IB Maths AA Notes

1: All sub-topics combined

View the notes for all 12 of the IB maths aa topic 1 subtopics combined.

1.1: Scientific notation

Master operations with scientific notation. Learn to manipulate numbers in standard form efficiently and confidently.

1.2: Arithmetic sequences

Explore the world of arithmetic sequences and series. Discover the formulae for nth terms, sums, and sigma notation to describe patterns in numbers.

1.3: Geometric sequences

Dive into geometric sequences and their powerful properties. Master the formulae for nth terms, finite sums, and the convergence of infinite series.

1.4: Interest

Apply sequences and series to real-world financial contexts. Understand simple and compound interest, depreciation, and how to model imperfect arithmetic patterns in practice.

1.5: Exponents & logs

Unlock the power of exponents and logarithms. Master the laws governing both, change of base, and techniques for solving exponential equations.

1.6: Deductive Proofs

Build your mathematical reasoning from the ground up. Learn to construct clear deductive proofs and distinguish between equality and identity.

1.7: Binomial theorem

Expand your algebraic toolkit with the binomial theorem. Harness Pascal's triangle and combinatorial notation to expand expressions with precision.

1.8: Counting principles (HL)

Count the possibilities with permutations and combinations. Extend the binomial theorem to fractional and negative indices for deeper algebraic insight.

1.9: Partial fractions (HL)

Decompose rational expressions into simpler components. Master partial fractions as a key technique for integration and algebraic manipulation.

1.10: Complex numbers (HL)

Enter the realm of complex numbers. Journey through Cartesian, polar, and Euler forms, De Moivre's theorem, and the rich geometry of the complex plane.

1.11: Additional proofs (HL)

Strengthen your proof techniques with advanced methods. Master proof by induction, proof by contradiction, and the strategic use of counterexamples.

1.12: Systems of equations (HL)

Tackle systems of linear equations in up to three unknowns. Understand unique solutions, infinite solutions, and when no solution exists.

2: All sub-topics combined

View the notes for all 7 of the IB maths aa topic 2 subtopics combined.

2.1: Forms of lines

Master the equations of straight lines in all their forms. Explore gradients, intercepts, and the conditions for parallel and perpendicular lines.

2.2: Functions

Dive deep into the world of functions. From domain and range to quadratics, reciprocals, exponentials, and logarithmic functions — master graphing, inverses, composites, and key features.

2.3: Solving functions

Sharpen your equation-solving skills. Tackle equations graphically and analytically, and apply these techniques to real-life situations.

2.4: Graph transformations

Transform your understanding of graphs. Master translations, reflections, stretches, and composite transformations to manipulate any function.

2.5: Advanced functions (HL)

Explore polynomial and rational functions in depth. Discover the factor and remainder theorems, and the relationships between roots and coefficients.

2.6: Inequalities (HL)

Solve inequalities with confidence. Tackle modulus equations and compare functions both graphically and analytically.

2.7: Additional transformations (HL)

Extend your graphing repertoire with advanced transformations. Analyse the effects of modulus, reciprocal, and squared transformations on function graphs.

3: All sub-topics combined

View the notes for all 12 of the IB maths aa topic 3 subtopics combined.

3.1: Fundamentals of geometry

Navigate three-dimensional space with confidence. Calculate distances, midpoints, volumes, surface areas, and angles between lines and planes.

3.2: Introduction to trigonometry

Build your trigonometric foundations. Apply sine, cosine, and tangent ratios alongside the sine rule, cosine rule, and area formulae for triangles.

3.3: Applied trigonometry

Put trigonometry to work in real-world contexts. Solve problems involving angles of elevation and depression, and construct labelled diagrams from written descriptions.

3.4: Circles

Measure the circle with precision. Master radian measure, arc lengths, and sector areas to describe circular geometry.

3.5: Unit circle

Define trigonometric functions through the unit circle. Explore exact values, the ambiguous case of the sine rule, and symmetry properties of trigonometric graphs.

3.6: Trigonometric identities

Prove and apply key trigonometric identities. Solve equations using the Pythagorean identity, double angle formulae, and quadratic trigonometric forms.

3.7: Trigonometric graphs

Visualise the circular functions in action. Analyse the amplitude, period, and transformations of sine, cosine, and tangent graphs.

3.8: Advanced trigonometry (HL)

Extend your trigonometric toolkit. Explore reciprocal ratios, advanced Pythagorean identities, and inverse trigonometric functions with their domains and graphs.

3.9: Compound angles (HL)

Master compound and double angle identities. Apply sum and difference formulae for sine, cosine, and tangent to simplify and solve problems.

3.10: Vectors (HL)

Enter the world of vectors. From basic operations and scalar products to vector products and geometric proofs, build a complete understanding of vector algebra.

3.11: Lines (HL)

Describe lines using vectors in two and three dimensions. Explore intersections, angles between lines, and applications to kinematics.

3.12: Planes (HL)

Navigate the geometry of planes in three dimensions. Master vector and Cartesian equations, and find intersections and angles involving lines and planes.

4: All sub-topics combined

View the notes for all 8 of the IB maths aa topic 4 subtopics combined.

4.1: Fundamentals of statistics

Lay the foundations of statistical analysis. Explore populations, samples, data types, central tendency, and measures of spread.

4.2: Visualising statistics

Bring data to life with visual tools. Master histograms, cumulative frequency graphs, and box-and-whisker diagrams to reveal patterns and distributions.

4.3: Distribution properties

Quantify the spread of data with precision. Understand interquartile range, standard deviation, variance, and how constant changes affect distributions.

4.4: Linear statistics

Uncover relationships in bivariate data. Master correlation coefficients, scatter diagrams, and regression lines to make predictions and interpret trends.

4.5: Probability

Quantify uncertainty with the language of probability. Apply Venn diagrams, tree diagrams, and the rules for combined, conditional, and independent events.

4.6: Probability distributions

Model randomness with probability distributions. Explore discrete random variables, the binomial distribution, and the normal distribution including inverse calculations.

4.7: Bayes theorem (HL)

Update your probabilities with new evidence. Apply Bayes' theorem to solve problems involving up to three events.

4.8: Advanced distribution properties (HL)

Deepen your understanding of random variables. Explore variance, probability density functions, and the effect of linear transformations on distributions.

5: All sub-topics combined

View the notes for all 13 of the IB maths aa topic 5 subtopics combined.

5.1: Introduction to derivatives

Take your first steps into the world of calculus. Understand limits, interpret derivatives as gradient functions and rates of change, and master the power rule.

5.2: Applying derivatives

Put derivatives to work. Find tangents, normals, turning points, and points of inflexion, and solve optimisation problems using first and second derivatives.

5.3: Advanced derivatives

Expand your differentiation skills. Differentiate trigonometric, exponential, and logarithmic functions using the chain rule, product rule, and quotient rule.

5.4: Introduction to integration

Discover integration as the reverse of differentiation. Calculate definite and indefinite integrals, and find areas under and between curves.

5.5: Advanced integration

Master advanced integration techniques. Work with indefinite integrals, composite functions, and the reverse chain rule to tackle more complex problems.

5.6: Kinematics

Apply calculus to the study of motion. Solve problems involving displacement, velocity, acceleration, and total distance travelled.

5.7: Advanced limits (HL)

Deepen your understanding of limits, continuity, and differentiability. Evaluate challenging limits using l'Hôpital's rule and explore higher derivatives.

5.8: Implicit differentiation (HL)

Differentiate beyond explicit functions. Master implicit differentiation, related rates of change, and advanced optimisation problems.

5.9: Challenging derivatives (HL)

Differentiate the full range of functions. Master derivatives of reciprocal trigonometric, general exponential, logarithmic, and inverse trigonometric functions.

5.10: Challenging integration (HL)

Conquer the most demanding integrals. Apply partial fractions, substitution, and integration by parts to tackle complex integrands.

5.11: Applying integration (HL)

Calculate areas and volumes using integration. Find regions enclosed by curves and the y-axis, and compute volumes of revolution.

5.12: Differential equations (HL)

Solve first-order differential equations using a range of techniques. Master separation of variables, Euler's method, homogeneous equations, and integrating factors.

5.13: Maclaurin series (HL)

Approximate functions with infinite series. Derive and manipulate Maclaurin expansions for key functions, and develop series from differential equations.