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MathematicsGrade 12Quality review 0/4

Grade 12 Mathematics: Series, Finance, Calculus and Trigonometry

A focused Grade 12 course covering arithmetic and geometric series, logarithms and inverse functions, annuities and amortisation, differential calculus, and compound-angle trigonometry. Every example is set in a South African context, from stokvel savings to home loans and Eskom pylons.

≈ 13 h 55 min7 sections · 33 lessonsNo ratings yet
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What you'll learn

  • Find general terms and sums for arithmetic and geometric sequences, including convergent infinite series
  • Use log laws and inverse functions to solve exponential equations and describe inverse graphs
  • Apply the future- and present-value annuity formulas to savings plans, loans and outstanding balances
  • Differentiate from first principles and by rule, and interpret the derivative as a gradient and a rate of change
  • Sketch cubic graphs using intercepts, stationary points and the point of inflection, and solve optimisation problems
  • Use compound- and double-angle identities together with the sine, cosine and area rules in two- and three-dimensional problems

Before you start

  • Work confidently with exponents, surds and the exponent laws
  • Factorise quadratic and simple cubic expressions and solve quadratic equations
  • Sketch and interpret linear, quadratic and exponential graphs
  • Apply the basic trigonometric ratios and the sine, cosine and area rules in a triangle

Course content

0/33 lessons
1. Patterns, Functions and Financial Mathematics3 lessons
  1. Arithmetic and Geometric SeriesLesson25 min
  2. Logarithms and Inverse FunctionsLesson25 min
  3. Annuities and AmortisationLesson30 min
2. Differential Calculus and Trigonometry3 lessons
  1. Limits, First Principles and the Rules of DifferentiationLesson25 min
  2. Cubic Graphs, Optimisation and Rates of ChangeLesson30 min
  3. Compound Angles and 3D TrigonometryLesson25 min
3. Sequences and Series Mastery4 lessons
  1. Solving Arithmetic Sequence ProblemsLesson25 min
  2. Solving Geometric Sequence ProblemsLesson25 min
  3. Sigma Notation and Finite SeriesLesson25 min
  4. Convergence of Infinite Geometric SeriesLesson25 min
4. Inverse Functions, Logarithms and Finance4 lessons
  1. Domains, Ranges and Inverse FunctionsLesson25 min
  2. Logarithmic Equations and LawsLesson25 min
  3. Annuity Timelines and Payment TimingLesson25 min
  4. Loan Balances and RefinancingLesson25 min
5. Differential Calculus in Depth7 lessons
  1. Limits from Graphs and TablesLesson25 min
  2. Algebraic Limits and Indeterminate FormsLesson25 min
  3. Differentiation from First PrinciplesLesson25 min
  4. Polynomial Differentiation RulesLesson25 min
  5. Stationary Points and ClassificationLesson25 min
  6. Sketching Cubic FunctionsLesson25 min
  7. Optimisation and Rates of ChangeLesson25 min
6. Advanced Trigonometry and Coordinate Geometry6 lessons
  1. Deriving Compound-Angle IdentitiesLesson25 min
  2. Double-Angle IdentitiesLesson25 min
  3. Equations with Compound and Double AnglesLesson25 min
  4. Three-Dimensional TrigonometryLesson25 min
  5. Equations of CirclesLesson25 min
  6. Tangents to Circles in Analytical GeometryLesson25 min
7. Proof, Counting and Data Modelling6 lessons
  1. The Proportionality TheoremLesson25 min
  2. Similarity Proofs and ApplicationsLesson25 min
  3. The Fundamental Counting PrincipleLesson25 min
  4. Permutations and RestrictionsLesson25 min
  5. Regression and CorrelationLesson25 min
  6. Probability with Counting PrinciplesLesson25 min