Math & Problem Solving

Math Level G

Advanced functions, conics, limits, and the foundations of calculus.

Grade 10, Grade 11, Grade 12

What Happens in Every Class

Concept Instruction

Advanced topics such as complex numbers, rational functions, conic sections, limits, and derivatives are introduced through worked examples and proof-based discussion. Students develop the fluency and precision expected in first-year university courses.

Applied Problem Solving

Students use calculus and analytic geometry to model and optimize: maximizing area and volume, analyzing velocity and acceleration, and describing curves through their equations. Choosing the right method is as important as executing it.

Logic and Strategy Challenges

Every class includes a problem that reaches across topics, such as a proof by induction, a limit that resists direct substitution, or a system that mixes algebra and geometry, stretching reasoning beyond any single technique.

Homework Review and Discussion

Homework is unpacked as a group, with emphasis on method and justification. Students compare how they set up an optimization or evaluated an indeterminate limit, and reasoning is examined as carefully as the final result.

Curriculum Spotlight

Where Every Tool Comes Together

In Lesson 8, students are asked to inscribe a rectangle inside a right triangle so that its area is as large as possible. It looks like a geometry problem, but no single measurement gives the answer, because the rectangle can be drawn in infinitely many ways.

Students learn to express the rectangle’s area as a function of a single variable, using the geometry of the triangle to link its width and its height. From there the question becomes analytic: where does that area function reach its maximum? Whether they complete the square or take a derivative and set it to zero, they arrive at the same elegant result – the largest rectangle is exactly half the triangle.

Geometry defines the problem, algebra models it, and calculus solves it. Learning to move fluently between these domains is precisely the preparation students need for university mathematics.