Syllabus breakdown

AI SL Functions and Modelling syllabus points

Official syllabus requirements assessed across Paper 1 and Paper 2 in Topic 2.

  1. 2.1Linear models: $f(x) = mx + c$, interpreting gradient $m$ as rate of change and $c$ as initial value
  2. 2.2Concept of a function: domain, range, $f(x)$ notation, finding roots and intersections using GDC
  3. 2.3Direct and inverse variation: power functions $y = kx^n$, inverse models $y = \frac{k}{x^n}$, and horizontal/vertical asymptotes
  4. 2.4Quadratic models: $f(x) = ax^2 + bx + c$, vertex $(h, k)$ as maximum/minimum, projectile motion, and roots
  5. 2.5Exponential models: $f(x) = ka^x + c$, continuous compounding, population doubling time, and radioactive half-life
  6. 2.6Modelling skills: selecting appropriate models from contextual data, domain restrictions, and commenting on model validity

Interactive guides

Topic 2 Interactive Study Guides

Each guide features full notes, 10 progressive practice exercises with complete markschemes, formula sheets with common pitfalls, and an exam mini test.

Lesson 2.1 & 2.2

Linear Models & Gradients

Interpreting gradient as constant rate of change, $y$-intercept as initial condition, domain constraints, and piecewise cost functions.

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Lesson 2.4 & 2.5

Quadratic & Exponential Models

Vertex form, projectile height trajectories, exponential growth/decay ($f(x) = ka^x + c$), half-life, and GDC curve intersections.

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Lesson 2.3 & 2.6

Direct & Inverse Variation

Power functions $y = kx^n$, inverse proportional relationships $y = \frac{k}{x^n}$, identifying asymptotes, and evaluating model realism.

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Exam insights

Key modelling principles in Math AI

  • Interpreting Contextual Parameters: Always specify units. If $m = 4.5$, write "The cost increases by 4.5 dollars per additional kilometer driven."
  • Physical Constraints on Domain: Real-world quantities like time ($t \ge 0$), volume ($V > 0$), or population cannot be negative. State suitable domains.
  • Horizontal Asymptotes in Decay Models: In $T(t) = 80(0.85)^t + 20$, the horizontal asymptote $y = 20$ represents ambient room temperature.

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Return to the AI SL Course Hub or proceed to Topic 3: Geometry & Trigonometry.