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Strand 4 Leaving Certificate Higher Level Algebra - Revised
Enhance your mathematical knowledge from Algebra to Numbers
Description
Algebra is the natural language and the lifeblood of Mathematics and perfectly links between number, trigonometry, geometry and functions. It would be impossible to solve or even formulate real-world problems without algebraic notation.
Firstly, students are introduced to representing numbers with letters and then they move on to look at how to convert problems into equations which can be solved by various well-known techniques in algebra.
Students are taught how to solve quadratic, cubic and simultaneous equations and then they expand their knowledge to the solutions of inequalities. Using trial and error to search for roots and using synthetic division is covered in this strand.
Start Course NowModules
Expressions and Formulae
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Expressions and Formulae - Learning Outcomes
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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
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Expressions and Formulae - Lesson Summary
Solving Equations - Part 1
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Solving Equations - Part 1 - Learning Outcomes
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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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Solving Equations - Part 1 - Lesson Summary
Solving Equations - Part 2
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Solving Equations - Part 2 - Learning Outcomes
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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
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Solving Equations - Part 2 - Lesson Summary
Inequalities
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Inequalities - Learning Outcomes
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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 Inequalities
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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
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Inequalities - Lesson Summary
Complex Numbers
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Complex Numbers - Learning Outcomes
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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
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Complex Numbers - Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
- Recognize how to factorise quadratics
- Identify how to expand brackets using both the grid and FOIL methods
- Discuss and define binomial Expansion
- Recognize how to solve linear equations that contain fractions
- Recognize how to solve quadratic equations, using formula and graphics
- Recognize how to solve simultaneous equations
- Identify how to solve logarithmic and exponential equations
- Recognize how to solve Quadratic inequalities using the Graphical Method
- Recognize how to solve Quadratic inequalities using three different methods
- Define Rational Inequalities and recognize how to solve them
- Identify how to work out and calculate modulus inequalities and functions algebraically and graphically
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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