Table of Contents

 

 Unit 1 | Algebra

Page 1 | Expressions and Formulae

Page 2 | Index notation

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 1 | Transformations

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 5 | Circle geometry

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 6 | Decimals

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

Algebraic Proof


L.O To be able to determine whether a statement is true or false through algebraic explanation.

Simplifying, factorising and solving numerical problems are only one aspect of algebra. The test of true algebraic understanding is using it to prove different concepts and mathematical statements.

A few Algebraic expressions you should know :

Notice how they both have 1,2 and 3 after the same starting terms of n or 2n. n is usually used as it is a simpler term.

Notice how they both have multiples of the specified number before n. They also go up in a linear orderr multiples so they are consecutive.

Example 1:

Prove if the sum of any 3 consecutive integers is a multiple of 3.

So, the sum of any 3 consecutive numbers where n + 1 is an integer will always be a multiple of 3.

Example 2:

Prove if the sum of 4 consecutive odd numbers is a multiple of 8.

So, the sum of any 4 consecutive odd numbers, where n + 2 is an integer will always be a multiple of 8.

Example 3:

Prove that the sum of the squares of 2 consecutives even numbers is never a multiple of 8.

Here the sum of the squares of 2 consecutive even numbers is never a multiple of 8.

Example 4:

Prove that if you have 2 consecutive even numbers, if they are squared and you find the difference, it is the same as adding the two numbers and multiplying the total sum by 2.

Here both values are the same hence multiplying the sum of 2 consecutive even numbers acquires the same value after squaring and finding the difference.

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“Winners are not people who never fail,
But those who never quit.” Edwin Louis Cole.

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