Curriculum Topics – Grades 9-10-11
- Advanced Number Theory and Proof
- Properties of integers, divisibility, and modular arithmetic
- Rational and irrational number classification
- Prime factorization, Euclidean algorithm
- Direct proof, contradiction, and counterexample
- Olympiad-style number puzzles and Diophantine problems - Algebra, Expressions, and Equations
- Polynomial identities and factoring techniques
- Rational expressions and complex fractions
- Quadratic equations (factoring, formula, completing square)
- Systems of equations (substitution, elimination, graphing)
- Radical and exponential equations - Functions and Graphical Analysis
- Linear, quadratic, exponential, and piecewise functions
- Function transformations and inverse functions
- Domain, range, intercepts, asymptotes
- Modelling real-life data with functions
- Graphical problem solving and intersections - Inequalities and Optimization
- Linear and quadratic inequalities
- Compound and absolute value inequalities
- Systems of inequalities and feasible regions
- Word problems involving constraints and maximum/minimum values
- Intro to optimisation and linear programming - Coordinate Geometry and Vectors
- Equations of lines, distances, and midpoints in the plane
- Slopes, perpendicularity, and parallelism
- Circle and parabola equations
- Vectors: representation, magnitude, direction
- Dot product and basic vector geometry - Geometry, Constructions, and Trigonometry
- Triangle similarity, congruence, and geometric reasoning
- Circles: chords, tangents, cyclic quadrilaterals
- Compass-straightedge constructions
- Trigonometric ratios, identities, and equations
- Laws of sines and cosines, area of triangles, bearing problems - Sequences, Series, and Recursion
- Arithmetic and geometric sequences and sums
- Sigma notation and nth-term formulas
- Recursive patterns and iterative processes
- Real-life modelling with growth and decay - Probability and Combinatorics
- Conditional probability and independence
- Tree diagrams and Bayes' Theorem (introductory)
- Permutations, combinations, and Pascal’s Triangle
- Inclusion-exclusion principle
- Olympiad-style probability reasoning - Data Analysis, Statistics, and Modelling
- Interpreting large datasets: mean, median, mode, standard deviation
- Correlation and regression lines
- Statistical fallacies and misleading graphs
- Confidence intervals (conceptual) and sampling methods
- Using data in modelling and decision-making - Critical Thinking and Mathematical Investigations
- Mathematical modelling of real-world problems
- Logical reasoning and paradoxes
- Functional equations and creative constraints
- Inquiry projects and proofs of patterns
- Student-designed problems and explorations