IB Math AA SL study plan

Compute derivatives of polynomial, exponential, logarithmic, and trigonometric functions using the power, product, quotient, and chain rules in a 20-item mixed set.

Determine equations of tangent and normal lines at a stated point and verify the gradient by substitution.

Classify stationary points as local maxima, minima, or neither using a sign table and the second derivative, and justify each classification.

Solve displacement-velocity-acceleration problems by differentiating and integrating simple motion functions over a stated interval.

Evaluate definite integrals of polynomial and simple power functions over stated limits.

Calculate the area between a curve and the x-axis over a given interval, splitting the integral at any roots.

Compute probabilities from two-way tables, Venn diagrams, and tree diagrams, including conditional probability.

Apply the binomial distribution to find probabilities and expected value for a stated number of trials and probability.

Calculate mean, median, mode, range, interquartile range, and standard deviation from raw data and a frequency table.

Construct a box-and-whisker plot and identify outliers using the 1.5×IQR rule.

Standardize normal variables and solve forward and inverse normal problems using a GDC.

Solve 2D and 3D problems using the sine rule, cosine rule, and area formula for a triangle.

Solve trigonometric equations in a stated interval and express all solutions in radians.

Simplify expressions using the Pythagorean identity and double-angle identities for sine and cosine.

Calculate arc length and sector area in radians and apply them to composite shapes.

Solve 3D geometry problems involving angles between lines and planes by drawing and labeling a right triangle.

Determine domain and range of rational, radical, exponential, and logarithmic functions from their equations.

Find inverse functions algebraically and verify them by composition.

Sketch transformations of a parent graph and state asymptotes, intercepts, and vertex where applicable.

Solve quadratic equations and inequalities and interpret the discriminant in context.

Solve exponential and logarithmic equations using log laws and check for extraneous solutions.

Find the nth term and sum of arithmetic and geometric sequences, including real-world growth/decay contexts.

Expand binomial expressions using the binomial theorem and identify a specified term without full expansion.

Perform complex number arithmetic in Cartesian form and compute modulus and argument for a given complex number.

Solve sequence and series word problems by choosing arithmetic versus geometric models and justifying the choice.

Use the binomial theorem to find a coefficient in a given expansion and verify with a small case.

Recompute a mixed 12-item derivative/integral set without notes and correct every error.

Interpret a definite integral as accumulated change in a context and state units.

Complete two full timed IB-style papers under exam conditions and record per-domain scores.

Re-solve the five highest-error calculus items and five highest-error statistics items from the error log.

State the exact calculator and formula-sheet steps for normal, binomial, and definite-integral questions.

Write a 10-line exam routine covering timing, checking, and when to skip and return.