
Free Course

Advance Learning

610 Hours

Assessment

Certification

Academic  Secondary  Level 2

50 Pts
Strand 4 Higher Level Algebra

Description

Outcome

Certification

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. 
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.

All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.
Having an official Alison document is a great way to celebrate and share your success. It is: Ideal to include with CVs, job applications and portfolios
 A way to show your ability to learn and achieve high results
Modules List( 5 )

PROJECT MATHS STRAND 4 HIGHER LEVEL ALGEBRA

Module
1 Expressions and Formulae
Learn more about expressions and formulae.

Factorising quadratics
Start Topic

Factorising – Difference of two squares
Start Topic

Expanding brackets (grid method)
Start Topic

Expanding brackets (FOIL method)
Start Topic

Expanding any two brackets
Start Topic

Rearranging simple formulae
Start Topic

Rearranging simple formulae  2 steps
Start Topic

Rearranging formulae with squares and square roots
Start Topic

Rearranging formulae new subject appearing twice
Start Topic

Simplifying Surds
Start Topic

Further Calculations with Surds
Start Topic

Completing the Square
Start Topic

General Completing the Square
Start Topic

Binomial expansion
Start Topic


Module
2 Solving Equations
Learn more about solving equations.

Equations with linear functions in the denominator
Start Topic

Quadratic equations using the formula
Start Topic

Quadratic equations non unitary x squared
Start Topic

Quadratic equations both brackets the same sign
Start Topic

Quadratic equations brackets with different signs
Start Topic

Quadratic equations that have to be rearranged
Start Topic

Solving simultaneous equations graphically
Start Topic

Simultaneous equations both negative signs
Start Topic

Simultaneous equations negative and positive signs
Start Topic

Simultaneous equations both positive
Start Topic

Hidden quadratics
Start Topic

Use of the discriminant
Start Topic

Equations with indices
Start Topic

Logarithmic equations
Start Topic

Solving exponential equations
Start Topic

From roots to functions
Start Topic

Nonlinear simultaneous equations
Start Topic

Factor Theorem
Start Topic

The Remainder Theorem
Start Topic

General Remainder and Factor Theorem
Start Topic

Finding roots of cubic equation
Start Topic

Modulus equations
Start Topic

Using graphs to solve modulus equations
Start Topic


Module
3 Inequalities
Learn more about inequalities.

Finding inequalities from shaded regions
Start Topic

Solving linear inequalities with fractions
Start Topic

Solving quadratic inequalities – Method 1
Start Topic

Solving quadratic inequalities – Method 2
Start Topic

Solving quadratic inequalities – Method 3
Start Topic

Nonunitary x^2  Trial and error method
Start Topic

Nonunitary x^2  Algebra method
Start Topic

Nonunitary x^2  Graphical method
Start Topic

Solving quadratic inequalities  special cases
Start Topic

Rational functions
Start Topic

Modulus equations
Start Topic

Using graphs to solve modulus equations
Start Topic

Modulus inequalities
Start Topic

Modulus function on a graph
Start Topic

Graphical solution of modulus inequalities
Start Topic


Module
4 Complex Numbers
Learn more about complex numbers.

Manipulating complex numbers and the complex conjugate
Start Topic

The Argand Diagram and Modulus
Start Topic

The meaning of i
Start Topic

Patterns with imaginary numbers
Start Topic

Writing complex numbers in polar form
Start Topic

Multiplying and dividing in polar form (proof)
Start Topic

Multiplying and dividing in polar form (example)
Start Topic

Proof of De Moivre’s Theorem
Start Topic

Complex numbers when solving quadratic equations
Start Topic

Cubic equations with complex roots
Start Topic

Finding the cube roots of 8
Start Topic


END OF COURSE ASSESSMENT

Strand 4 Higher Level Algebra Assessment

Learn more about algebra.

Strand 4 Higher Level Algebra Assessment
Start Topic


RESOURCE

Resource: Examination Material Archive View Resource