Stonelaw Mathematics Department
Green Course
Revision Sheets
Block D
GD1
Fractions, Ratio and Proportion
GD2
Percentages
GD3
Money
GD4
Sequences
GD5
Graphs and Charts.
GD1
Fractions, Ratio and Proportion
GD1.1 I understand how to express a ratio and can simplify ratios.
1.
2.
Simplify each of the following ratios
(a)
3 : 6
(b)
10 : 5
(c)
8 : 2
(d) 9 : 12
(e) 2 : 6
(f)
6 : 2
(g)
3 : 9
(h)
5 : 20
(i)
8 : 6
(j)
12 : 15
(k)
18 : 8
(l)
20 : 24
(m) 30 : 25
(n)
30 : 40
(o)
25 : 75
(p)
10 : 15
(q)
10 : 150
(r)
(s)
35 : 25
(t)
15 : 60
16 : 4
On a school trip to the zoo, 36 boys and 54 girls get on the coach.
Write down the ratio of girls to boys in simplest form
3.
Simplify each of the following ratios.
Make sure that both quantities are in the same unit.
(a)
£5 : £10
(b) 10 p : 25 p (c) 9 kg : 15 kg
(d)
8 cm : 6 cm
(e)
24 p : 32 p
(f)
(h)
5 mm : 1 cm
25 p : £1
(g) £2 : 50 p
GD1.2 I can calculate a quantity given a ratio and one of the
related quantities.
1. a) Prize money is split between winners Dan and Jess in the ratio 3:2.
If Dan receives £450 how much will Jess receive?
b) The ratio of boys to girls in 3m3 is 5:4.
If there are 12 girls in the class, how many boys are there?
c) James, Hannah and John share sweets in the ratio 3:2:1.
If Hannah has 14 sweets how much will
(i) John
(ii) James have?
d) Grant and Amy share holiday money they saved up in the ratio 4:3.
If Amy has £240, how much holiday money did they save
altogether?
BD1.3 I can write simple fractions from diagrams.
1. Write down the fraction represented in each diagram.
a)
b)
c)
d)
GD1.4 I can simplify fractions.
1.
Simplify:
a)
4
8
b)
3
12
c)
5
25
d)
8
12
e)
6
9
f)
14
21
g)
15
25
h)
16
24
i)
35
49
j)
42
60
k)
27
63
l)
95
100
GD1.5 I can add and subtract commonly used fractions.
GD1.6 I can easily convert between mixed numbers and fractions.
1.
2.
Calculate:
a)
2
e)
3
i)
2
5
4
5
+
−
1
5
1
4
3
+5
b)
1
f)
5
j)
3
12
5
6
1
+
c)
3
+
3
12
2
+6
g)
k)
3
10
7
8
+
−
2
15
1
10
3
8
4
+ 15
Copy the table below and fill in the blanks
Mixed number
Vulgar fraction
𝟏
2𝟐
𝟏
3𝟑
𝟓
𝟒
𝟕
𝟑
𝟑
8𝟒
𝟐𝟑
𝟖
d)
1
h)
5
l)
1
3
6
2
+
−
1
3
3
6
1
+4
3.
4.
Calculate:
a)
3
e)
2
4
5
1
−3
1
+ 10
b)
5
f)
5
8
6
+4
c)
1
2
g)
2
3
−9
2
3
2
− 10
1
+4
Copy the table below and fill in the blanks
Mixed number
Vulgar fraction
𝟏𝟐
𝟒
𝟏
4𝟓
𝟗
𝟒
𝟏𝟕
𝟑
𝟑
4𝟓
𝟓𝟎
𝟔
d)
5
h)
4
6
5
3
−4
2
+3
GD1.7
I can use direct proportion to solve simple problems using the
unitary method
1.Fred walked at a steady rate of 5km/h for 7 hours. The table below represents
his distance, from the start, at the end of each hour.
Time (t) hours
0
1
Distance (D)
km
2
5
3
4
5
6
7
20
(a)
Copy and complete the table.
(b)
Draw a graph of distance (D) against time (t).
(c)
Explain why the relationship between D and t is directly proportional.
2.
300g of flour is used to make 6 cakes. How much flour is needed to make:
(a)
3.
12 such cakes?
(b)
3 cakes?
(c)
9 cakes?
Eight bars of chocolate cost £3.36. Calculate the cost of:
(a)
1 bar of chocolate
(b)
3 bars
(c)
11 bars.
4.
A stack of six identical books weighs 1 38 kg. How much would a stack of
10 books weigh?
5.
(a)
4 cakes cost £3.12. Find the cost of 9 cakes.
(b) The height of 12 stacked CD cases is 136  8 mm. Calculate the height
of 7 such cases.
(c)
A row of 24 staples measures 14  4 mm. How long would a row of 38
staples be?
(d)
The weight of 3 baskets of fruit is 5  4 kg. Calculate the weight of 5
baskets.
Percentages
GD2.1 I understand the concept of a percentage and understand that it comes from a
Latin phrase meaning out of one hundred.
1.
a)
Write each of the following percentages as a decimal fraction :
32%
f) 90%
b) 87%
c) 20%
d) 8%
g) 7%
h) 12 12 %
i) 3 12 %
e) 3%
GD2.2 I can calculate simple percentage quantities based on 10% without a calculator.
1.
Find
10%
of
300kg
2.
Find
20%
of
420m
3.
Find
60%
of
210ml
4.
Find
5%
of
$940
5.
Find
15%
of
£560
6.
Find
70%
of
180 litres
7.
Find
90%
of
6200g
8.
Find
110%
of
£650
9.
Find
95%
of
570cm
10.
Find
6%
of
$500
GD2.3
I can calculate simple percentage quantities based on 20%, 25%, 33⅓%,
50% without a calculator.
1.
Find
40%
of
500g
2.
Find
80%
of
4000mm
3.
Find
25%
of
240ml
4.
Find
75%
of
$860
5.
Find
2
66⅓%
of
921ml
6.
Find
33⅓%
of
180 litres
GD2.4
I can calculate percentage increase and decrease with the aid of a
calculators.
1.
A maths tutor charges £30 per hour.
He decides to increase his charge by 5%.
What will his new charge be?
2.
The average attendance at Fir Park last season was 6800.
This season it dropped by 8.5%.
What is the average attendance this season?
3.
Mary normally runs a total of 28 miles per week.
She decides to increase her distance by 10% a week for the next four
weeks. How many miles will she run in the fourth week?
4.
It is estimated that an iceberg weighs 84000 tonnes.
As the iceberg moves into warmer waters, its weight decreases by
25% each day.
What will the iceberg weigh after 3 days in the water?
5.
A cottage, bought for £90000 in 2013, was put on the market last
week.
Its value had appreciated (went up in value) by 15% since 2013.
What is the cottage now worth?
6.
Mrs King bought a new car for £17000.
In the first year its value depreciated (fell in value) by 20% and in the
second year its value fell by a further 15%.
What was her car worth at the end of year 2?
Money
GD3.3
I can compare different ways of purchasing quantities in order to decide on
the best buy.
GD3.1
I can compare and contrast contracts and services.
GD3.2
I can identify advantages and disadvantages in different types of contract or
services.
1.
Investigate the meaning of the term “Hire Purchase” and find some
examples of items which could be paid for this way. Summarise your
findings in five sentences.
2.
Write down the advantages and disadvantages of paying for an item
through Hire Purchase and paying cash.
3.
Two companies are selling the same tablet.
Tablets4sale
Toptech
£50 deposit
Only £149 cash
plus six monthly payments
of £18
Which company offers the cheaper deal?
GD4.1
I have explored a number of sequences.
GD4.2
I can write out the numbers in a sequence given a simple linear rule
(using a number machine or similar representation).
GD4.3
I can determine and write out a rule (using a number machine
or similar representation) for a given linear sequence.
1.
2.
Describe the rule used to obtain the next term in these
sequences and list the next three terms
a)
5, 10, 15, 20, ……….
b) 40, 37, 34, 31, ……….
c)
1, 2, 4, 8, 16, ……….
d) 4, 9, 16, 25, ……….
e)
1, 3, 6, 10, ……….
f)
0, 1, 1, 2, 3, 5, ……….
You may need to do some research for this question on the internet
a) Write down the first 10 square numbers.
b) Write down the first 5 triangular numbers
c) Make up a sequence of your own and write down a rule to
describe it.
3.
A car hire company charge £100 deposit plus £45 per day.
No. of
days
(N)
Cost
(C)
1
2
3
4
5
£145
a) Copy and complete the table above
b) Find a formula connecting the letters C and H.
c) Use your formula to find the cost of hiring a car for one week.
d) Michael was charged £595 for hiring a car.
How many days did he hire it for?
4.
Find a formula connecting the variables in each table below :
(a)
a
1
2
F
4
7
(c)
p
1
2
g
5
7
3
4
5
10
13
16
3
4
5
10
13
16
(b)
g
1
2
P
3
8
(d)
X
1
2
t
5
9
3
4
5
13
18
23
3
4
5
10
13
16
GD5
Graphs and Charts
I can construct, interpret and extract data from:
GD5.1 a line graph,
1.
A crowd of ten thousand people attended a football match which
started at 3 pm. The graph below shows the number of people who
had entered the ground at various times.
Number of people in the ground
Attendance at football match
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
12 NOON
12.30 PM
1.00 PM
1.30 PM
2.00 PM
2.30 PM
3.00 PM
Time
(a)
(b)
How many people had entered the ground by the following
times?
(i)
1.15 pm
(ii)
2.15 pm
(iii)
12.45 pm
(iv)
1.45 pm
(v)
2.45 pm
(i)
During which half-hour period did most people enter the
ground.
(ii)
How many people entered the ground between these
times?
2.
The driver of a car recorded the number of litres of petrol in the tank at
the end of every hour.
The results are shown in the table below.
Time
8
am
9
am
10
am
11
am
12
noon
1
pm
2
pm
3
pm
4
pm
Number of
litres of petrol
in tank
60
55
45
40
40
40
30
20
5
(a)
Construct a line graph to represent the above data.
Use the following scales
Horizontal axis (Time)
: 1 cm = I hour
Vertical axis
(Number of litres in petrol tank) : 1 cm = 10 litres
(b)
Using your graph :
(i)
(ii)
Between which two times does the driver use most petrol?
How do you know?
Why does the amount of petrol in the tank between 11 am
and 1 pm remain the same?
GD5.2 a pie chart,
1.
In a statistical survey, 1200 people were asked which of five countries they
would like to visit on holiday. The results are shown below.
Country
Percentage
3.
America
24
France
18
Greece
36
Italy
10
Spain
12
(a)
How many people would like to visit France?
(b)
Calculate the angle needed to represent each country in a pie
chart.
A sample of people was asked which type of food they preferred. The
results are shown below.
Type of food
Number of
people
British
Chinese
Indian
Italian
MacDonald’s
3
6
12
3
6
(a)
What percentage of people preferred MacDonald’s?
(b)
Calculate the angle needed to represent each type of food in a pie
chart.
GD5.3 a stem and leaf diagram,
1.
A busy filling station records the number of motorists who buy diesel fuel
for their cars each day.
The number on each of 50 consecutive days is shown below.
28
13
9
28
33
2.
19
17
14
19
26
17
12
15
32
28
30
27
8
21
31
45
10
26
23
30
37
17
30
26
22
43
23
26
34
21
36
23
22
16
21
36
9
19
17
15
12
10
20
18
19
(a)
Construct a stem and leaf diagram to represent this data.
(b)
Comment on your results.
Over a period of 40 school days, the school canteen recorded the
number of packets of crisps bought, each day, by boys and girls at the
school.
The results are shown below.
Girls
10
39
28
32
25
13
36
29
43
26
27
34
10
11
44
24
35
38
31
23
48
13
29
27
19
16
18
16
11
32
33
44
11
18
41
25
21
30
40
11
Boys
17
47
34
20
34
40
22
28
39
31
49
44
42
26
36
42
26
32
38
29
24
37
14
41
20
46
10
42
22
28
32
17
20
41
28
25
19
42
11
48
(a) Construct a back to back stem and leaf diagram to represent the
above data.
(b) Comment on your results i.e. When it comes to buying crisps, is there any
difference between boys and girls?
GD5.4 a scattergraph,
.
.
..
.
. .
..
.
.. .
..
. .
Rainfall
Temperature
1.
.
Sales of sun cream
Sales of ice cream
Temperature
Hours of sunshine
Describe the trends in the graphs shown above.
Sales of scarves
Price of fish
Make a copy of the above graphs and fill in the points
you would expect to see.
2.
The English and History marks of eight pupils are shown below.
English
mark (%)
History
mark (%)
26
34
48
58
63
65
72
80
30
49
45
63
72
74
80
75
(a)
Construct a scatter graph for this data.
(b)
Comment on the relationship between the pupils’ English and
History marks.
(c)
Draw the line of best fit.
(d)
Using your line of best fit, if a pupil has an English mark of 50, what
would you predict their History mark to be?
3.
The height above sea level, in metres, and the temperature, in °C, of nine
towns are shown below.
Height above
sea level (m)
Temperature
(°C)
200
300
350
450
500
600
700
1100
1300
18
16
15
13
14
13
10
7
6
(a)
Construct a scatter graph for this data.
(b)
Comment on the relationship between the height above sea level
and the temperature.
(c)
Draw the line of best fit.
(d)
Using your line of best fit, if a town is 400 metres above sea level,
what would you predict the temperature to be?
GD5.5 and a frequency table
1) People were asked to name their favourite holiday destination and the results were as
follows:
America
Spain
America
Spain
Spain
America
Spain
Italy
Spain
Britain
America
Spain
Italy
Britain
Spain
America
Spain
France
France
America
Spain
Spain
Britain
Spain
Britain
America
America
France
France
Britain
a) Copy and complete the following frequency table:
Country
America
Britain
France
Italy
Spain
Tally
Frequency
b) On the grid below, use your frequency table and a ruler to draw a neat,
labelled bar chart.