Increasing and Decreasing Functions
AA SL · Topic 5 · SL 5.2
Read the sign of the derivative to identify where a function rises, falls or is stationary.
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Power Rule Differentiation
AA SL · Topic 5 · SL 5.3
Differentiate polynomial terms efficiently and connect the algebra to gradient.
Tangents and Normals
AA SL · Topic 5 · SL 5.4
Use derivatives to construct tangent and normal lines at a point on a curve.
Anti-Differentiation and Boundary Conditions
AA SL · Topic 5 · SL 5.5
Reverse the power rule, include the constant of integration and use a point to determine a particular function.
Differentiation Rules
AA SL · Topic 5 · SL 5.6
Differentiate standard functions and combinations using chain, product and quotient rules.
Second Derivative and Graphical Behaviour
AA SL · Topic 5 · SL 5.7
Use the second derivative to describe concavity and identify changes of curvature.
Stationary Points and Derivative Tests
AA SL · Topic 5 · SL 5.8
Classify stationary points reliably with first- and second-derivative tests.
Optimisation
AA SL · Topic 5 · SL 5.8
Build and analyse an objective function, including closed-domain endpoint checks.
Kinematics
AA SL · Topic 5 · SL 5.9
Move fluently between displacement, velocity and acceleration and distinguish displacement from total distance.
Standard Integrals
AA SL · Topic 5 · SL 5.10
Recognise standard antiderivatives and integrate linear composites with correct scale factors.
Integration by Substitution
AA SL · Topic 5 · SL 5.10
Recognise an inner function and its derivative, then change variable to simplify the integral.
Definite Integrals: Evaluation and Properties
AA SL · Topic 5 · SL 5.11
Evaluate definite integrals analytically, then use reversing limits, interval splitting, linearity and symmetry.
Areas Using Definite Integrals
AA SL · Topic 5 · SL 5.11
From signed area and its applications to total geometrical area and area between two curves.
Arithmetic Sequences and Series
AA HL · Topic 1 · SL 1.2
Recognise arithmetic patterns, use nth-term and finite-sum formulas, work with sigma notation and model constant additive change.
Geometric Sequences and Series
AA HL · Topic 1 · SL 1.3
Recognise geometric patterns, use flexible nth-term formulas, sum finite series and solve threshold and modelling problems.
Reading and Writing Sigma Notation
AA HL · Topic 1 · SL 1.3 skill
Read, expand and write finite sums using sigma notation, including shifted indices.
Financial Mathematics
AA HL · Topic 1 · SL 1.4
Model compound interest and depreciation using geometric sequences; solve financial problems by hand and with the TI-Nspire Finance Solver.
Infinite Geometric Series
AA HL · Topic 1 · SL 1.8
Decide when an infinite geometric series converges and calculate or use its sum to infinity.
Binomial Theorem
AA HL · Topic 1 · SL 1.9
Use exponent patterns, Pascal’s triangle, binomial coefficients and the general term to expand binomials and solve IB-style coefficient problems.
Straight Lines
AA HL · Topic 2 · SL 2.1
Gradients, intercepts, three equation forms, and parallel and perpendicular lines, with worked examples and practice.
Functions, Domain, Range and Inverses
AA HL · Topic 2 · SL 2.2
Understand function notation, domain, range, mathematical models and inverse graphs, with step-by-step worked examples and practice.
Composite and Inverse Functions
AA HL · Topic 2 · SL 2.5
Combine functions, track domains and ranges, and find, check and sketch inverses, with 16 worked examples and 15 practice questions.
Transformations of Graphs
AA HL · Topic 2 · SL 2.11
Translate, reflect and stretch graphs; follow points, domains, ranges and asymptotes through complete worked sequences. Includes a labelled HL extension.
Limits and the Derivative
AA HL · Topic 5 · SL 5.1
Approach limits numerically and graphically, then interpret the derivative as gradient and rate of change.