Strand 4 Higher Level Algebra
Learn about simultaneous, quadratic and cubic equations and then extend your knowledge to the solution of inequalities.
Description
Algebra is the lifeblood and the natural language of Mathematics and provides a perfect link between number, geometry, trigonometry and functions. It would be impossible to formulate and solve realworld problems without algebraic notation.
Students are first introduced to representing numbers with letters and then they are taught how to convert problems into algebraic equations which can be solved by means of wellknown techniques.
Students are taught how to solve simultaneous, quadratic and cubic equations and then extend their knowledge to the solution of inequalities. Searching for roots by trial and error and the use of synthetic division is also covered in this strand.
Modules
Strand 4 Higher Level Algebra Assessment
Module 1: Expressions and Formulae

Factorising quadratics

Factorising – Difference of two squares

Expanding brackets (grid method)

Expanding brackets (FOIL method)

Expanding any two brackets

Rearranging simple formulae

Rearranging simple formulae  2 steps

Rearranging formulae with squares and square roots

Rearranging formulae new subject appearing twice

Simplifying Surds

Further Calculations with Surds

Completing the Square

General Completing the Square

Binomial expansion
Module 3: Inequalities

Finding inequalities from shaded regions

Solving linear inequalities with fractions

Solving quadratic inequalities – Method 1

Solving quadratic inequalities – Method 2

Solving quadratic inequalities – Method 3

Nonunitary x^2  Trial and error method

Nonunitary x^2  Algebra method

Nonunitary x^2  Graphical method

Solving quadratic inequalities  special cases

Rational functions

Modulus equations

Using graphs to solve modulus equations

Modulus inequalities

Modulus function on a graph

Graphical solution of modulus inequalities
Module 4: Complex Numbers

Manipulating complex numbers and the complex conjugate

The Argand Diagram and Modulus

The meaning of i

Patterns with imaginary numbers

Writing complex numbers in polar form

Multiplying and dividing in polar form (proof)

Multiplying and dividing in polar form (example)

Proof of De Moivre’s Theorem

Complex numbers when solving quadratic equations

Cubic equations with complex roots

Finding the cube roots of 8
Module 2: Solving Equations

Equations with linear functions in the denominator

Quadratic equations using the formula

Quadratic equations non unitary x squared

Quadratic equations both brackets the same sign

Quadratic equations brackets with different signs

Quadratic equations that have to be rearranged

Solving simultaneous equations graphically

Simultaneous equations both negative signs

Simultaneous equations negative and positive signs

Simultaneous equations both positive

Hidden quadratics

Use of the discriminant

Equations with indices

Logarithmic equations

Solving exponential equations

From roots to functions

Nonlinear simultaneous equations

Factor Theorem

The Remainder Theorem

General Remainder and Factor Theorem

Finding roots of cubic equation

Modulus equations

Using graphs to solve modulus equations
Learning Outcomes
Having completed this course students will be able to:
 Solve linear simultaneous equations with 3 unknowns;
 Factorise expressions of order 2 and 3;
 Search for roots of cubic equations and solve them;
 Solve one linear equation and one equation of order 2 with two unknowns;
 Solve basic inequalities;
 Solve inequalities involving fractions.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
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