**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 **

*Circle Geometry*

L.O – To be able to recognise and apply the rules of circle geometry

Don’t worry too much about the explanations in blue – they can be a bit confusing!

Make sure you memorise all the rules and be able to recognise the rules when you see the images as shown below

**1. Angle in a semicircle = 90º**

**x = 90º**

**A triangle where the base is the diameter of the circle will always make an angle of 90º, where the triangle hits the edge of the circle.**

(The angle we are referring too is the one opposite the diameter/not in contact with the diameter of the circle)

**2. Angle at the centre is double the angle at the edge**

**y = 2x**

**The angle subtended (made) at the centre of a circle is double the angle at the edge from the same two points.**

**3. Angles in the same segment are equal**

**x = y**

**Angles subtended (made) by the same arc at the circumference are equal**

**4. Opposite angles of a cyclic quadrilateral add up to 180º**

**x + y = 180º**

**A cyclic quadrilateral is a 4 sided shapes formed inside a circle, with all 4 vertices touching the circumference of the circle**

**5.The angle between a tangent and radius is 90º**

A tangent to a circle is a line which touches the circle at one point

**A tangent is always at right angles to the radius at the point it touches the circles**

**6. Chord bisector is a diameter**

A chord is any line drawn across a circle

**The line that cuts the chord in half (bisects it), is the diameter of the circle as it goes through the centre of the circle.**

**7. Alternate segment theorem**

**The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment.**

**8. Tangents from a point outside the circle are equal in length**

**Two tangents to a circle from a point (T) are equal**

**Example 1:**

Find angle BAC

**Angle ACB = 90º**

** Angle in a semicircle = 90º**

**Angle BAC = 35º**

** Angles in a triangle add up to 180º**

Find angle POQ

**Angle POQ= 124º**

** Angle at the centre is double the angle at the edge**

Find angle CBX

**Angle ACB = 32º**

** Angles in the same segment are equal**

**Angle CBX = 63º**

** Angles in a triangle add up to 180º**

Find angle WXY

**Angle WXY = 111º**

** Opposite angles in a cyclic quadrilateral add up to 180º**

Find angle SRT

**Angle SOT = 144º**

** Angle at the centre is twice angle at circumference**

**Angle RSO and RTO = 90º**

** Angle between a tangent and radius is 90º**

**Angle SRT = 36º**

** Angles in a quadrilateral add up to 360º**

Tips

- Always show your working and write out the rules you are using, especially in the exam!

- You may have to use several rules in order to find some angles!