IB Analysis and Approaches (AA) notes
This is the index for this IB Analysis and Approaches online reference. The syllabus points refer to the AA subject guide available on ibo.org.
It should be noted that questions very often incorporate many parts of the syllabus. That is, connections between contents should be taught and studied.
Contents
- Internal assessment
- Skills
- Algebra
- Functions
- Geometry and trigonometry
- Stats and probability
- Calculus
Internal assessment
Skills
| link |
|---|
| Graphing calculators |
| TI-84 Plus quick reference |
| Word problems |
| Problem solving strategies |
| Notations |
Algebra
| syllabus content | link |
|---|---|
| 1.1 | Scientific notation and significant figures |
| 1.5, 1.7 | Exponents and logarithms |
| 1.2, 1.3, 1.4, 1.8 | Sigma notation, sequences, series, finance |
| 1.6 | Direct and LHS to RHS proofs |
| 1.9, AHL 1.10 | Binomial theorem |
| AHL 1.10 | Counting |
| AHL 1.11 | Partial fractions |
| AHL 1.12, AHL 1.13, AHL 1.14 | Complex numbers |
| AHL 1.15 | Induction, contradiction, counterexample |
For systems of 3-variable equations (HL), see AHL 3.18 in vectors HL
Functions
functions SL
| syllabus content | link |
|---|---|
| 2.2, 2.4, 5.2, Overview | Functions notations, terminology, key concepts |
| 2.4 | Graphing functions and curves |
| 2.4, 2.10, AHL 2.15 | Solving equations and inequalities by graphing |
| 2.1, AHL 2.15, AHL 2.16 | Linear equations and inequalities |
| 2.2, 2.5 | Inverse of invertible functions |
| 2.5 | Composite functions |
| 2.2, 2.11 | Transformations |
| 2.6, 2.7 | Quadratics |
| 2.9 | Exponential and logarithmic functions |
| 2.8 | Linear over linear rational functions |
functions HL
| syllabus content | link |
|---|---|
| AHL 2.14 | Odd and even functions |
| AHL 2.12, AHL 2.15 | Polynomials including cubics |
| Bonus | Polynomial division |
| AHL 2.12 | Factor theorem and remainder theorem |
| AHL 2.13 | More rational functions |
| AHL 2.14 | Self-inverse functions |
| AHL 2.14 | Inverse with domain restriction |
| AHL 2.16 | Absolute value functions |
| AHL 2.16 | Reciprocal and square of functions |
Geometry and trigonometry
trigonometry
| syllabus content | link |
|---|---|
| 3.1 | Midpoint, volume, surface area |
| 3.1 | Distance, equation of circle |
| Review | Properties of triangles |
| 3.2, 3.3 | Right triangle trigonometry |
| 3.4 | Circle and the radian measure |
| 3.5, 3.6 | Unit circle and trig functions |
| 3.2 | Areas of triangle and segment |
| 3.2, 3.5 | Sine rule and cosine rule |
| 3.6 | Double angle identities |
| AHL 3.9, AHL 3.10, AHL 3.11 | More trig identities |
| 3.7 | Graphs of trig functions |
| 3.8 | Solving trig equations |
vectors HL
| syllabus content | link |
|---|---|
| AHL 3.12 | Vector definitions |
| AHL 3.12 | Vector arithmetics |
| AHL 3.13, AHL 3.16 | Dot product and cross product |
| AHL 3.16 | Area and volume using vectors |
| AHL 3.14 | Equations of lines in 3D |
| AHL 3.15 | Intersection of 3D lines |
| AHL 3.17 | Equations of planes |
| AHL 3.18 | Intersection of line and plane |
| AHL 3.18 | Intersection of 2 planes |
| AHL 1.16, AHL 3.18 | Intersection of 3 planes |
| AHL 3.14, AHL 3.18 | Angles using vectors |
| AHL 3.14, Bonus | Distances and projection |
| AHL 3.13, Bonus | Reflections using vectors |
Stats and probability
| syllabus content | link |
|---|---|
| 4.1, 4.3 | Statistics and probability definitions |
| 4.1 | Sampling techniques |
| 4.2, 4.3 | Data lists |
| 4.2, 4.3 | Grouped data |
| 4.3 | Effects of changes on mean and standard deviation |
| 4.4, 4.10 | Correlation and regression |
| 4.5, 4.6, 4.11 | Venn diagrams |
| 4.5, 4.6 | Sample space diagrams |
| 4.6, 4.11, AHL 4.13 | Tree diagrams |
| 4.7, AHL 4.14 | Discrete random variables |
| 4.8 | Binomial distributions |
| 4.9, 4.12 | Normal distributions |
| AHL 4.14 | Continuous random variables |
| AHL 4.14 | Linear transformations of random variables |
Calculus
differentiation
| syllabus content | link |
|---|---|
| 5.1 | Limits from table of values |
| 5.1, 5.2, 5.4 | Interpretations of derivatives |
| 5.3, 5.6 | Common derivatives |
| AHL 5.15 | More derivatives |
| 5.2, 5.7, 5.8, AHL 5.12 | Extrema and concavity |
| 5.8 | Optimization |
| AHL 5.12 | Limits, continuity, differentiability |
| AHL 5.13 | Limits in indeterminate forms |
| AHL 5.14 | Implicit differentiation |
| AHL 5.14 | Related rates |
integration and diff. eq.
| syllabus content | link |
|---|---|
| 5.5, 5.10 | Indefinite integrals |
| 5.5, 5.10, 5.11 | Definite integrals |
| 5.10, AHL 5.16 | Integration by substitution |
| 5.11 | Area between functions |
| 5.9 | Kinematics |
| AHL 5.17 | Area between curves |
| AHL 5.17 | Volume of revolution, disk method |
| AHL 5.15 | Rational functions integration |
| AHL 5.16 | Integration by parts |
| Diff. Eq. Overview | Differential equations overview |
| AHL 5.18 | Euler’s numerical method |
| AHL 5.18 | Separable differential equations |
| AHL 5.18 | Homogeneous differential equations |
| AHL 5.18 | Method of integrating factor |
| AHL 5.13, AHL 5.19 | Maclaurin series |
Instead of learning nuances and strategies from doing problems, you can simply read what they are.
That’s the goal, anyway.
Notes should supplement not replace practice problems.
Explanations and definitions are simplified for high school students in the International Baccalaureate program. Thus, they may at times be incomplete, inaccurate or even wrong in context of higher mathematics.
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As of late 2024, minor updates are rolled out several times a month. Current goals include adding more diagrams and graphs, and rewriting few Functions pages.