Pre-Calculus

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

• Graphing calculators and/or Desmos

• Algebra tiles, visual manipulatives

• Math modeling tools

• Opportunities for cross-topic projects