**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 **

*Changing the subject of a formula *

**L.O To be able to rearrange equations to change the subject using the inverse methods used in linear equations.**

In linear equations we solved the problem by working out the value of the term exactly in the problem. However sometimes you may not be able to work out the exact value but instead find the value in terms of another algebraic expression for example:

The “subject of a formula” is what the formula is in terms of, with this term appearing on the left hand side of the equation.

**Example 1:**

**Example 2 : **

**Example 3 : **

**Example 4 : **

**Example 5 :**

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__Word Problems__

**a) Gravitational field strength** is denoted by the **energy** plus **three times the field strength** **divided by 2**. However NASA want to work out the field strength on **Friendo**, **Theus** and ** Germus,** three theoretical planets.

b) Greg is re-carpeting some of the university rooms. The spare room is** rectangular shaped **and has a widths of

**15.5m**. He gets a discount which is the same as

**The total coast of carpet was**

__square rooting the area of the room.__

__£18 costing £4.50 per square metre__**Work out the length of the room.**

c) Eleanor has a set of 2 cone shaped lava lamps for her bedroom. She has to buy some synthetic liquid to fill them up. The widths of each lava lamp are **5 cm** but the heights are different. The larger lamp is **2 times the height of the smaller one**. If the small lava lamp requires **14 litres of fluid**, how many litres will she need for the larger one? ( 2 d.p accuracy)

D) Salma draws a cross section of her rose patch in her garden. She simplifies and draws it in the form of a right angled triangle with a semicircle underneath covering the full width. She realises that the **areas** of both parts of the flower patch are **the same**. If this is true write a formula expressing the height of the triangle **“a”** in terms of the full rose patch.