**Table of Contents**

** Unit 1 | Algebra**

Page 1 | Expressions and Formulae

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

** Unit 2 |Graphs**

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

** Unit 3 |Geometry and Measure **

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

**Unit 4 | Numbers**

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

** Unit 5 | Statistics and Probability **

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

**Unit 4 | Calculus **

* Solving Linear Equations *

**L.O To be able to use inverse operations to solve algebraic expressions**

Equations always include an **equals sign** so then there are two parts to the expression. The key to solving equations is balancing out both sides which usually involves making the algebraic term the subject.

**Example 1:** Solve the equation 2s + 1 = 29

**Example 2:** Solve the equation 3p – 4 = 38

**Example 3:** Solve the equation 5 (b – 3 ) = 35

However there is also an alternative and quicker way of answering this question:

**Example 4:** Solve the equation 7 – 8x = 15

**Example 5:** Solve the equation 7 – a = 3a + 5

**Word Problems **

Sometimes you will have to write the expression itself before you solve it.

a) John thinks of a number. He multiplies the number 9 then subtracts 6 from that total. If he is left with 21, which number did John initially think of?

b)A triangle has the angles 3x +20 , x and 2x. Samantha wants to work out the value of x in this triangle.

c) Amelia is x years old. Her brother Bailey is 6 years older than her. Amelia’s mum is 3 times the age of bailey and Amelia’s father is 5 years younger than Amelia’s mum. Write **separate expressions **for the ages of Amelia, Bailey, mum and dad in terms of Amelia’s age.

d) Using the information from the question above. If Amelia’s mum is 45 years old then how old is each member of the family age.

e) Aadil has moved into his university apartment. He found some blue prints of the bathroom and a spare room in the house (diagram below). He has a lot of furniture to fit in so worked out the perimeter of each room. If the **perimeters of each room are the same** what is the **area of the bathroom**?

f) Amina’s Lawn is pictured on the side. She wanted to apply some fresh soil to the lawn and worked out that the area was **60cm ^{2}**. However after applying the soil she notices foxes and rabbits burrowing into the lawn so decides to put up a fence along the full perimeter of the lawn. If a fence cost

**£2.50 per cm**, how much will a full fence for her lawn cost?