GFS Maths Year 7
Revision Booklet
Student Name:
Student Tutor
Maths Class:
Maths teacher:
Group:
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!
Area of Quadrilateral, Triangles and Trapeziums.
Area of Quadrilaterals
(Total 8 Marks)
Area of Triangles
(Total 6 Marks)
Area of Trapeziums
(Total 6 Marks)
Basic Angles and Angles in Triangles
Basic Angles
Calculate the size of the unknown angle.
(Total 6 Marks)
Angles in Triangles
Calculate the size of the unknown angles.
(Total 6 Marks)
Mixed Angles
Calculate the size of the unknown angles.
Algebra: Collecting Like Terms
Collecting Like Terms
Simplify (HINT: think about fruit in a fruit bowl it cannot be mixed, so we cannot mix different letters)
a) 3g + 5g =
b) e + f + e + f + e =
c) 5p + 2q – 3p – 3q =
d) 2xy + 3xy – xy =
e) 5x² + 2x – 3x² =
(Total 5 Marks)
Simplify
a) p x p x p x p =
b) 2r x 5p =
c) 4p x 2q =
d) 3b x 4b² x 2c² =
(Total 5 Marks)
Algebra: Expanding and Factorising Brackets.
Expanding Brackets
(HINT: all terms in the bracket are multiplied by the term outside the bracket)
a) Expand 3(x + 2)
b) Expand 3(5p – 2)
c)
Expand 4x(1 + 3x)
d) Expand 7a(2a – 3)
e) Expand and Simplify 4b(3 +2b) - b²
f) Expand and Simplify 2(3x + 1) + 5(3x – 1)
g) Expand and Simplify 2(r + 3) + 3(2r + 1)
(Total 10 Marks)
Factorising Brackets
(HINT: The HCF goes outside of the bracket)
a) Factorise 5t + 20
b) Factorise 8p – 6
c)
Factorise 5x + 15
d) Factorise 16y – 4y
e) Factorise 48f + 6f
f)
Factorise y³ - y²
g) Factorise 24xy + 6x²
(Total 10 Marks)
Algebra: Substitution.
Substitution Positive
(HINT: think in sport you take a player off and replace him/her with another player – in algebra we replace
letters with numbers)
If x = 6 and y = 2, calculate the following:
a) x²
b) 5x + y
c) X + y²
d) y + 16
x
(Total 5 Marks)
Substitution Negative
a) Work out the value of 2a + ay, when a = -5 and y = -3
b) Work out the value of 5t² - 7, when t = -4
(Total 5 Marks)
Substitution into a Formula
V = 3b + 2b²
a) Find the value of V, when b = 4.
h = 5t² + 2
b) Work out the value of h, when t = -2
V = u + at
c) Work out the value of V, when a = 4, t = 3, u = 23
d) Work out the value of U, when v = 30, a = 2, t = 8
(Total 10 Marks)
Fractions: Simplify, Equivalent, Convert Mixed to Improper and Vice Versa
Simplifying Fractions
(HINT: divide the numerator and
denominator by the same until you can’t anymore)
Equivalent Fractions
(HINT: equivalent means equal, so you need the
fractions to equal each other by multiplying or
dividing)
(Total 5 Marks)
(Total 5 Marks)
Converting Fractions
Mixed to Improper
Improper to Mixed
(Total 10 Marks)
Fractions: Multiply, Divide, Add and Subtract.
Multiply Fractions
(HINT: remember to simplify your answers)
Multiply each of the fractions.
Dividing Fractions
(HINT: Keep the first, Flip the second, Change the
sign)
Which is larger?
(Total 7 Marks)
(Total 5 Marks)
Add and Subtract Fractions
(HINT: denominator MUST be the same before you add or subtract)
(Total 8 Marks)
Percentages.
Finding a Percentage
(HINT all percentages are out of 100%)
f) 50% of £24 =
g) 25% of £200 =
h) 10% of 60g =
i) 75% of 12ml =
j) 35% of £40 =
(Total 5 Marks)
Percentage Increase
(HINT find the percentage and add it to the original amount)
e) Increase £24 by 50% =
f) Increase £200 by 25% =
g) Increase £60 by 10% =
h) Increase £30 by 1% =
i) Increase £12 by 0.5% =
(Total 5 Marks)
Percentage Decrease
(HINT find the percentage and subtract it from the original amount)
a) Decrease 12m by 75% =
b) Decrease £80 by 20% =
c) Decrease 20kg by 5% =
d) Decrease £240 by 1% =
e) Decrease £20 by 0.5% =
(Total 5 Marks)
Applications: Worded Questions
a) Simon’s salary last year was £35400, he saved 10% of his salary. Simon wants to buy a car costing
£3650. Has he saved enough money?
b) A packet of breakfast cereal contains 750g of cereal plus ‘20% extra free’. Work out how much
extra cereal the packet contains.
c) Jeevan buys a van for £20000. The van depreciates in value by 25% in one year. How much is it now
worth?
d) Last year 1650 people came to see a school play. This year attendance was down by 20%. How
many people came to see the school play?
e) Martin had to buy some cleaning materials. The cost of the materials was £64 plus VAT at 20%.
Work out the total cost of the materials.
(Total 5 Marks)
Fractions, Decimals and Percentages.
Converting Decimals into Fractions
(HINT: think about place value, and simplify your fraction)
h) 0.5
i) 0.03
j) 0.125
k) 0.35
l) 2.75
(Total 5 Marks)
Converting Fractions into Decimals
(HINT: think about place value, and simplify your fraction)
a)
b)
c)
d)
e)
(Total 5 Marks)
Converting between Fractions and Percentages
(Total 10 Marks)
Ratio
Ratio Skills
1) Write the following ratios as fractions:
a.
b.
c.
2) Write a ratio of black to white counters for each of the following, put your answer in the simplest
form:
a.
b.
3) Find the equivalent ratios:
a. 3 : 6
9 : ____
b. 18 : 4
9 : ____
c. ____:5
30 : 10
(Total 8 Marks)
Dividing an Amount into a Ratio
(Hint ADAM – Add, Divide and Multiply)
1) Abby and Brian share the following amounts of money in the given ratios. Work out how
much each of them recieves.
a. £400 in the ratio 2:3
b. £280 in the ratio 2:5
c. £1000 in the ratio 19:1
2) Amy, Jack and Tony share £60 in the ratio 3:4:5. How mcuh money does each of them receive?
(Total 4 Marks)
Application of ratio: Worded Questions
1) A school raises money for two charities. Mind and Oxfam in the ratio of 2:3. In Janury the
school raises £180. How much does the school give to each charity?
2) Mike and Jenn split some money in the ratio of 3:4. If Mike gets £21, how much does Jenn get?
3) Jodie and Ade share some sweets in the ratio 2:7. Jodie gets 18 sweets, how many sweets does
Ade get?
4) Nara, Rebecca and Jorden share some easter eggs in the ratio 2:5:7. If Rebecca gets 60 eggs,
how many do the other get?
(Total 8 Marks)
Calculations; Powers of 10; BIDMAS, Types of a Number
Calculations
You must show your working for each of these questions
1) 24 x 7
…………………………………………………..
2) £1.35 x 32
…………………………………………………..
3) 525 ÷ 5
…………………………………………………..
4) 318 ÷ 6
…………………………………………………..
BIDMAS
Types of Number