**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 **

*Quadratic Equations *

**L.O To be able to solve quadratic equations through factorising, completing the square and using the quadratic formulae.**

On the previous sheet we learnt how to factorise quadratic equations. If you are told to solve a problem like **x ^{2} + 6x + 8 = 0** then the way to tackle it is to

**factorise**first. After factorising you get

**(x+4) (x+2) = 0**you have to work out different values of x that can go in the brackets that will make the equation work.

**Example 1:**

Solve the equation x(3x-2)=0

Solve the equation x(3x-2)=0

**Example 2:**

__ Solving by Completing the Square__

Sometime the quadratic equation can’t easily be factorised, in that case you have to “complete the square”, this is denoted by the following equation:

**Example 1:**

**Example 2:**

**Solving using the Quadratic Formula**

In calculator papers you will be expected to use this method of solving quadratic equations. It is simpler than it appears, you have to insert the correct numbers into the correct part of the equation and write the answers to the specified degree of accuracy.

The formula for a quadratic equation in the form **ax ^{2} + bx + c** is :