Topic 2 in Maths AI focuses on using functions as models for real-world data. Students learn to choose, fit, and evaluate mathematical models, with heavy use of technology (GDC/software).
Linear: y = mx + c for constant rate of change (e.g., taxi fare, temperature conversion). Quadratic: y = ax² + bx + c for projectile motion, revenue/profit optimisation. Using vertex form to identify maximum/minimum. Interpreting coefficients in context.
Exponential growth: y = aeᵏˣ (k > 0) for population, compound interest. Exponential decay: y = ae⁻ᵏˣ for radioactive decay, cooling. Logarithmic scale for large-range data (pH, earthquake magnitude). Semi-log plots to identify exponential relationships.
y = a·sin(b(x − c)) + d for periodic phenomena: tides, temperature cycles, Ferris wheels. Amplitude |a|, period 2π/b, phase shift c, vertical shift d. Fitting sinusoidal models to real data using GDC regression.
Using GDC to perform linear, quadratic, exponential, power, and sinusoidal regression. Correlation coefficient r and R² for goodness of fit. Choosing the best model: residual analysis, domain appropriateness, extrapolation warnings. HL: logistic models for bounded growth.
You must be proficient with your GDC (TI-84, TI-Nspire, or Casio) for: entering data into lists, performing regression (LinReg, QuadReg, ExpReg, SinReg), finding R² values, graphing functions, finding intersections, and using the equation solver. AI exams assume fluent calculator use — practice is essential.
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