S2 Credit / General
Block 1
Revision Booklet
Shawlands Academy
Mathematics Department
Performing Calculations
Exercise 1 - Percentages of Quantities
Exercise 2 - One Quantity as a percentage of another
Exercise 3 - Percentage Profit and Loss
Exercise 4 - Inverse Percentage Questions
Exercise 5 - Compound Interest, Appreciation/Depreciation
Exercise 6 - Compound Interest, Appreciation/Depreciation
Exercise 7 - Significant Figures
Exercise 8 - Adding and Subtracting Decimals
Exercise 9 - Multiplying Decimlas
Exercise 10 – Multiplying and Dividing by Multiples of 10, 100 and 1000
Exercise 11 – Rounding to given number of decimal places / significant figures
Area
Exercise 12 – Basic area and perimeter questions
Exercise 13 – Area of a Parallelogram
Exercise 14 – Shape Revision (including area of a trapezium)
Exercise 15 – Are of a Rhombus and a Kite
Part 16
- Area of Shapes, Formula sheet
Pythagoras
Exercise 17 – Squares and Square Roots
Exercise 18 – Pythagoras Theorem
Performing Calculations
Percentages of Quantities
Exercise 1
Work out the following:
Non – Calculator
1) 10% of ₤150
2) 20% of ₤150
3) 40% of ₤150
4) 80% of ₤150
5) 10% of 60m
6) 5% of 60m
7) 2.5% of 60m
8) 50% of 60m
9) 30% of 120
10) 45% of 90
11) 85% of 40
12) 67.5% of 80
13) 65% of 34m
14) 25% of 86p
15) 17.5% of ₤18
16) 37.5% of 48cm
17) 85% of 98kg
Calculator
18) 96% of 184mm
22) 16% of ₤16
19) 34% of 89cm
20) 21% of ₤13
23) 14% of ₤45
24) 44% of 82m
21) 49% of ₤86
One Quantity as a Percentage of Another
Exercise 2
1. The table shows the marks a student gets in his course assignments.
Find his % mark for each assignment.
Assignment
1
18
2
56
3
52
4
66
30
70
80
120
Mark
out of
%
Round your answer to nearest percent
Q1 Work out your percentage if you got 12 out of 25
Q2 Work out your percentage if you got 15 out of 25
Q3 Work out your percentage if you got 17 out of 20
Q4 Work out your percentage if you got 19 out of 24
Q5 Work out your percentage if you got 17 out of 31
Q6 A player scores 3 times out of 6 shots. What is their score a s a
percentage?
Q7 A player scores 4 times out of 10 shots. What is their score as a
percentage?
Q8 A player scores 44 times out of 69 shots. What is their score
percentage?
Q9 Work out 12.5 out of 26 as a percentage
10 Calculate the score percentage if out of 15 shots 12 are successful
Percentage Profit and Loss
Exercise 3
1. Alan bought a bowling ball for £12 and sold it for £15.
a. What was his profit?
b. What was his percentage profit?
2. Michael sold a mobile for £400. His bought the mobile for £360.
a. What was his profit?
b. What was his percentage profit?
3. A shop is selling a television set for £1 200.
The television set cost them £1 000.
a. What was their profit?
b. What is the percentage profit?
4. Jonathan bought a house at £250 000 and later sold it for £300 000.
a. What was his profit?
b. What was his percentage profit?
5. Zack bought a car for £20 000. Later he sold it at £18 000.
a. What was his loss?
b. What was his percentage loss?
6. A group of students were selling drinks at a school carnival. They sold 250 drinks
at £1 each. Their total cost for the drinks is £80.
a. Did they make a profit or a loss?
b. How much was the profit or loss?
c. What was their percentage profit or percentage loss?
Inverse Percentages
Exercise 4
1. Between the years 2001 and 2002 a stereo system increased in value
by 20%. If the stereo cost £660 in 2002 what was its value in 2001?
2. The price of a car has increased in value by 30%. If the car is now
valued at £7800 what was its previous value?
3. John is 136 cm tall. If John is 85% of the height of David, find David’s
height.
4. A student pays an aeroplane fare of £240. If this represents 60% of the
adult fare, find the adult fare.
5. The cost of a season ticket for Hillside Town is £273 for a child. If this
represents 65% of the cost of an adult ticket, find the cost of an adult
season ticket.
6. Amanda and Roomila decide to see who can cycle further over an hour.
Amanda covers 6 kilometres which is 80% of the distance covered by
Roomila. How far did Roomila cycle?
7. In a maths examination Michael scored 75% of what Brian scored. If
Michael scored 66% what did Brian score?
8. The average cost of a computer has fallen in price by 45% since 1999.
If the average cost is now £660, find the average cost in 1999.
9. The roll of a school has fallen by 15% since the year 2001. If the school
roll is now 1190, what was the roll in 2001?
10. The population of a Scottish village has dropped by 35%. If the population
is now 420, what was the population originally?
11. The cost of a holiday increased by 8% from the years 2001 to 2002. If it
cost £540 for the holiday in 2002, what was the cost in 2001?
12. Laura’s wages have increased by 6%. She now earns £19080, find her
wage before the increase.
Appreciation / Depreciation 1
Exercise 5
For each of the following, calculate
(a)
The current value of their savings
(b)
The current value of their car
(c)
Their new salary after the increase / decrease
SIAN
£2000 savings 7%
interest for 2 yrs.
Clio bought for
£8000 2 yrs ago
loses 6% per year.
Earns £12800 5%
decrease.
ADRIAN
£1600 savings 5%
interest for 3 yrs.
Passat bought for
£16000 3 yrs ago
loses 13% per year.
Earns £13200 9%
increase.
DANIEL
£50 savings 30%
interest for 50 yrs.
Laguna bought for
£16000 5 yrs ago
loses 12% per year.
Earns £13800 20%
decrease.
JODIE
£5000 savings 12%
interest for 9 yrs.
Rover75 bought for
£18000 8 yrs ago
loses 14% per yr.
Earns £14750 27%
increase.
TRUDIE
£3000 savings 10%
interest for 25 yrs.
Mini bought for
£11500 2 yrs ago
loses 2% per year.
Earns £12950 5%
increase.
WASIM
£1400 savings 4½%
interest for 3 yrs.
A4 bought for
£19000 5 yrs ago
loses 8% per year.
Earns £13400 11%
decrease.
LAUREN
£10000 savings 9%
interest for 5 yrs.
BMW bought for
£26000 8 yrs ago
loses 4% per year.
Earns £14050 22%
increase.
SARAH
£1000 savings 5%
interest for 10 yrs.
Limo bought for
£40000 20 yrs ago
loses 5% per year.
Earns £14850 21%
decrease.
SCOTT
£3000 savings 7%
interest for 2 yrs.
Astra bought for
£13000 4 yrs ago
loses 8% per year.
Earns £12500 7%
increase.
SCOTT C
£5000 savings 12%
interest for 10 yrs.
Fiesta bought for
£7500 7 yrs ago
loses 11% per year.
Earns £13000 7%
decrease.
CHRISTOPHER
£1500 savings 4%
interest for 3 yrs.
Fiat uno bought for
£5500 6 yrs ago
loses 16% per year.
Earns £13700 15%
increase.
BECKY
£750 savings 25%
interest for 3 yrs.
Freelander bought
for £21000 11 yrs
ago loses 1% per yr.
Earns £14100 25%
decrease.
ADELLE
£100 savings 20%
interest for 10 yrs.
Jeep bought for
£22000 15 yrs ago
loses 3% per year.
Earns £14900 22%
increase.
Appreciation / Depreciation 2
Exercise 6
1. Calculate the compound interest on
(a) a sum of £1500 at a rate of 7% p.a. for 4 years.
(b) a sum of £15 000 at a rate of 5.5% p.a. for 5 years.
(c) a sum of £120 000 at a rate of 11.2% p.a. for 10 years.
2. A plot of land is valued at £30 000. The value of the land is expected to
increase at a rate of 14% p.a. for the next 3 years.
Find the value of the land in 3 years time.
3. A people carrier cost £11 000 new in 2005. The value of the car will
depreciate at a rate of 15% per annum for each of the next 4 years.
Find the value of the car in 4 years time.
Give your answer correct to 2 significant figures.
4. On retiring from work Mr. Smith received a lump sum of £52 500.
He decided to invest his lump sum in a Premium account earning
9.5% interest per annum.
How much interest would Mr. Smith get after 5 years.
5. A painting valued at £70 000 in 2001 has appreciated at a
steady rate of 12% per annum for each of the last 6 years.
What was the value of the painting in 2007?
6. The number of bacteria in a jar is 36 000. Every 15 minutes the
number of bacteria in the jar will increase by 70%.
Calculate the number of bacteria in the jar after one hour.
Give your answer correct to 3 significant figures.
7. A van rental company purchases vans costing £22 000 each.
The value of a van depreciates by 30% in its first year and
then by 15% in each successive year.
A van is replaced at the end of the year in which its value
falls below half its original price.
After how many years will the company replace a van?
8. At 1.00 p.m., a pan containing 1.3 litres of water,
is left on the window sill of a house.
The water in the pan evaporates at a rate of 11%
per hour.
How much water remained in the pan at 5 p.m.?
9. A geologist measures stalactites in a cave. The longest
measured is 235 centimetres long.
If the stalactite grows at a rate of 4.5% every 10 years,
How long will it be in 50 years time?
10. The number of flamingos in one lake in Africa is estimated at 45 000.
Due to changes in habitat the number of flamingos is falling at a rate
of 8% per annum.
Calculate the number of flamingos there will be in 6 years time.
Give your answer correct to 2 significant figures.
11. The population of the country Liberia was 3.75 million in the year 2007.
If the population is growing at a steady rate of 4.5% per annum, what
would the population be in 2015?
12. Amanda is a secondary school teacher. She earns £32 500 per annum.
Her union agree a 3-year pay deal which will see her get an annual
rise of 2.6%.
How much will Amanda earn in 3 years time?
13. In 2004 a house was valued at £85 000 and its contents were
valued at £32 000.
The value of the house appreciates at a rate of 12% each year.
The value of the contents depreciates at a rate of 4% each year.
What will be the total value of the house and its contents in the
year 2010?
14. A water tank contains 650 litres of water. A hole in the tank means
that water is leaking from the tank at a rate of 3.65% every 10 minutes..
How much water will be left in the tank after an hour?
Rounding and Estimating – Significant Figures
Exercise 7
1. Write down the number of significant figures on each of these numbers?
a) 3.8457
b) 0.243
c) 0.00030
d) 34.017
2. Round these numbers to 1 significant figure.
a)15 b) 549
c) 3029
d) 9999
e) 0.455
f) 305567
3. Round these numbers to 2 significant figures.
a)15 b) 549
c) 3029
d) 9999
e) 0.455
f) 305567
4. Round off the figures to the nearest whole number and use this to estimate the
answers to the calculations.
a) 6.81 + 9.13 + 17.93
b) 63.56 – 42.85
c) 8.63 x 7.42
d) 4.35 x 2.86
1.92
e) 9.12 – 72.4
17.68
f) 99.8 x 4.7
9.84
Adding and Subtracting Decimals
Exercise 8
Calculate the following :
1.
2.06 + 9.77
2.
0.87 + 1.79
3.
23.7 – 19.08
4.
9.23 – 2.07
5.
13 + 91.03 + 12.3
6.
2.37 + 0.94
7.
44.9 + 172.9 + 87.36
8.
5.05 + 3.9 + 8 + 0.97
9.
18.97 + 2.9 –17.86 + 5.04
10. £204.67 – £49.20
11. A piece of string measures 5m. A piece of length 84cm is cut off it. How much
string is left (in metres)? (remember: 1m = 100cm)
12. Daniel was given £20.00 for Christmas. He bought a CD costing £7.89 and a
poster costing £3.49. How much money does he have left?
13. A large container of oil contains 20 litres. On Monday, 2.34 litres is used, and
on Tuesday 1.56 litres is used. How much oil is left in the container?
14. A new exercise book costs 65 pence, a ruler costs 39 pence, and a calculator
costs £3.98. How much will the three items cost altogether?
15. Chloe wants to buy 33/4 metres of red fabric. The shopkeeper says he has only
2.80m left. How much short is this of what Chloe wants?
16. Robbie buys a bottle of Coke for 79p and a bar of chocolate costing 34p. He
give the shopkeeper a £2 coin and he gets 77p change. Is this correct?
17. The next day, Robbie buys a loaf of bread costing £1.09, some apples costing
£1.85, and some cheese costing 77p. He hands the shopkeeper a £5 note and
receives £1.29 in change. Is this the correct change?
Multiplying and Dividing Decimals
Exercise 9
Multiplying decimals
1) 1.2 x 3
2) 1.2 x 4
3) 1.2 x 5
4) 2.2 x 20
5) 2.2 x 400
6) 2.2 x 5000
7) 5.6 x 50
8) 8.5 x 700
9) 3.4 x 5000
10) 5.4 x 30
11) 6.5 x 600
12) 4.5 x 9000
13) 3.44 x 20
14) 3.44 x 300
15) 3.44 x 9000
16) 4.91 x 80
17) 4.76 x 400
18) 8.91 x 3000
19) 4.7 x 90
20) 34.5 x 300
21) 76.1 x 7000
22) 45.1 x 30
23) 7.8 x 500
24) 23.4 x 8000
25) 12.2 x 90
1) 1.6 x 13
2) 1.6 x 14
3) 1.6 x 15
4) 2.7 x 12
5) 2.7 x 14
6) 2.7 x 15
7) 5.4 x 15
8) 8.5 x 17
9) 3.6 x 50
10) 4.5 x 13
11) 5.6 x 26
12) 5.4 x 29
13) 1.41 x 22
14) 1.41 x 23
15) 1.41 x 24
16) 0.56 x 80
17) 0.76 x 400
18) 0.91 x 3000
19) 0.7 x 90
20) 0.345 x 300
21) 0.761 x 7000
22) 0.451 x 300
23) 0.0078 x 50
24) 0.00024 x 8000
25) 0.0022 x 19
Exercise 10
Dividing decimals

10

100

1000

10

100

1000

20

300

4000

20

400
2
3.5
7.6
10.9
14.75
2
3.5
7.6
10.9
14.75
2
3.5
7.6
10.9
14.75
24
3.2
7.2
10.4
14.72

800
What is worse than finding a worm in the
apple you are eating?
To find out, answer each question and find it below. There will be a letter
beside it. The number of the question tells you where to put the answer in
the grid.
a) Write 32.489 correct to
1. one decimal place__________
2. two decimal places_________
3. three decimal places_________
b) Write 0.5804 correct to
4. One decimal place ___________
5. Two decimal places ___________
6. Three decimal places
___________
c) Write 4,698,693 correct to
7. Five significant figures
_________
8. Four significant figures
_________
9. Three significant figures
_________
d) Write these to the nearest whole numbers.
10. 63.29_______
11. 1.689 ________
12.
0.892_______
M
4,698,700
N
4,700,000
W
32.5
S
32.4
H
0.6
A
0.58
I
32.489
D
2
R
32.49
O
4,699,000
G
63
L
1
E
0
F
0.580
2
K
4,600,000
B
0.5
6 3 9 11
4 5 12
6
5
1 8 2 7
Answer:
3 9 10
AREA AND PERIM ETER
Exercise 12
1.
Find the area of these shapes, be careful to state the units:
a)
b)
c) This square has
6sides
cm of 7 cm
12 m
10 cm
3m
d)
e)
5m
f)
12 cm
6 cm
9 cm
13 cm
5 cm
6m
14 cm
5 cm
2. Find the perimeter of these shapes, state the units of your answer:
a)
b)
c)
9 mm
10 mm
7m
10 cm
6 cm
8 cm
5m
8mm
10 cm
d)
e)
3 cm
5 cm
6 cm
15 mm
This square has sides
of 7 cm
Area of a Parallelogram
Exercise 13
Remember the area of a parallelogram is BASE x HEIGHT.
height
base
Find the area of the following:
(Not drawn to scale)
a)
b)
3cm
9cm
7cm
4cm
c)
d)
5cm
12cm
14cm
4cm
e)
f)
19cm
6cm
15cm
7cm
Shape Revision
To get full marks, show all your working and give correct units.
Exercise 14
1) Calculate the area of the following shapes:
a)
b)
c)
3m
5 cm
15mm
6m
12 cm
5mm
2) Calculate the perimeter of each of the shapes in question 1.
3) Calculate the area of the following shapes:
a)
b)
c)
4m
8cm
8cm
10cm
6m
4cm
6cm
b) The formula to find the area of a trapezium is:
a
h
( a  b)  h
Area =
2
b
4 cm
Use the formula to find the area of:
4 cm
8 cm
Area of Shapes – Formula Sheet
Part 16
* Area of a square
=
l²
(length x length)
* Area of a rectangle = lb
(length x breadth)
* Area of a triangle
(½ x base x height)
= ½bh
* Area of a rhombus = ½ d1 xd2
(½ x diagonal 1 x diagonal 2)
* Area of a kite
(½ x diagonal 1 x diagonal 2)
= ½ d1 xd2
* Area of a parallelogram = BH
(base x height)
* Area of a trapezium = ½(a + b)h
height
½ x (total length of parallel sides) x
Pythagoras
Square and Square Root Worksheet
Exercise 17
Without using a calculator.
a)
Find:
i) 92
ii) 112
iii) 152
iv) 100
v) 169
vi) 36
b)
Find x in each of the following equations:
i)
x2 = 1
ii) x2 = 49
iii) x2 = 400
iv) x2 = 196
Use a calculator to do these and give your answers correct to 1 decimal place:
c) Find:
i) 5.52
iv) 35
b)
ii)
ii) 2.32
v) 90.65
iii) 7.82
vi) 49.55
Find x in each of the following equations:
x2 = 9.75
iii) x2 = 75
ii) x2 = 146.65
iv) x2 = 56.89
PYTHAGORAS’ THEOREM
Exercise 18
Pythagoras’ Theroem states that:-
c
a
FOR ANY RIGHT-ANGLED TRIANGLE eg
b
a2 + b2 = c2
Examples:Calculate the length of c.
We know that
 a2+ b2 = c2
 3 + 72 = c
 9 + 49 = c2
 c2 = 58
c = 58 which is 7.6cm
c
3c
m
7c
m
Calculate the length of b.
We know that
 a2+ b2 = c2
 42 + b2 = 102
 16 + b2 = 100
 b2 = 84 (100 - 16)
 b = 84 which is 9.2cm
10c
m
9cm
12c
b
m
4c
m
Calculate the length of a.
We know that
 a2 + b2 = c2
 a2 + 72 = 132
 a2 + 49 = 139
 a2 = 90 (139 - 40)
 a = 90 which is 9.5cm.
13c
m
9cm
7c12c
mm
a
QUESTIONS:Calculate the value of a, b or c for each of the following.
1
a
4
11
9cm
12c
6m
10
9cm
12c
m
b
2
7
17
a
2
5
c
9cm
12c
6m
5
11
a
8
b
6
9
4
8
12
9
c
9cm
12c
7m
12
6
a
6
3
Answers
to
below:1) 9.2
2) 7.8
3) 12.7
4) 9.8
5) 10.2
6) 11.4
7) 15.9
8) 8.9
9) 10.4

15
8
b