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GFS Maths Year 7 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!

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)

(Total 5 Marks)

Equivalent Fractions (HINT: equivalent means equal, so you need the fractions to equal each other by multiplying or dividing)

(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)

(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 b. 18 : 4 c. ____:5 9 : ____ 9 : ____ 30 : 10

(Total 8 Marks)

a)

b)

c)

d)

e)

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