Precalculus – Scheme of Work

Course Duration: One Academic Year (40 Weeks)

Level: Grade 10, 11 or 12 | Prerequisite: Algebra II or equivalent

Term 1: Functions and Algebraic Foundations (Weeks 1–10)

Weeks 1–2 – Review of Algebra Essentials

  • Properties of real numbers
  • Exponents and radicals
  • Factoring techniques
  • Solving linear and quadratic equations

Weeks 3–4 – Functions & Their Graphs

  • Function notation and evaluation
  • Domain and range
  • Graphing basics, transformations
  • Even and odd functions

Weeks 5–6 – Polynomial and Rational Functions

  • Polynomial division (long and synthetic)
  • Zeros of polynomials
  • Graphing polynomial and rational functions
  • Asymptotes, holes, end behavior

Weeks 7–8 – Exponential and Logarithmic Functions

  • Exponential growth and decay
  • Properties of logarithms
  • Solving exponential and log equations
  • Applications: finance, population models

Weeks 9–10 – Systems of Equations & Inequalities

  • Solving systems algebraically and graphically
  • Matrix methods (intro)
  • Linear programming (optional)

Term 2: Trigonometry (Weeks 11–20)

Weeks 11–12 – Trigonometric Ratios and Functions

  • Right triangle trigonometry
  • Unit circle and radian measure
  • Six trigonometric functions

Weeks 13–14 – Graphs of Trig Functions

  • Sine, cosine, tangent graphs
  • Amplitude, period, phase shift
  • Inverse trig functions

Weeks 15–16 – Trig Identities & Equations

  • Fundamental identities
  • Sum/difference, double/half angle formulas
  • Solving trig equations

Weeks 17–18 – Law of Sines & Cosines

  • Oblique triangles
  • Area using trigonometry
  • Ambiguous case

Weeks 19–20 – Trigonometric Applications

  • Harmonic motion
  • Bearings and navigation
  • Angle of elevation/depression problems

Term 3: Advanced Functions & Analytic Geometry (Weeks 21–30)

Weeks 21–22 – Analytic Geometry

  • Conic sections: circle, ellipse, parabola, hyperbola
  • Standard and general forms
  • Focus-directrix definitions

Weeks 23–24 – Parametric Equations

  • Parametric representations of curves
  • Elimination of parameter
  • Real-world motion modeling

Weeks 25–26 – Polar Coordinates & Complex Numbers

  • Polar graphing and equations
  • Conversion between polar and rectangular
  • Complex numbers in polar form
  • De Moivre’s Theorem

Weeks 27–28 – Sequences & Series

  • Arithmetic and geometric sequences
  • Sigma notation
  • Infinite series and convergence
  • Binomial theorem

Weeks 29–30 – Introduction to Limits (Optional Preview of Calculus)

  • Concept of a limit
  • One-sided and two-sided limits
  • Graphical and numerical approaches

Term 4: Review & Project-Based Application (Weeks 31–40)

Weeks 31–34 – Review & Mastery Weeks

  • Mixed review of all major units
  • Thematic problem sets
  • Graphical calculator integration

Weeks 35–36 – Modeling with Mathematics

  • Real-world modeling projects
  • Curve fitting, regression, sinusoidal modeling

Weeks 37–38 – Final Project or Research Task

  • Topics could include: Trigonometry in architecture, Growth models, Game theory basics, etc.

Weeks 39–40 – Final Review & Exams

  • Practice exams
  • Concept reinforcement
  • Individualized support and reflection

🧮 Tools & Resources