Biggar High School
Mathematics Department
S1 Block 1
Revision Booklet
SILVER
Contents
Block 1
MNU 3-01a
Page
Round a number using an appropriate degree of accuracy, having
taken into account the context of the problem.
MNU 3-03a
Whole number and decimal number problems
MNU 3-03b
Whole number calculations
MTH 3-05a
Common factors and common multiples
MTH 3-05b
Introduction to prime numbers
MTH 3-06a
Calculating powers
MTH 3-20a
Robust, vague and misleading statistics
MTH 3-20b
Bias and sample size
MTH 3-17a
Properties of 2D shape
MNU 3-04a
Integer calculations
MTH 3-18a
Coordinates
MTH 3-14a
Simplifying expressions and substitutions
MTH 3-15a
Solving equations
MTH 3-15b
Creating equations
Learning Intentions:

MNU 3-01a
I can round a number using an appropriate degree of accuracy, having taken into
account the context of the problem.
Rounding to the nearest decimal place
1.
Round the following to the nearest whole number:
(a)
2.
(c)
08
(d) 399 9
2 37
(b)
5 95
(c) 20 86
5 761
(b)
2 958
(c) 13 006
A new speed boat is on sale at the Marina for £54 475.
Round this amount to the nearest:
(a)
5.
15 9
Round the following to 2 decimal places:
(a)
4.
(b)
Round the following to 1 decimal place:
(a)
3.
26
£10
(b)
£100
(c)
£1000
Gerard is paying up his £6130 second-hand car over 38 months.
Round each number to 1 figure accuracy, then give an estimate
for each monthly payment.
6.
Use a calculator each time and then round to one decimal place
(a)
(b)
(c)
A barrel holds 140 63 litres of water. How much would 17 barrels hold?
A field with area 1875 metres is fenced into four equal section. What is the area
of each section?
The perimeter of a square is 13 5 cm. What is the length of one side?
Learning Intentions:

MNU 3-03a
I can use a variety of methods to solve number problems in familiar contexts, clearly
communicating my processes and solutions.
Whole number and decimal problems
1.
How much change will I receive from a £10 note in a bakers shop when I buy:
1 Cheese Softie at £ 1 45
1 Sultana Cake at £2 78
1 Doughnut at 59 pence?
2.
The cost of a holiday to split equally among seven friends.
If the total bill for the holiday came to £2436, how much
did each have to pay?
3.
Graham the gardener managed to fit all of the strawberry plants he purchased into
His small allotment. He formed 60 rows, each containing 45 plants.
How many strawberry plants in total had Graham purchased?
4.
Woolco’s buy Easter eggs in boxes of 12 for £24 95.
Each egg is sold for £4 85.
How much profit is made when a whole box of 12 eggs is sold?
5.
Arrange the following group of numbers in order, smallest first
0
6.
0
0
1
0
0
Susan, Kathleen and Bridget compare their salaries.
Susan is paid £425 75 per week. Kathleen is paid £1820 00 per month
Bridget earns an annual salary of £21975 60.
Which of them earns most money (show all working)?
Learning Intentions:

MNU 3-03b
I can continue to recall number facts quickly and use them accurately when making
calculations.
Whole number calculations
1.
2.
Do the following mentally. Simply write down the answers.
(a)
(b)
(c)
(d)
57 + 48
123 + 490
530 - 170
11000 - 8550
(e)
A train carrying 84 passengers stops at a station and 27 get off the train.
How many passengers are still on the train?
(f)
The population of Hillside is 48 700. The population of Muirglen is 57 500
What is the total population of both towns?
(g)
During the summer ten thousand flies are produced every day in a forest.
How many flies will be produced in July?
There are 1000ml (milliltres) in 1 litre.
How many ml in:(a)
(b)
(c)
(d)
4 litres
30 litres
12 litres
100 litres
3.
How many seconds are there in a day?
4.
Mr Jones borrows £2400 for a family holiday.
He promises to make equal payments every 4 months for 2 years.
How much is each payment?
Learning Intentions:

MTH 3-05a
I have investigated strategies for identifying common multiples and common factors,
explaining my ideas to others, and can apply my understanding to solve related
problems.
Common factors and common multiples
1.
Write down the first five (non-zero) multiples of 7
2.
Write down all the multiples of four between 50 and 70
3.
Find the lowest common multiple of:
(a)
(b)
4.
3 and 4
3 , 4 and 5
Three cyclists train at different speeds around a circuit.
Cyclist A completes a track circuit every 2 minutes.
Cyclist B completes a track circuit every 3 minutes.
Cyclist C completes a track circuit every 5 minutes.
If they all start together, how long will it be before they all
meet each other again?
5.
Write down all the factors of 36
6.
Write down all the factors of 120 which lie between 7 and 21.
7.
Find the highest common factor of:
(a)
(b)
8.
8 and 12
5, 12 and 20
The combination of a safe is A-B-C, where A, B and C are the lowest 3 factors of 24.
Write down all possible combinations of the safe.
Learning Intentions:

MTH 3-05b
I can apply my understanding of factors to investigate and identify when a number is
prime.
Prime numbers
1.
List the first twelve prime numbers.
2.
List all the prime numbers between 100 and 110
3.
Is 39 a prime number?
4.
Using the ‘factor tree’ find all the prime factors of 54.
5.
Copy the diagram below into your jotter
Explain your answer
Following the arrows, use the instructions below.
Find the path which:



starts with a multiple of 4,
moves to a prime number,
finishes with a square number.
Shade in the correct path.
6.
What is the only prime number between 32 and 40?
7.
Explain why 23 642 is not a prime number.
8.
Is 1233 a prime number?
Learning Intentions:

MTH 3-06a
Having explored the notation and vocabulary associated with whole number powers
and the advantages of writing numbers in this form, I can evaluate powers of whole
numbers mentally or using technology.
Calculating powers
1.
Copy and complete the table below, without using a calculator
Square Numbers
1
12
2
22
3
4
42
52
6
7
8
82
92
10
102
1
4
9
25
12
2.
3.
Without using a calculator work out the following:
(a)
23
(b)
103
(c)
202
(d)
1100
(e)
34
Using a calculator work out the following:
(a)
43
(b)
105
(c)
192
(d)
55
(e)
38
Learning Intentions:

MNU 3-20a
I can work collaboratively, making appropriate use of technology, to source
information presented in a range of ways, interpret what it conveys and discuss
whether I believe the information to be robust, vague or misleading.
Robust, vague and misleading statistics
1.
For each of the following data displays:
(a)
(b)
State whether you think the information they provide is robust, vague or
misleading. Give 2 reasons for each of your answers.
Give 2 reasons for each of your answers.
Learning Intentions:

MNU 3-20b
When analysing information or collecting data of my own, I can use my understanding
of how bias may arise and how sample size can affect precision, to ensure that the
data allows for fair conclusions to be drawn.
Bias and sample size
1.
Shane asked 8 of his friends what their favourite sport was.
Shane used a bar graph to present his results
(a)
(b)
2.
How did bias and sample size affect his data?
Suggest 2 or more ways Shane could improve his survey, to ensure that the data
allows for fair conclusions to be drawn.
A group of business men and women who earn over £150 000 a year were asked their
opinions on paying 50% tax on all earnings over £150 000.
The pie chart below shows the results of the survey.
(a)
(b)
How could bias have affected this survey?
Suggest 2 or more ways in which this survey could be carried out, to ensure that
the data allows for fair conclusions to be drawn.
Learning Intentions:

MTH 3-17a
I can name angles and find their sizes using my knowledge of the properties of a range
of 2D shapes and the angle properties associated with intersecting and parallel lines.
Properties of 2D shape
1.
Copy the diagrams into your jotter.
What types of angles are shown below?
Choose from: acute, obtuse, right, straight, reflex and full turn.
2.
Copy the diagrams into your jotter
Using 3 CAPITAL letters name all the angles in the triangle
opposite.
3.
Copy the diagram into your jotter
Calculate the size of the missing angle a in the diagram below.
a
26
4.
Copy the diagram into your jotter.
Calculate the sizes of the missing angles in the diagram below.
38 
26
5.
Copy the diagram into your jotter.
Calculate the sizes of angles a b and c shown below.
23
a
90
120
6.
c
90
b
64
Copy the diagram into your jotter.
Triangle ABC is isosceles and  BAC=72
Calculate the size of :
C
a)  ABC
b)  ACB
72
A
B
7.
Copy the diagram into your jotter.
Calculate the sizes of the missing angles h and g in the diagram below.
ho
105
60
go
8.
Use your knowledge of corresponding and alternate angles to calculate missing angle
for each of the diagrams below.
9.
Copy the diagram below and use your knowledge of angle properties to fill in ALL the
missing angles.
Learning Intentions:

MNU 3-04a
I can use my understanding of numbers less than zero to solve simple problems in
context.
Integer calculations
1.
Work out the following:
2.
Work out the following:
3.
Work out the following:
4.
Calculate:
Learning Intentions:

MTH 3-18a
I can use my knowledge of the coordinate system to plot and describe the location of a
point on a grid.
Coordinates
1.
Use this grid of the zoo to identify the coordinates where you can find each of the
animals listed.
For example: Lion (12 , 5)
2.
Draw a coordinate grid with values of
between 0 and 10 and values of
between 0 and 10.
Now plot the following points on the grid:
Learning Intentions:

MTH 3-14a
I can collect like algebraic terms, simplify expressions and evaluate using substitution.
Simplifying expressions and substitution
1.
Find a mathematical way of expressing how many apples and bananas there are below.
2.
Copy each of the following and then simplify:
3.
Copy each of the following and then simplify:
4.
For a = 3, b = 7, and c = 4, calculate the value of:-
Learning Intentions:

MTH 3-15a
Having discussed ways to express problems or statements using mathematical
language, I can construct, and use appropriate methods to solve, a range of simple
equations.
Solving equations
1.
Solve for
2.
Solve for
3.
Solve for
Learning Intentions:

MTH 3-15b
I can create and evaluate a simple formula representing information contained in a
diagram, problem or statement.
Creating equations
1.
Write down a formula for the perimeter of each shape and then solve:
2.
Write down a formula for the area of each shape and then solve:
Answers
Block 1
MNU 3-01a
Round a number using an appropriate degree of accuracy, having taken into
account the context of the problem.
1
2
3
4
5
6
MNU 3-03a
1
2
3
4
5
6
MNU 3-03b
1
2
3
4
MTH 3-05a
1
2
3
4
5
6
7
8
(a)3 (b)16 (c)1 (d)400
(a)2 4 (b) 6 0 (c) 20 9
(a)5 76 (b) 2 96 (c) 13 01
(a)54480 (b)54500 (c)54000
6000 40 = 150
(a)8 3 (b) 6 0 (c) 20 9
Whole number and decimal number problems
£5 18
£348
2700
£33 25
0
0
0
Susan:
£425 75 52 = £22139 00
Kathleen: £1820 00 12 = £21840 00
Bridget:
£21975 60 1 = £21975 60
Susan earns the most
1
Whole number calculations
(a)105 (b)613 (c)2450 (d)57 (e)106200
(a)4000 (b)30000 (c)12000 (d)100000
86400
£400
Common factors and common multiples
7, 14, 21, 28, 35
52, 56, 60, 64, 68
(a)12 (b)60
30
1, 2, 3, 4, 6, 9, 12, 18, 36
8, 10, 12, 20
(a)4 (b)1
123, 132, 213, 231, 312, 321
(f)310000
MTH 3-05b
Introduction to prime numbers
1 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
2 101, 103, 107, 109
3 No; 39 has more than 2 factors : 1, 3, 13,39
4
5
6
7
8
MTH 3-06a
2, 3 (2 3 3 3 = 54)
24, 43, 36
37
It is an even number – more than 2 factors ( 1, itself and 2 …)
No
Calculating powers
1 32, 16, 5, 62, 36, 72, 49, 64, 9,81, 100, 122, 144
2 (a)8 (b)1000 (c)400 (d)1 (e)81
3 (a)64 (b)100000 (c)361 (d)3125 (e)6561
MTH 3-20a
Robust, vague and misleading statistics
Class discussion
MTH 3-20b
Bias and sample size
Class discussion
MTH 3-17a
Properties of 2D shape
1 acute, right, obtuse, reflex
2 Circle: SUT, star: UTS, square:UST
3 26
4
38 
26
5 a =6
6 (a) 72
7 g = 60
8 (a)108
b = 150
c = 26
(b) 36
h = 75
(b)99
(c)67
(d)20
(e)100
(f)77
MNU 3-04a
Integer calculations
1 (a)-1 (b)-4 (c)-4 (d)-4 (e)-10 (f)-9 (g)1 (h)2 (i)-3 (j)-1
(k)-15 (l)-30
2 (a)3 (b)7 (c)-3 (c)0 (d)-6 (e)15 (f)15 (g)-10 (h)-10 (i)-29
(j)-29 (k)-8 (l)-100
3 (a)10 (b)6 (c)5 (d)12 (e)21 (f)55 (g)1 (h)3 (i)-1 (j)0 (k)-2
4 (a)-15 (b)-21 (c)-2 (d)56 (e)-5 (f)-36 (g)20 (h)-3 (i)-2 (j)7
(k)4 (l)-5
MTH 3-18a
Coordinates
1 Lion (12,5) Tiger (0,9) Bear (6,7)
Elephant (10,10) Giraffe (7,0)
MTH 3-14a
Panda (2,6)
Gorilla (4,2)
Simplifying expressions and substitutions
1 3b + 6a
2 (a)3a (b)b (c)2c (d)7d (e)3e (f)30f (g)6g (h)10h (i)12i
(j)-7j (k)14k (l)45x
3 (a)2x + y (b)2x + 2y (c)30x -30 (4)18x + 5y (e)18b – a +32
(f)20 + 20a -3b (g)155 +
4 (a)14 (b)9 (c)14 (d)40 (e)17 (f)30 (g)4 (h)5 (i)21
(j)28 (k)9 (l)25
MTH 3-15a
Solving equations
1 (a)6
(k)90
2 (a)10
(k)5
3 (a)5
(l)5
MTH 3-15b
(b)5 (c)7 (d)8 (e)10 (f)20 (g)9 (h)20 (i)12 (j)35
(l)40
(b)9 (c)6 (d)5 (e)8 (f)7 (g)9 (h)82/7 (i)12 (j)24
(l)5
(b)5 (c)7 (d)9 (e)8 (f)10 (g)3 (h)6 (i)3 (j)7 (k)-1
(m)6.5 (n)7 (o)7 (p)6
Creating equations
1 (a)P = 3a +3a +a +a = 8a
(b)P = b + b + b + b + b = 5b
(c)P = 2c + 2c + 5 = 4c + 5
2 (a)A = 2a
a=3
(b)A = 3b
b = 1.5
2
(c)A = c
c=7
a=3
b = 11
c=9
(l)-1