Download GFS Maths Year 8 Revision Booklet

GFS Maths Year 8
Revision Booklet
Student Name:
Student Tutor Group:
Maths Class:
Maths teacher:
How to use this revision booklet
Repeat these steps till you are 100% with EVERY topic.
Step 1
Look at the scheme of work – this lists all the topics you are learning this
year, and those in previous years. Highlight or note down the topics you are
not 100% confident with.
Step 2
Revise the topics you need to go over, using a revision guide or any of the
following resources, ranked from 1st to 5th in how useful:
 Hegartymaths.com
(videos and practice questions for EVERY TOPIC UP TO GCSE)
Choose any lesson from each of the 6 strands or search for the lesson in the search
bar at the top
 corbettmaths.com
(really good resource, with videos and lots of practice)
 khanacademy.com
(helpful videos walked through clearly)
 mathsisfun
(good examples to work through and understand)
 GCSE bbc bitesize
(clear examples in sections)
Step 3
Practise questions on that topic using this revision booklet, and the other
resources.
Step 4: Ask your maths teacher for extra help if you are still stuck!
In Year 7 you should have studied the following topics:
In this booklet there will be information and questions on the topics covered in Year 8.
Therefore if you see any topics in the Year 7 scheme of work that you think you need to
revise visit websites mentioned above or speak to your teacher.
These are the topics we have looked at in Year 8:
Note, some pupils may have covered less material dependent on their starting point.
Autumn 1 Revision
Primes
A prime number is a number that only has two factors: itself and 1.
The following numbers are prime numbers:
2, 5, 7, 11, 13, 17, ….
a) What are the next 5 prime numbers?
b) Why is 1 not a prime number?
Indices
Write these numbers in index form:
Example
3
3
a)
b) 2
2
2
c) 5
5
5
5
3
3
3
3
HCF and LCM
This section introduces the idea of the highest common factor and lowest common multiple of a
pair of numbers.
The highest common factor (HCF) of two whole numbers
is the largest whole number which is a factor of both.
HCF Example
Consider the numbers 12 and 15:
The factors of 12 are : 1, 2, 3, 4, 6, 12.
The factors of 15 are : 1, 3, 5, 15.
1 and 3 are the only common factors (numbers which are factors of both 12 and 15).
Therefore, the highest common factor of 12 and 15 is 3.
The lowest common multiple (LCM) of two whole numbers
is the smallest whole number which is a multiple of both.
LCM Example
Consider the numbers 12 and 15 again:
The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, ....
The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....
60 is a common multiple (a multiple of both 12 and 15), and there are no lower common
multiples.
Therefore, the lowest common multiple of 12 and 15 is 60.
Prime Factorisation
Example
Write each of the following numbers as a product
of their prime factors:
72
So
2
3
60
85
52
100
Using Venn diagrams to find the LCM and HCF
(a) Find the highest common factor and lowest common multiple of 50 and 70 by following the
steps below:
What is 50 as a product of its prime factors?
What is 70 as a product of its prime factors?
What is the HCF of 50 and 70? (find it by multiplying together the factors which appear in both lists
above)
What is the LCM of 50 and 70? (find it by multiplying together the factors which appear in either list
above)
(b) Find the highest common factor and lowest common multiple of 900 and 270 by following
the steps below:
What is 900 as a product of its prime factors?
What is 270 as a product of its prime factors?
What is the HCF of 900 and 270? (find it by multiplying together the factors which appear in both lists
above)
What is the LCM of 900 and 270? (find it by multiplying together the factors which appear
in either list above)
Adding and Subtracting Fractions
Autumn 2 Revision
Negative Numbers
Adding and Subtracting
Multiplying and Dividing
Formulae and expressions
Extension
Linear Equations
Bronze
Silver
Gold
Linear Sequences: nth terms
Example
2, 5, 8, 11, 14
The difference is 3. So it is like the 3 times table but everything has shifted
down one. So the formula is 3n – 1.
Spring 1 Revision
Angles on a straight line, around a point, vertically opposite angles and angles
in parallel lines
Types of triangles and angles in triangles
Types of quadrilaterals and angles in quadrilaterals
Name each of the following shapes:
Area and perimeter of composite shapes
Calculate the area and perimeter of these shapes:
1.
2.
Area of trapeziums and parallelograms
Conversions between units of length and units of area
Convert these following units of length
Convert these units of area
Spring 2 Revision
Convert between fractions, decimals and percentages
Finding a percentage of an amount
Percentage increase and decrease
Finding the whole given the percentage
Ratio
Speed, Distance and Time
Summer 1 Revision
Rounding to decimal places
Rounding to significant figures
Parts of a circle
Area and circumference of a circle
Work out the area and circumference of:
3D shapes and their nets
Question 1: Name each of the shapes below and work out how many edges,
faces and vertices they have:
Surface area
Volume of cuboids and other prisms
Summer 2 Revision
Tables and charts
Averages, range and outliers