IB Maths AA HL Skill Progression Mastery Tracker

Sequences & Series

0 / 32 skills mastered

Exponentials & Logarithms

0 / 33 skills mastered

Proof, Logic, Induction & Contradiction

0 / 31 skills mastered

Binomial Expansions & Coefficients

0 / 32 skills mastered

Complex Numbers

0 / 33 skills mastered

Permutations & Combinations

0 / 34 skills mastered

Systems of Linear Equations

0 / 9 skills mastered

Easy — Foundations

1Solving a \(2\times2\) systemSolve a pair of simultaneous linear equations by elimination/substitution.ApplicationSolves everyday two-unknown problems like price-and-quantity puzzles.Easy
2Disguised-linear \(2\times2\) systemsClear fractions or substitute to reveal a linear system, then solve.ApplicationSolves disguised-linear systems hidden behind fractions.Easy
3Solving a \(3\times3\) systemSolve three equations in \(x,y,z\) by systematic elimination.ApplicationSolves three-unknown problems such as balancing mixtures or circuits.Easy

Medium — Applications

4Row reduction with an augmented matrixApply elementary row operations to reach row-echelon form.ApplicationOrganises a system into a matrix for systematic elimination.Medium
5Classifying the solution setRead the final row as unique, no solution, or infinitely many.ApplicationDiagnoses whether a system has one, none, or infinitely many solutions.Medium

Hard — Structured IB Questions

6Parameter in one coefficientInvestigate how a parameter \(k\) affects solvability.ApplicationStudies how a parameter changes a system’s solvability.Hard
7Conditions on \(a,b\) for each caseFind \(a,b\) giving a unique, no, or infinite solution set.ApplicationFinds the parameter values that switch between solution types.Hard

Very Hard — Integrated AA HL Challenge

8General parametric solutionExpress a dependent system’s solutions in terms of a free parameter \(\lambda\).ApplicationDescribes a whole family of solutions for a dependent system.Very Hard
9Integrated systems challengeCombine linear systems with polynomials, geometry, modelling and proof.ApplicationCombines systems with polynomials, geometry, modelling and proof.Very Hard

Straight-Line Functions & Coordinate Graphs

0 / 32 skills mastered

Linear Graphs, Function Notation & Core Skills

0 / 32 skills mastered

Quadratic Functions, Models & Graphs

0 / 32 skills mastered

Exponential & Logarithmic Functions

0 / 32 skills mastered

Rational Functions & Reciprocal Graphs

0 / 16 skills mastered

Polynomial Functions

0 / 12 skills mastered

Transformations of Graphs

0 / 13 skills mastered

Algebraic & Graphical Inequalities

0 / 19 skills mastered

Absolute Value Functions & Advanced Transformations

0 / 32 skills mastered

Geometry of Circles, Sectors & Arcs

0 / 32 skills mastered

Geometry of 3D Shapes

0 / 16 skills mastered

Trigonometry: Exact Values & Identities

0 / 10 skills mastered

Non-Right Triangle Trigonometry

0 / 12 skills mastered

Trigonometric Graphs & Modelling

0 / 12 skills mastered

Inverse & Reciprocal Trigonometric Functions

0 / 12 skills mastered

Advanced Trigonometric Equations & Proof

0 / 24 skills mastered

Basic Operations & Vector Properties

0 / 34 skills mastered

Vector Equations of Lines

0 / 35 skills mastered

Vector Planes & Properties

0 / 34 skills mastered

Exploring & Summarising Data

0 / 32 skills mastered

Correlation & Regression

0 / 32 skills mastered

Probability

0 / 32 skills mastered

Discrete Probability Distributions

0 / 32 skills mastered

Binomial Distributions

0 / 32 skills mastered

Normal Distribution & z-Score

0 / 32 skills mastered

Probability Density Functions

0 / 34 skills mastered

Differentiation

0 / 31 skills mastered

Differentiation: Rules, Graphs & Applications

0 / 34 skills mastered

Integration

0 / 34 skills mastered

Integration: Methods, Areas & Applications

0 / 34 skills mastered

Optimisation

0 / 34 skills mastered

Kinematics

0 / 34 skills mastered

Limits & Continuity

0 / 34 skills mastered

Advanced Differentiation Techniques & Applications

0 / 34 skills mastered

Further Integration & Applications

0 / 34 skills mastered

Differential Equations

0 / 34 skills mastered

Maclaurin Series

0 / 32 skills mastered

Limits with l’Hôpital & Series

0 / 34 skills mastered

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