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Strand 4 Higher Level Algebra

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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 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.

  • 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 share your success. Plus it’s:

    • Ideal for including in CVs, job applications and portfolios
    • An indication of your ability to learn and achieve high results
    • An incentive to continue to empower yourself through learning
    • A tangible way of supporting the Alison mission to empower people everywhere through education.

Modules List( 5 )
  • 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 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
    • Non-linear 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
    • 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
    • Non-unitary x^2 - Trial and error method
    • Non-unitary x^2 - Algebra method
    • Non-unitary 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
  • Strand 4 Higher Level Algebra Assessment
    • Strand 4 Higher Level Algebra Assessment
  • Resource: Examination Material Archive
Topics List ( 1 )
Strand 4 Higher Level Algebra Assessment
Learn more about algebra.
Course Features
  • Duration

    6-10 Hours

  • Publisher

    Advance Learning

  • Video


  • Audio


  • Assessment


  • Certification


  • Price


  • Reward

    50 Pts

  • Responsive


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