
Free

Advance Learning

610 Hours

Assessment

Certification

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

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Modules List( 5 )

PROJECT MATHS STRAND 4 HIGHER LEVEL ALGEBRA

Module
1 Expressions and Formulae
Learn more about 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
2 Solving Equations
Learn more about 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


Module
3 Inequalities
Learn more about 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
Learn more about 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


END OF COURSE ASSESSMENT

Strand 4 Higher Level Algebra Assessment

Learn more about algebra.

Strand 4 Higher Level Algebra Assessment


RESOURCE

Resource: Examination Material Archive View Resource