What Happens in Every Class
Concept Instruction
New ideas in exponents, radicals, logarithms, trigonometry, and progressions are introduced through worked examples and guided discussion. Students build algebraic fluency and the vocabulary of proof before working independently.
Applied Problem Solving
Students apply the toolkit to real contexts: compound interest and financial growth, solving triangles that cannot be measured directly, and modelling patterns with arithmetic and geometric sequences. Setting up the problem matters as much as the computation.
Logic and Strategy Challenges
Every class includes a problem that sits outside the day’s topic, such as a combinatorics puzzle, a number theory question, or a proof by induction, building the kind of reasoning that no single procedure can replace.
Homework Review and Discussion
Homework solutions are unpacked as a group. Students compare how they proved an identity or chose between the sine and cosine law, and errors in reasoning are discussed openly, not just marked wrong on a page.
Curriculum Spotlight
When One Answer Isn't Enough
In Lesson 17, students meet a deceptively simple task: solve a triangle given one angle and two sides. It looks like a routine application of the Sine Law, until they discover that the very same three measurements can describe two completely different triangles.
Instead of reaching for a formula, students learn to reason about how many solutions exist and why. By comparing the given side to the triangle’s height, they test each case: is the side too short to reach the base, just long enough to form a right angle, or long enough to swing across and meet it twice? The algebra produces a number; the mathematics is knowing which of those numbers are real.
This is where students stop asking ‘what is the answer?’ and start asking ‘how many answers are there, and can I justify each one?’ – the shift in thinking that university mathematics demands.
What Topics Do we Cover in this Level?
Algebra and Number
- Laws of exponents and radicals
- Rational exponents and radical equations
- Operations on polynomials
- Simple and compound interest
- Repeating decimals as rational fractions
- Logarithms and logarithmic equations
and more
Sequences, Proof and Counting
- Arithmetic progressions and series
- Geometric progressions and series
- The method of mathematical induction
- Factorials and counting principles
- Combinatorics: permutations and combinations
- Systems of equations
and more
Trigonometry and Geometry
- Trigonometric ratios and special angles
- Solving right and oblique triangles
- Sine law and the ambiguous case
- Cosine law and its applications
- Trigonometric identities
- Axioms and problem solving in 3-D geometry
and more
How Does Brain Power Compare?
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