Module 1 of 46Lesson 5 of 5 · Topic Revision — Course Map (all 88 pages)
IB Mathematics: Analysis & Approaches
Your one-stop revision course for SL and HL. Every subtopic gives you the short notes you must know, the by-hand method for Paper 1, the exact TI-Nspire CX II steps for Paper 2, and at least 10 exam-style questions with full step-by-step solutions.
How to use this course
- Read the “What you must know” box — it is short on purpose.
- Try each question on paper before opening the solution.
- Follow the GDC screens on your own TI-Nspire CX II, key by key.
- SL students skip anything marked HL only. HL students do everything.
Topic 1 · Number and Algebra
- 1.1 Operations with numbers in standard form SL & HL 11 Qs
- 1.2 Arithmetic sequences and series SL & HL 12 Qs
- 1.3 Geometric sequences and series SL & HL 11 Qs
- 1.4 Financial applications of geometric sequences SL & HL 12 Qs
- 1.5 Laws of exponents with integer exponents; introduction to logarithms SL & HL 11 Qs
- 1.6 Simple deductive proof and identities SL & HL 11 Qs
- 1.7 Rational exponents and the laws of logarithms; exponential equations SL & HL 12 Qs
- 1.8 Sum of infinite convergent geometric sequences SL & HL 11 Qs
- 1.9 The binomial theorem SL & HL 11 Qs
- P1 Paper 1 drill: Number & Algebra without a calculator SL & HL 16 Qs
- 1.10 Counting principles; permutations and combinations; extended binomial theorem HL only 12 Qs
- 1.11 Partial fractions HL only 11 Qs
- 1.12 Complex numbers in Cartesian form HL only 11 Qs
- 1.13 Modulus–argument (polar) and Euler form HL only 11 Qs
- 1.14 Complex conjugate roots, powers and roots of complex numbers (De Moivre) HL only 12 Qs
- 1.15 Proof by induction, contradiction and counterexample HL only 12 Qs
- 1.16 Systems of linear equations (up to 3 unknowns) HL only 11 Qs
Topic 2 · Functions
- 2.1 Equations of straight lines SL & HL 11 Qs
- 2.2 Functions: domain, range, notation SL & HL 11 Qs
- 2.3 The graph of a function SL & HL 10 Qs
- 2.4 Key features of graphs; intersections using technology SL & HL 10 Qs
- 2.5 Composite functions, identity and inverse functions SL & HL 11 Qs
- 2.6 The quadratic function SL & HL 11 Qs
- 2.7 Quadratic equations and inequalities; the discriminant SL & HL 11 Qs
- 2.8 The reciprocal function and simple rational functions SL & HL 10 Qs
- 2.9 Exponential and logarithmic functions SL & HL 11 Qs
- 2.10 Solving equations analytically and graphically SL & HL 11 Qs
- 2.11 Transformations of graphs SL & HL 11 Qs
- P1 Paper 1 drill: Functions without a calculator SL & HL 16 Qs
- 2.12 Polynomial functions; factor and remainder theorems; sum and product of roots HL only 12 Qs
- 2.13 Rational functions with quadratic denominators HL only 11 Qs
- 2.14 Odd and even functions; self-inverse functions; restricting the domain HL only 11 Qs
- 2.15 Solving inequalities g(x) ≥ f(x) HL only 11 Qs
- 2.16 Graphs of |f(x)|, f(|x|), 1/f(x), f(ax+b) and [f(x)]² HL only 11 Qs
Topic 3 · Geometry and Trigonometry
- 3.1 3D geometry: distance, midpoint, volume, surface area, angles SL & HL 11 Qs
- 3.2 Right-angled and non-right-angled trigonometry; area of a triangle SL & HL 11 Qs
- 3.3 Applications of trigonometry; bearings, elevation and depression SL & HL 11 Qs
- 3.4 The circle: radians, arc length and sector area SL & HL 12 Qs
- 3.5 The unit circle and exact values; the ambiguous case SL & HL 11 Qs
- 3.6 The Pythagorean identity and double angle identities SL & HL 11 Qs
- 3.7 Circular functions and their transformations SL & HL 11 Qs
- 3.8 Solving trigonometric equations SL & HL 11 Qs
- P1 Paper 1 drill: Geometry & Trigonometry without a calculator SL & HL 16 Qs
- 3.9 Reciprocal trigonometric ratios and inverse trigonometric functions HL only 12 Qs
- 3.10 Compound angle identities; double angle for tan HL only 12 Qs
- 3.11 Symmetry properties of trigonometric graphs HL only 12 Qs
- 3.12 Vectors: concepts, algebra and unit vectors HL only 12 Qs
- 3.13 The scalar product; angle between vectors HL only 12 Qs
- 3.14 Vector equation of a line HL only 11 Qs
- 3.15 Parallel, intersecting and skew lines HL only 11 Qs
- 3.16 The vector product; areas HL only 11 Qs
- 3.17 Vector equations of a plane HL only 12 Qs
- 3.18 Intersections and angles: lines and planes HL only 12 Qs
Topic 4 · Statistics and Probability
- 4.1 Population, sample and sampling SL & HL 13 Qs
- 4.2 Presentation of data: histograms, cumulative frequency, box plots SL & HL 12 Qs
- 4.3 Measures of central tendency and dispersion SL & HL 14 Qs
- 4.4 Correlation and the regression line of y on x SL & HL 12 Qs
- 4.5 Probability: trials, outcomes, expected number SL & HL 14 Qs
- 4.6 Venn diagrams, tree diagrams and sample space diagrams SL & HL 13 Qs
- 4.7 Discrete random variables and expected value SL & HL 13 Qs
- 4.8 The binomial distribution SL & HL 11 Qs
- 4.9 The normal distribution SL & HL 11 Qs
- 4.10 The regression line of x on y SL & HL 11 Qs
- 4.11 Conditional probability and independence SL & HL 11 Qs
- 4.12 Standardising normal variables; finding unknown μ and σ SL & HL 11 Qs
- P1 Paper 1 drill: Statistics & Probability without a calculator SL & HL 16 Qs
- 4.13 Bayes’ theorem HL only 11 Qs
- 4.14 Continuous random variables; E(aX+b) and Var(aX+b) HL only 11 Qs
Topic 5 · Calculus
- 5.1 Limits and the derivative as a gradient and rate of change SL & HL 11 Qs
- 5.2 Increasing and decreasing functions SL & HL 11 Qs
- 5.3 Differentiating axⁿ SL & HL 11 Qs
- 5.4 Tangents and normals SL & HL 11 Qs
- 5.5 Introduction to integration; definite integrals and area SL & HL 11 Qs
- 5.6 Derivatives of standard functions; chain, product and quotient rules SL & HL 12 Qs
- 5.7 The second derivative SL & HL 11 Qs
- 5.8 Stationary points, optimisation and points of inflection SL & HL 11 Qs
- 5.9 Kinematics SL & HL 11 Qs
- 5.10 Indefinite integration; integration by inspection and substitution SL & HL 11 Qs
- 5.11 Definite integrals and areas between curves SL & HL 11 Qs
- P1 Paper 1 drill: Calculus without a calculator SL & HL 16 Qs
- 5.12 First principles; continuity and differentiability; higher derivatives HL only 11 Qs
- 5.13 Limits and L’Hôpital’s rule HL only 12 Qs
- 5.14 Implicit differentiation and related rates HL only 11 Qs
- 5.15 Further derivatives and integrals: tan, sec, aˣ, logₐx, inverse trig; partial fractions HL only 11 Qs
- 5.16 Integration by substitution and by parts HL only 11 Qs
- 5.17 Area with the y-axis; volumes of revolution HL only 11 Qs
- 5.18 First-order differential equations HL only 11 Qs
- 5.19 Maclaurin series HL only 11 Qs