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Mathematics

IB Mathematics: Applications and Interpretation SL and HL

36 lessons at SL. 67 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
36
HL lessons
67
Questions
379
Key terms
108
Formulas
62

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 algebra8 SL · 15 HL lessons · free
  1. 1.1Standard form
  2. 1.2Arithmetic sequences
  3. 1.3Geometric sequences
  4. 1.4Financial applications
  5. 1.5Exponents and logarithms
  6. 1.6Approximation and errors
  7. 1.7Loans and annuities
  8. 1.8Equations with technology
  9. 1.9Laws of logarithmsHL
  10. 1.10Rational exponentsHL
  11. 1.11Infinite geometric seriesHL
  12. 1.12Complex numbersHL
  13. 1.13Polar and Euler formHL
  14. 1.14MatricesHL
  15. 1.15Eigenvalues and eigenvectorsHL
Topic 2 · Functions6 SL · 10 HL lessons
  1. 2.1Straight lines
  2. 2.2Functions and inverses
  3. 2.3–2.4Key features of graphs
  4. 2.5Linear and quadratic models
  5. 2.5Exponential and variation models
  6. 2.5–2.6Sinusoidal models and modelling
  7. 2.7Composite and inverse functionsHL
  8. 2.8Transformations of graphsHL
  9. 2.9Logistic and piecewise modelsHL
  10. 2.10Logarithmic scales and linearisingHL
Topic 3 · Geometry and trigonometry7 SL · 13 HL lessons
  1. 3.1Points and angles in 3D
  2. 3.1Volume and surface area
  3. 3.2Right-angled trigonometry
  4. 3.2Sine rule, cosine rule and area
  5. 3.3Elevation, depression and bearings
  6. 3.4Arcs and sectors
  7. 3.5–3.6Perpendicular bisectors and Voronoi diagrams
  8. 3.7–3.8Radians and the unit circleHL
  9. 3.9Transformations with matricesHL
  10. 3.10–3.11Vectors and vector linesHL
  11. 3.12–3.13Motion, scalar and vector productsHL
  12. 3.14–3.15Graph theoryHL
  13. 3.16Graph algorithmsHL
Topic 4 · Statistics and probability8 SL · 15 HL lessons
  1. 4.1Data and sampling
  2. 4.2–4.3Summarising data
  3. 4.4Correlation and regression
  4. 4.5–4.6Probability
  5. 4.7–4.8Random variables and the binomial
  6. 4.9The normal distribution
  7. 4.10Spearman's rank correlation
  8. 4.11Hypothesis testing
  9. 4.12–4.13Data design and non-linear regressionHL
  10. 4.14–4.15Combining variables and the CLTHL
  11. 4.16Confidence intervalsHL
  12. 4.17The Poisson distributionHL
  13. 4.18Critical regions and errorsHL
  14. 4.18Testing for correlationHL
  15. 4.19Markov chainsHL
Topic 5 · Calculus7 SL · 14 HL lessons
  1. 5.1Rates of change
  2. 5.2–5.3Differentiating powers
  3. 5.4Tangents and normals
  4. 5.6Stationary points
  5. 5.7Optimisation
  6. 5.5Integration and area
  7. 5.8The trapezoidal rule
  8. 5.9Further differentiationHL
  9. 5.9–5.10Second derivative and related ratesHL
  10. 5.11Further integrationHL
  11. 5.12Areas and volumes of revolutionHL
  12. 5.13KinematicsHL
  13. 5.14–5.16Differential equationsHL
  14. 5.17–5.18Coupled systems and phase portraitsHL

Try a question

From “Standard form”.

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

Write 0.000315 in standard form.

  1. A3.15 × 10⁻⁴
  2. B3.15 × 10⁴
  3. C31.5 × 10⁻⁵
  4. D3.15 × 10⁻³
Show the answer

A. 3.15 × 10⁻⁴

Move the decimal point 4 places to the right to get 3.15, so k = −4.

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The first unit is free. No card needed.

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