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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 real-world 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 well-known 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
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Factorising quadratics
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Factorising – Difference of two squares
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Expanding brackets (grid method)
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Expanding brackets (FOIL method)
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Expanding any two brackets
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Rearranging simple formulae
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Rearranging simple formulae - 2 steps
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Rearranging formulae with squares and square roots
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Rearranging formulae new subject appearing twice
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Simplifying Surds
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Further Calculations with Surds
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Completing the Square
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General Completing the Square
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Binomial expansion
Module 3: Inequalities
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Finding inequalities from shaded regions
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Solving linear inequalities with fractions
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Solving quadratic inequalities – Method 1
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Solving quadratic inequalities – Method 2
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Solving quadratic inequalities – Method 3
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Non-unitary x^2 - Trial and error method
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Non-unitary x^2 - Algebra method
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Non-unitary x^2 - Graphical method
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Solving quadratic inequalities - special cases
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Rational functions
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Modulus equations
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Using graphs to solve modulus equations
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Modulus inequalities
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Modulus function on a graph
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Graphical solution of modulus inequalities
Module 4: Complex Numbers
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Manipulating complex numbers and the complex conjugate
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The Argand Diagram and Modulus
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The meaning of i
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Patterns with imaginary numbers
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Writing complex numbers in polar form
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Multiplying and dividing in polar form (proof)
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Multiplying and dividing in polar form (example)
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Proof of De Moivre’s Theorem
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Complex numbers when solving quadratic equations
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Cubic equations with complex roots
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Finding the cube roots of 8
Module 2: Solving Equations
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Equations with linear functions in the denominator
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Quadratic equations using the formula
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Quadratic equations non unitary x squared
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Quadratic equations both brackets the same sign
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Quadratic equations brackets with different signs
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Quadratic equations that have to be rearranged
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Solving simultaneous equations graphically
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Simultaneous equations both negative signs
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Simultaneous equations negative and positive signs
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Simultaneous equations both positive
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Hidden quadratics
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Use of the discriminant
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Equations with indices
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Logarithmic equations
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Solving exponential equations
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From roots to functions
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Non-linear simultaneous equations
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Factor Theorem
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The Remainder Theorem
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General Remainder and Factor Theorem
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Finding roots of cubic equation
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Modulus equations
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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:
Ideal for sharing with potential employers - include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Certificates for completed Certificate courses:
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