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Mathematics

IB Mathematics: Analysis and Approaches SL and HL

38 lessons at SL. 63 at HL, with every HL-only topic. Five-minute lessons, exam-style questions and timed mock papers.

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Units
5
SL lessons
38
HL lessons
63
Questions
390
Key terms
104
Formulas
71

What you will study

Every lesson follows the current IB guide. Lessons marked HL are in the HL course only. The first unit is free.

Topic 1 · Number and algebra6 SL · 12 HL lessons · free
  1. 1.1Standard form
  2. 1.2Arithmetic sequences and sigma notation
  3. 1.3, 1.8Geometric sequences and infinite series
  4. 1.4Financial applications
  5. 1.5, 1.7Exponents and logarithms
  6. 1.6, 1.9Proof and the binomial theorem
  7. 1.10Counting and the extended binomial theoremHL
  8. 1.11Partial fractionsHL
  9. 1.12Complex numbersHL
  10. 1.13, 1.14Polar form and De Moivre’s theoremHL
  11. 1.15Proof by induction, contradiction and counterexampleHL
  12. 1.16Systems of linear equationsHL
Topic 2 · Functions7 SL · 11 HL lessons
  1. 2.1, 2.2Lines, domain and range
  2. 2.5Composite and inverse functions
  3. 2.6, 2.7Quadratic functions and equations
  4. 2.8Rational functions
  5. 2.9Exponential and logarithmic functions
  6. 2.3, 2.4, 2.10Graphs and solving equations
  7. 2.11Transformations of graphs
  8. 2.12Polynomial functionsHL
  9. 2.13, 2.14More rational functions; odd and even functionsHL
  10. 2.15Solving inequalitiesHL
  11. 2.16Modulus and graph transformationsHL
Topic 3 · Geometry and trigonometry7 SL · 13 HL lessons
  1. 3.13D geometry
  2. 3.2, 3.3Triangle trigonometry
  3. 3.4Radians, arcs and sectors
  4. 3.5The unit circle
  5. 3.6Trigonometric identities
  6. 3.7Circular functions
  7. 3.8Solving trigonometric equations
  8. 3.9Reciprocal and inverse trig functionsHL
  9. 3.10, 3.11Compound angle identitiesHL
  10. 3.12, 3.13Vectors and the scalar productHL
  11. 3.14, 3.15Vector equations of linesHL
  12. 3.16, 3.17The vector product and planesHL
  13. 3.18Intersections and angles in 3DHL
Topic 4 · Statistics and probability8 SL · 10 HL lessons
  1. 4.1, 4.2Sampling and presenting data
  2. 4.3Averages and spread
  3. 4.4, 4.10Correlation and regression
  4. 4.5, 4.6Probability basics
  5. 4.6, 4.11Conditional probability and independence
  6. 4.7Discrete random variables
  7. 4.8The binomial distribution
  8. 4.9, 4.12The normal distribution
  9. 4.13Bayes’ theoremHL
  10. 4.14Continuous random variablesHL
Topic 5 · Calculus10 SL · 17 HL lessons
  1. 5.1, 5.2Limits and the derivative
  2. 5.3The power rule
  3. 5.4Tangents and normals
  4. 5.5Introduction to integration
  5. 5.6Chain, product and quotient rules
  6. 5.7The second derivative
  7. 5.8Optimisation and inflexion
  8. 5.9Kinematics
  9. 5.10Integration techniques
  10. 5.11Areas and definite integrals
  11. 5.12, 5.13First principles and L’Hôpital’s ruleHL
  12. 5.14Implicit differentiation and related ratesHL
  13. 5.15Further derivatives and integralsHL
  14. 5.16Substitution and integration by partsHL
  15. 5.17Volumes of revolutionHL
  16. 5.18Differential equationsHL
  17. 5.19Maclaurin seriesHL

Try a question

From “Standard form”.

Questions are in English, like the exam. Every answer comes with an explanation.

Which of these is 0.000 307 written in standard form?

  1. A3.07 × 10⁻⁴
  2. B3.07 × 10⁻³
  3. C30.7 × 10⁻⁵
  4. D3.07 × 10⁴
Show the answer

A. 3.07 × 10⁻⁴

The point moves 4 places to the right to give 3.07, so k = −4. 30.7 × 10⁻⁵ has the right value but is not standard form, because 30.7 ≥ 10.

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