race. What is his average speed in:
i)
Metres per minute.
ii)
Kilometres per hour?
b. Richard ran in spurts. What was his highest average speed?
c. Who won the race and by how much?
(6) A walker sets off at 9.00am from point P to walk along a trail at a steady pace
of 6km per hour. 90 minutes later, a cyclist sets off from P on the same trail at
a steady pace of 15km per hour. At what time did the cyclist overtake the
walker? You may use a graph to help you solve this question.
10.1. Distance-Time Graphs
(7) Three school friends set off from school at the same time, 3.45pm. They all
lived 12km away from the school. The distance-time graph illustrates their
journeys:
One of them went by bus, one cycled and one was taken by car.
a.
i)
Explain how you know that Sue used the bus.
ii)
Who went by car?
b. At what times did each of them get home?
c.
i)
When the bus was moving, it covered 2km in 5minutes. What is
ii)
this speed in kilometres per hour?
Overall, the bus covered 12km in 35minutes. What is this speed,
in kilometres per hour?
iii)
How many stops did the bus make before Sue got off?
Area and circumference of circles
Bronze: Calculate the area and circumference of circles (D)
Silver: Use the formula for area and circumference to find the radius or diameter (C)
2. Find the missing lengths in these circles
e)
f)
? cm
Area = 78.5 cm2
? cm
Circumference = 50.3 cm
Gold: Solve worded problems involving the area and circumference of circles (C)
1. Trevor needs a new bicycle tire. His tire has a circumference of about 113.04
inches. What diameter tire does he need to buy?
2. A rope is wrapped eight times around a cylindrical post, the diameter of which
is 35cm. How long is the rope?
3. a) Daniel is putting a circular flower bed in his garden with a diameter of 2m.
He wants to put plastic fencing around the flower bed, how many metres of
fencing will he need to buy?
b) How many square metres of land are in Daniel’s garden?
4. Anna is covering her circular swimming pool with a heavy-duty cover for the
winter. The pool has a diameter of 7m. The cover extends 1m beyond the
edge of the pool, and a rope runs along the edge of the cover to secure it in
place.
a) What is the area of the cover?
b) What is the length of the rope?
5. How many square centimetres greater is the area of a 30cm diameter circular
mirror than an 18cm diameter circular mirror?
6. GCSE question
Averages
Finding Mode, Median, Mean and Range
Mode= The value that occurs the most
Example:
4, 9, 4, 6,10,6,3,5,4, 9
Arranged in order
Median= The middle value when the values
are put in order from smallest to biggest
Mean=
Sum of all values in the set
Number of values in the set
(sometimes referred to as the “average”)
Range= Biggest value- smallest value
3, 4, 4, 4, 5, 6, 6, 9, 9, 10
Mode= 4
Median= 3, 4, 4, 4, 5, 6, 6, 9, 9, 10
If there are 2 numbers left in the
middle, add them up and divide by
2!
Tip:
So median=
Putting the values in order from smallest to biggest
will make it easier to work out your averages!
Mean=
𝟓+𝟔
𝟐
= 5.5
𝟑+𝟒+𝟒+𝟒+𝟓+𝟔+𝟔+𝟗+𝟗+𝟏𝟎
𝟏𝟎
Range= 10-3=7
1) The set of values shows the number of goals scored by a school football team in their first 10
matches: 2, 4, 1, 0, 2, 3, 2, 6, 2, 4
Find: a) Mode=
c) Median=
a) Mean=
d) Range
Find the mode, mean, median and range for each set of values given:
2) 7,2,5,3,8,5,5
Mode =
Median =
Mean =
Range =
3) 1,7,2,5,3,1,1,4
Mode =
Median =
Mean =
Range =
4) 6,9, 9,1,5
Mode =
Median =
Mean =
Range =
=6
5) 9,3,2,4,6,5,4,8,4
Mode =
Median =
Mean =
Range =
6) 6,3,8,1,9,3
Mode =
Median =
Mean =
Range =
Section B- Using the mean to find unknown values
1) The mean of 4 numbers is 9. Three of the numbers are 6, 8 and 11. What is the fourth number?
2) The results of a Maths test scores were 15,17,22,19 and X. The mean test score was 18. Find the
value of X.
3) In his first 11 basketball games, John scored on average (mean) 18 points. His mean increases to
19 points after his 12th game. How many points did he score in his 12th game?
4) The mean of the number of ice lollies sold each hour for 7 hours is 4. The number of ice lollies
sold in the first fist 6 hours were 2, 10, 4, 2, 4, 1
5) There are 15 employees in an office. Their mean age is 35. A new employee joins the office. The
mean age decreases to 31. How old is the new Employee?
6) Ricky has a mean score of 23 runs this season in 6 cricket matches. His mean score must be at least
25 runs for him to win a scholarship. How many runs must he score in his next match?
2
Averages from Frequency tables
1) The table shows the number of minutes taken by students in a year 5 class to solve a Maths
problem
Number of
Minutes
Frequency
2
3
4
5
6
7
1
6
7
10
3
1
Find the:
a) Mode
c) Range
b) Median
d) Mean
2) A die is thrown and the scores are recorded. The
results are shown in this table
Find the:
a) Mode
b) Range
c) Median
Die Score
Frequency
1
15
2
12
3
8
4
14
5
10
6
13
d) Mean
3) The weights of people in a fitness club are measured. The results are shown in the table.
Weight in Kg
Frequency
45≤W˂50
6
50≤W˂55
4
55≤W˂60
5
60≤W˂65
2
65≤W˂70
8
a) How many people are in the fitness class?
b) What is the modal class?
c) In which class is the median?
Answer=________________________
Answer=___________________________
Answer=__________________________
3
ANSWERS
Averages
Finding Mode, Median, Mean and Range
1) Mode= 2
Mean=2.6
Median=2
Range=6-0=6
2) Mode=5
Median-5
Mean=5
Range=5
3) Mode= 1
Median=2.5
Mean=3
Range=6
4) Mode=9
Median=6
Mean=6
Range=8
5) Mode=4
Median=4
Mean=5
Range=7
6) Mode=3
Median=4.5
Mean=5
Range=5
Section B
1) 6+8+11=25
36-25=11
4x9=36
2) X=17
3) 11x18=198
228-198=30
12x19=228
4) 5 ice lollies
5) 29 Years old
6) 37 runs
Averages from a frequency table
1) Mode=5
Median=4
Range=5
Mean=4.39 (2dp)
2) Mode=1
Median=4
Range=5
Mean=3.43 (2dp)
3) a) 25 People
b) 65≤W˂ 70
c) 55≤W˂ 60
4
Name :
Score :
ES1
Surface Area - Cylinder
Find the exact surface area of each cylinder.
2)
1)
3)
7 in
13 ft
6
yd
12
10 ft
4 in
Surface Area =
Surface Area =
Surface Area =
5)
4)
6)
11 yd
13 ft
8 ft
13 in
18 yd
12 in
Surface Area =
Surface Area =
Surface Area =
8)
7)
9)
4i
n
10 ft
Surface Area =
n
9i
6 yd
15 ft
15 yd
Surface Area =
Printable Math Worksheets @ www.mathworksheets4kids.com
Surface Area =
yd
Name :
Score :
Answer key
ES1
Surface Area - Cylinder
Find the exact surface area of each cylinder.
2)
1)
3)
yd
7 in
13 ft
6
yd
12
10 ft
4 in
Surface Area =
Surface Area =
36π in2
5)
4)
Surface Area =
460π ft2
216π yd2
6)
11 yd
13 ft
8 ft
13 in
18 yd
12 in
Surface Area =
Surface Area =
360π yd2
8)
7)
336π ft2
9)
n
9i
6 yd
15 ft
15 yd
4i
500π ft2
n
10 ft
Surface Area =
Surface Area =
228π in2
Surface Area =
252π yd2
Printable Math Worksheets @ www.mathworksheets4kids.com
Surface Area =
104π in2
Mr Martin
Maths
Simplifying Ratio
Green – these questions are not too tricky so try these to get you started. Simplify:
e.g. 8 : 12 = 2 : 3
1) 4 : 8 =
2) 12 : 8 =
3) 5 : 10 =
4)
5)
6)
7)
6:9=
20 : 30 =
7 : 14 =
6 : 12 =
8) 6 : 18 =
9) 10 : 100 =
10) 9 : 18 =
11) 4 : 16 =
12)
13)
14)
15)
16 : 8 =
11 : 22 =
24 : 12 =
10 : 20 =
Orange – these questions are a little trickier than the green questions. Simplify:
e.g. 4 : 8 : 12 = 1 : 2 : 3
1) 6 : 8 : 12 =
2) 4 : 8 : 12 =
3) 9 : 9 : 27 =
4) 1 hour : 20 mins =
5) 2 hours : 30 mins =
6) 50p : £2.50 =
7) 20cm : 15cm =
8) 1 day : 6 hours =
9) £1 : 70p =
10) 70p : £1 =
11) 4km : 12km =
Red – these questions are the trickiest and may require you to interpret worded
questions.
e.g. 4 : 8 : 12 : 24 = 1 : 2 : 3 : 6
1) 3 : 9 : 15 : 24 =
4) 6 : 18 : 9 : 15 =
2) There are 32 pupils in a class. 20
of them are girls. What is the
ratio of boys
to girls in its
simplest
form?
5) There are 50 sweets in a mixed
pack. 25 are jellies, 10
are fizzy cola bottles
and the rest are
boiled. Write the ratio of each
type of sweet in its simplest form.
3) A fruit drink is made by mixing
60ml of orange juice with 180ml
of pineapple juice. What is the
ratio of orange juice to pineapple
juice in its simplest form?
6) Concrete is made by mixing sand,
water and concrete mix in the
ratio of 6 parts sand, 3 parts
water and 3 parts concrete mix.
What ratio is this in its simplest
form?
Ratio Bingo Card
3:5
4:1
£20 : £30
4:5
5:3
4:3
3:4
1:4
5:6
£40 : £10
£30 : £20
£10 : £40
1:3
5:4
6:5
3:1
Full horizontal row or vertical column wins
Mr Martin
Maths
Dividing Ratio
Steps
1.
2.
3.
4.
to Success
Add together the total number of parts of the ratio
Divide the given amount by the total number of parts
Multiply the answer by each ratio amount
Check that your answers add up to the same total given in the question
Green – these questions are not too tricky so try these to get you started.
1) Divide £50 into the ratio 1 : 4
2) Divide 40 litres into the ratio 1 : 3
3) Divide £10 into the ratio 2 : 3
4) Divide 500g into the ratio 2 : 3
5) Divide 100ml into the ratio 3 : 7
6) Divide 30cm into the ratio 2 : 4
Orange – these questions are a little trickier than the green questions.
1) Divide 49p in the ratio 4 : 2 : 1
2) Divide £350 in the ratio 4 : 2 : 1
3) Divide £250 in
4) Divide 120cm in the ratio 1 : 2 : 3
the ratio 3 : 6 : 1
5) Divide 51g in the ratio 1 : 2
6) Divide 68p in the ratio 1 : 2 : 1
Red – these questions are the trickiest and will require you to interpret worded
questions.
1) Mr Martin has 120 CDs. The ratio
of indie CDs to dance CDs is 5 : 7.
How many of each type of CD does
he have?
3) There are 1400 students in
Plantsbrook School with a ratio of
4 : 3 boys to girls. How many boys
and how many girls are there?
2) Mr Martin has 36 calculators in a
box. The ratio of ordinary
calculators to scientific is 5 : 1.
How many of each calculator does
he have?
4) 180 people go bowling,
the ratio of adults to
children is 5 : 4. How
many adults and how
many children go bowling?
Area and Volume of Cylinders (A)
Calculate the surface area and volume for each cylinder.
Surface Area = (πr2 × 2) + (πd × h)
Volume = πr2 × h
d = 2r
1.
2.
r
d
h
h
r = 1.2 km
d = 12.6 cm
h = 3.6 km
h = 7.5 cm
Surface Area =
Surface Area =
Volume =
Volume =
3.
4.
d
r
h
h
d = 12 m
h = 18.6 m
Surface Area =
r = 18 ft
h = 27.2 ft
Volume =
Surface Area =
Volume =
Math-Drills.com
Area and Volume of Cylinders (A) Answers
Calculate the surface area and volume for each cylinder.
Surface Area = (πr2 × 2) + (πd × h)
Volume = πr2 × h
d = 2r
1.
2.
r
d
h
h
r = 1.2 km
d = 12.6 cm
h = 3.6 km
h = 7.5 cm
Surface Area = 36.19 km2
Surface Area = 546.26 cm2
Volume = 16.29 km3
Volume = 935.17 cm3
3.
4.
d
r
h
h
d = 12 m
h = 18.6 m
Surface Area = 927.4 m2
r = 18 ft
h = 27.2 ft
Volume = 2103.61 m3
Surface Area = 5112 ft2
Volume = 27,686.23 ft3
Math-Drills.com
Mean and Mode from Frequency Tables
1. Majid carried out a survey of the number of school dinners
students had in one week. The table shows this
information. Copy and complete the table.
a) Write down the mode.
b) How many students were there altogether?
c) How many school dinners were served during the
week?
d) Calculate the mean number of school dinners
Number of
school
dinners
0
1
2
3
4
5
Frequency
0
8
12
6
4
2
2. Josh asked some adults how many cups of coffee they each drank yesterday.
The table shows his results. Copy and complete the
table
a) Write down the mode.
b) How many adults were asked altogether?
c) How many cups of coffee were drank altogether
yesterday by the people asked?
d) Calculate the mean number of cups of coffee drank
yesterday.
Number of
cups
0
1
2
3
4
5
Frequency
5
9
7
4
3
2
3. The table gives some information about the number of tracks on each CD. Copy and complete the
table.
Number of
Frequency
tracks
a) Write down the mode.
11
1
b) How many CDs were there?
12
3
c) How many tracks were there on these CDs?
13
0
d) Calculate the mean number of tracks per CD.
14
2
15
4
4. Sarah works in a post office.
She recorded the number of parcels posted on each of 16 days.
Here are her results.
2
3
2
6
5
4
3
6
2
2
4
2
2
3
2
3
a) Copy and complete the frequency table to
show Sarah’s results.
b)
c)
d)
Write down the mode.
Work out the range.
Calculate the mean.
Number of
parcels
2
3
4
5
6
Tally
Frequency
5. Some students were asked how many pets
they owned. The results are given in the bar
chart below.
a) Use the graph to copy and complete the table
Number of
pets
0
1
2
3
4
5
Frequency
16
14
12
10
8
6
4
2
0
0
1
2
3
4
5
b) Write down the mode
c) How many students were asked altogether?
d) How many pets are owned, in total, by all the students.
e) Find the mean number of pets owned.
6. The table gives information about the number of goals
Number of goals
0
1
2
3
4
scored by a football team in each match last
season.
a) Write down the modal number of goals scored.
b) Work out the total number of goals scored by
the team last season.
c) Work out the mean number of goals scored last
season.
Frequency
4
5
4
7
4
6. The table gives information about the number of cars sold by a company each day over a period of 20
days.
a) Write down the modal
number of cars scored.
c) Work out the mean
number of cars sold
during this time.
Number of cars sold daily
6
5
Frequency
b) Work out the total
number of cars sold over
the 20 day period.
7
4
3
2
1
0
0
1
2
3
Cars sold in one day
4
5