Syllabus map

Every AA HL syllabus point, and the chapter that teaches it.

All 83 syllabus points in Mathematics: Analysis and Approaches Higher Level, and the chapter that covers each one. Codes marked AHL are Higher Level only. Chapter numbers link to that chapter's PDF.

Topic 1 — Number and algebra

Code	Content	Chapter
1.1	Standard form	Ch 1
1.2	Arithmetic sequences and series	Ch 2
1.3	Geometric sequences and series	Ch 2
1.4	Financial applications: compound interest, depreciation	Ch 2
1.5	Laws of exponents with integer exponents; introduction to logarithms	Ch 1
1.6	Simple deductive proof; equality versus identity	Ch 3
1.7	Rational exponents; laws of logarithms; change of base; exponential equations	Ch 1
1.8	Sum of an infinite convergent geometric series	Ch 2
1.9	Binomial theorem; Pascal's triangle	Ch 2
1.10AHL	Counting principles; extension of the binomial theorem	Ch 2
1.11AHL	Partial fractions	Ch 6
1.12AHL	Complex numbers; Argand diagram	Ch 17
1.13AHL	Polar and Euler form	Ch 17
1.14AHL	Conjugate roots; De Moivre's theorem; powers and roots	Ch 17
1.15AHL	Proof by induction, contradiction, and counterexample	Ch 3
1.16AHL	Systems of linear equations	Ch 4

Topic 2 — Functions

Code	Content	Chapter
2.1	Straight lines; gradient; parallel and perpendicular	Ch 4
2.2	Functions; domain and range; inverse function	Ch 4
2.3	Graph of a function; sketching	Ch 4
2.4	Key features of graphs: intercepts, maxima, minima, asymptotes	Ch 4
2.5	Composite functions; identity function; existence of an inverse	Ch 5
2.6	Quadratic functions in three forms; vertex; axis of symmetry	Ch 4
2.7	Quadratic equations and inequalities; discriminant	Ch 4
2.8	Reciprocal and rational functions; asymptotes	Ch 5
2.9	Exponential and logarithmic functions and their graphs	Ch 5
2.10	Solving equations graphically and analytically	Ch 5
2.11	Transformations of graphs	Ch 5
2.12AHL	Polynomial functions; factor and remainder theorems; roots	Ch 6
2.13AHL	Extended rational functions; oblique asymptotes	Ch 5
2.14AHL	Odd, even and periodic functions; restricting the domain	Ch 5
2.15AHL	Inequalities between two functions	Ch 5
2.16AHL	Modulus and reciprocal graphs; modulus equations	Ch 5

Topic 3 — Geometry and trigonometry

Code	Content	Chapter
3.1	Distance and midpoint in 3D; volume and surface area of solids	Ch 7
3.2	Sine and cosine rules; area of a triangle; right-angled trigonometry	Ch 7
3.3	Applications: elevation, depression, bearings	Ch 7
3.4	Radians; arc length; area of a sector	Ch 7
3.5	Unit circle; exact values; ambiguous case	Ch 8
3.6	Pythagorean identity; double angle identities	Ch 8
3.7	Circular functions and their transformations	Ch 8
3.8	Solving trigonometric equations on an interval	Ch 8
3.9AHL	Reciprocal trigonometric ratios; inverse trigonometric functions	Ch 8
3.10AHL	Compound angle identities	Ch 8
3.11AHL	Symmetry properties of trigonometric graphs	Ch 8
3.12AHL	Vectors: components, operations, geometric proofs	Ch 9
3.13AHL	Scalar product; angle between vectors	Ch 9
3.14AHL	Vector equation of a line; kinematic applications	Ch 9
3.15AHL	Parallel, intersecting and skew lines	Ch 9
3.16AHL	Vector product; geometric interpretation	Ch 9
3.17AHL	Vector and Cartesian equations of a plane	Ch 9
3.18AHL	Intersections of lines and planes; angles between them	Ch 9

Topic 4 — Statistics and probability

Code	Content	Chapter
4.1	Population and sample; sampling techniques; outliers	Ch 10
4.2	Frequency distributions; histograms; cumulative frequency; box plots	Ch 10
4.3	Central tendency and dispersion; standard deviation	Ch 10
4.4	Correlation; scatter diagrams; regression of y on x	Ch 10
4.5	Probability; expected number of occurrences	Ch 11
4.6	Venn and tree diagrams; conditional probability; independence	Ch 11
4.7	Discrete random variables; expected value	Ch 12
4.8	Binomial distribution	Ch 12
4.9	Normal distribution; inverse normal	Ch 12
4.10	Regression of x on y; prediction	Ch 10
4.11AHL	Conditional probability formulae; testing for independence	Ch 11
4.12AHL	Standardisation; unknown mean or standard deviation	Ch 12
4.13AHL	Bayes' theorem	Ch 11
4.14AHL	Variance; continuous random variables and density functions	Ch 12

Topic 5 — Calculus

Code	Content	Chapter
5.1	Limits informally; the derivative as a rate of change	Ch 13
5.2	Increasing and decreasing functions	Ch 13
5.3	Differentiating powers; sums and multiples	Ch 13
5.4	Tangents and normals	Ch 13
5.5	Integration as anti-differentiation; boundary conditions	Ch 15
5.6	Standard derivatives; chain, product and quotient rules	Ch 13
5.7	Second derivative; concavity	Ch 13
5.8	Maxima and minima; optimisation; points of inflexion	Ch 13, Ch 14
5.9	Kinematics: displacement, velocity, acceleration	Ch 14, Ch 15
5.10	Indefinite integrals; integration by inspection and substitution	Ch 15
5.11	Definite integrals; areas under and between curves	Ch 15
5.12AHL	Continuity and differentiability; differentiation from first principles	Ch 13
5.13AHL	L'Hôpital's rule; limits using series	Ch 13
5.14AHL	Implicit differentiation; related rates; optimisation	Ch 14
5.15AHL	Further derivatives and their integrals; partial fractions in integration	Ch 13, Ch 15
5.16AHL	Integration by substitution and by parts	Ch 15
5.17AHL	Area between a curve and the y-axis; volumes of revolution	Ch 15
5.18AHL	First-order differential equations; Euler's method; integrating factor	Ch 16
5.19AHL	Maclaurin series	Ch 16

By chapter

The same map the other way round: each chapter and the syllabus points it covers.

Chapter	Syllabus points
1 Exponents & Logarithms	1.1, 1.5, 1.7	PDF
2 Sequences & Series	1.2, 1.3, 1.4, 1.8, 1.9, 1.10	PDF
3 Proofs	1.6, 1.15	PDF
4 Lines & Quadratics	1.16, 2.1–2.4, 2.6, 2.7	PDF
5 Functions & Graphs	2.5, 2.8–2.11, 2.13–2.16	PDF
6 Polynomials	1.11, 2.12	PDF
7 Shapes & Measures	3.1–3.4	PDF
8 Trigonometry	3.5–3.11	PDF
9 Vectors	3.12–3.18	PDF
10 Statistics	4.1–4.4, 4.10	PDF
11 Probability	4.5, 4.6, 4.11, 4.13	PDF
12 Probability Distributions	4.7, 4.8, 4.9, 4.12, 4.14	PDF
13 Limits & Derivatives	5.1–5.4, 5.6–5.8, 5.12, 5.13, 5.15	PDF
14 Derivative Applications	5.8, 5.9, 5.14	PDF
15 Integral Calculus	5.5, 5.9–5.11, 5.15–5.17	PDF
16 Differential Equations	5.18, 5.19	PDF
17 Complex Numbers	1.12–1.14	PDF

The content column paraphrases each syllabus point briefly, for identification only. For the exact wording, read the subject guide issued by the IB to your school.