Theme: The Engineer’s Launchpad
Phase 1: Abstract Dimensions (Weeks 1–6)
* Weeks 1-2: Sets, Relations & Functions
* The Hook: "How database networks like Facebook map friendships using set arrays."
* The Mission: Build a physical or visual structural web detailing relations, domains, and ranges of a local student network.
* The Play (Olympiad Tier): A young professor presentation demonstrating the real-world utility of cross-product mappings.
* Weeks 3-4: Trigonometric Functions
* The Hook: "The Math of Sound: How your headphones cancel out background noise using phase shifts."
* The Mission: Map trigonometric graphs ($\sin x, \cos x$) to visualize sound waves and explain destructive interference.
* Weeks 5-6: Principle of Mathematical Induction & Complex Numbers
* The Hook: "The Domino Effect and $\sqrt{-1}$: The math that runs quantum physics."
* The Mission: Map out complex vectors on an Argand plane to create visual fractal geometry artwork.
Phase 2: Discrete & Linear Systems (Weeks 7–12)
* Weeks 7-8: Linear Inequalities & Permutations and Combinations (P&C)
* The Hook: "How many chess games are possible? Cracking the lock of combinations."
* The Mission: Compute the total number of unique password iterations for the school cloud network and run a safety audit.
* Weeks 9-10: Binomial Theorem
* The Hook: "Pascal’s Triangle: The hidden pattern behind natural growth and inheritance."
* The Mission: Use binomial expansions to quickly project high-power polynomial values in a live speed sprint.
* Weeks 11-12: Sequences and Series (AP & GP)
* The Hook: "The Viral Loop: How a single meme scales to 10 Million views using Geometric Progression."
* The Mission: The Viral Simulator. Plot a mathematical model tracking exactly how an infection or piece of news spreads through a crowd.
Phase 3: Calculus & Vector space (Weeks 13–24)
* Weeks 13-14: Straight Lines ➔ Mission: Plot flight trajectories for two aircraft crossing paths to evaluate structural safety buffer regions.
* Weeks 15-16: Conic Sections (Parabola, Ellipse, Hyperbola) ➔ Mission: The Satellite Dish. Model a functional parabolic light mirror tracking focal convergence.
* Weeks 17-18: Introduction to Three-Dimensional Geometry ➔ Mission: Chart drone movement configurations through an array of three intersecting axes.
* Weeks 19-20: Limits and Derivatives (The Gateway to 12th) ➔ Mission: Calculate the instantaneous rate of structural deformation of a metal beam under variable weight load profiles.
* Weeks 21-22: Mathematical Reasoning & Statistics ➔ Mission: Conduct a statistical variance and standard deviation analysis comparing test consistency across separate class cohorts.
* Weeks 23-24: Probability ➔ Mission: The Risk Analyst. Apply conditional baseline probabilities to formulate a financial portfolio risk framework for a micro-investment tracker.
Revision & tests afterwards
