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