3.1 Algebra

Intro: PDF

Definition, solving equations by checking all possibilities: PDF, Video

Solving Inequalities by finding critical values and drawing a sign diagram: PDF, Video

Properties: PDF, Video

Solving Equations by Squaring: PDF, Video

Solving Inequalities by Squaring: PDF, Video

Solving Inequalities by formulas: PDF, Video

Graphing the modulus of linear functions: PDF, Video

Solving Equations and Inequalities by graphing: PDF, Video

Topical past paper: PDF, Video, Questions only

Resources and references

• • • https://www.desmos.com/calculator

    • https://www.symbolab.com/

    • https://www.basic-mathematics.com/properties-of-absolute-value.html

Intro: PDF

Polynomial long division: PDF, Video

Remainder theorem: PDF, Video

Factor theorem: PDF, Video

Horner's method of synthetic division: PDF, Video

Equating coefficients and algebraic manipulation: PDF, Video

Rational root theorem and factorizing completely: PDF, Video

Proof of the rational root theorem: PDF, Video

Topical past paper: PDF, Video, Questions only

Resources and references

• • • https://www.symbolab.com/solver/polynomial-long-division-calculator

    • https://billcookmath.com/sage/algebra/Horners_method.html

    • https://www.cuemath.com/algebra/rational-root-theorem/

Intro: PDF

Improper algebraic fractions: PDF, Video

3 Forms of partial fractions: PDF, Video

Equating coefficients: PDF, Video

Topical past paper: PDF, Video, Questions only

Resources and references

• • • https://www.symbolab.com/solver/partial-fractions-calculator

    • https://numberdyslexia.com/8-examples-of-partial-fractions-application-in-real-life/

Intro: PDF

The first few terms: PDF, Video

Manipulation to (1+x): PDF, Video

Valid for: PDF, Video

Proof of binomial expansion: PDF, Video

Topical past paper: PDF, Video, Questions only

Resources and references

• • • https://school.careers360.com/maths/binomial-theorem-chapter-pge#

    • https://www.wolframalpha.com/widgets/view.jsp?id=636e9129cd380c39edbe157a3303e887