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Algebra 1

Revision Notes

Section 1 - Polynomial expressions

Simplifying expressions

Multiplication - Expanding brackets

Perfect square quadratic expressions

Long division - array method


Section 2 - Polynomial functions

Problem in context

Adding/subtracting functions
Degree of a polynomial function

Evaluating polynomial functions


Section 3 - Factorising algebraic expressions

There are 6 methods of factorising required for the LCHL Course
  • HCF
  • Grouping
  • DOTS
  • Quadratic
  • Difference of Two Cubes
  • Sum of Two Cubes

 Difference of two squares (DOTS)

Factorising to simplify an algebraic fraction
DOTS and HCF

Factorising quadratic expressions

Sum and difference of two cubes


Section 4 - Simplifying algebraic expressions

Simplifying fractions with common factors

Adding/subtracting algebraic fractions

Simplifying fractions using multiplication


Section 5 -  Binomial expansions 

Using the Binomial Theorem


Section 6 - Algebraic identities 

Coefficients of like powers are equal on both sides of the equation


Section 7 - Manipulating formulae

Changing the subject of a formula - balance method


Section 8 - Algebraic patterns

Linear pattern problem

Quadratic pattern problem


Section 9 - Solving equations

Linear equations - Balance method


Section 10 - Solving simultaneous linear equations

Solving: 2 unknowns
​Substitution & Elimination methods

Solving: 3 unknowns
Elimination method

Problems in context


Some sample questions with solutions

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Solution

Evaluate Polynomial Functions

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Solution


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Solution
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Solution

Factorise including Sum and Difference of Two Cubes

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Solution

Add/subtract and Simplify Fractions

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Solution i
Solution ii

Manipulate Formula

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Solution

Polynomial Identities

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Soluton
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Solution

Solving Linear Equations

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Solution

Simultaneous Equations - Intersection of Two Lines

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Solution

Simultaneous Equations - Intersection of Three Planes

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Solution

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