IB Math Course Structure

Mathematics part of the six subject groups in the IB Diploma Programme. All IB students are expected to have at least the basic knowledge of Math and how that knowledge can be applied in other subject areas and in daily life. There are 4 different course options for the Mathematics subject group,

  • Mathematical Studies Standard Level
  • Mathematics Standard Level
  • Mathematics Higher Level
  • Further Mathematics Higher Level

Candidates are required to take at lease one Mathematics course. Not to worry, our experienced tutors will walk you through the key concepts, applications through examples and address any questions you may have to aid your understanding. Our course structure can be found below!

Mathematical Studies Standard Level

Math Studies Standard Level Course Structure

Session TopicsSubtopics
1Numbers and Algebra 1Number sets, Approximation and error,
Standard, SI units of measurement
Mathematical ModelsFunctions, Linear models, Quadratic models,
Exponential models, Graphs, Using GDC to solve equation graphs
Numbers and Algebra 2Arithmetic sequences, Geometric sequences,
Currency conversions, Compound interest
2 Descriptive StatisticsData classification, Grouping continuous or discrete data,
Cumulative frequency curves, Box and whisker graphs, Measures of dispersion
Statistical ApplicationsNormal distribution, Correlation, Regression line, Chi-Squared Test
Sets and ProbabilityBasic set theory, Venn diagrams, Basic probability theory,
Conditional probability, Sample space diagrams, Tree diagrams
LogicIntroduction to logic, Compound statements and symbols, Truth tables, Logical equivalence, Tautologies and contradictions, Arguments
3Geometry and trigonometry 1Gradient of line, Equations of lines, Sine and cosine rules,
Sine, Cosine and tangent ratios
Geometry and Trigonometry 2Geometry of three-dimensional solids, Distance between points,
Angles between two lines or a line and a plane,
Surface areas and Volume of three-dimensional solids
4Introducing Differential CalculusIntroduction to differentiation, Gradient function, Calculating gradient,
Tangent and the normal to a curve, Rates of change, Local maximum and minimum points,
Using differentiation in modeling: Optimization

Standard Level

Math SL Course Structure

Session TopicsSubtopics
1FunctionsFunction notation, composite/inverse functions, function transformations
Quadratic functionsSolving quadratic functions, quadratic roots, quadratic graphs
Exponential and logarithmic functionsSolving exponential equations, exponential functions, laws of logarithms and their functions/equations
Rational functionsReciprocals and their functions, rational functions
Patterns and SequencesSigma notation and series, arithmetic/geometric series, convergent series and sums to infinity
2ProbabilityVenn diagrams, sample space diagrams and product rule, conditional probability, probability tree diagrams
Descriptive statisticsUnivariate analysis, histograms, measures of central tendency/dispersion, cumulative frequency, variance, standard deviation
Bivariate analysisScatter diagrams, line of best fit, least squares regression, measuring correlation
Probability distributionsRandom variables, binomial and normal distributions
3TrigonometryRight-angled triangle trigonometry, sine and cosine rule, area of a triangle, radians, arcs, sectors
VectorsVector addition/subtraction, scalar product, vector equation of a line
Circular functionsThe unit circle, trigonometric identities, graphing circular functions, translation and scaling of trigonometric functions, combined transformations with sine and cosine functions
4Limits and derivativesLimits and convergence, tangent line, derivatives of polynomials and more, chain rule and higher order derivatives, rates of change and motion in a line, derivative and graphing, extrema and optimisation
IntegrationAntiderivatives, indefinite and definite integrals, fundamental theorem of Calculus, volume of revolution
Trigonometric calculus Derivatives of trigonometric functions, integrals of sine and cosine

Higher Level

Math HL Course Structure

HL Math students are required to study everything in the core curriculum and one topic under the option curriculum.

Sessions for core curriculum:
Session TopicsSubtopics
1aPatterns and SequencesSigma notation and series, arithmetic/geometric series, mathematical induction
Exponents and logarithmsLaw of exponents/logarithms, change of base
Counting principlesPermutations and combinations, binomial theorem
1bComplex numbersOperations with complex numbers, cartesian/polar form, complex plane, powers of complex numbers, complex roots, solving systems of equations
FunctionsFunction notation, odd/even functions, inverse/composite functions, one-to-one/many-to-one functions, graphs of functions, transformations of graphs, rational/exponential/logarithmic functions, polynomial functions and their graphs, factor and remainder theorems, fundamental theorem of algebra, solving quadratic equations, solving inequalities of functions
2 StatisticsPopulation, sample, random sample, frequency distribution of discrete/continuous data, grouped data, mean, variance, standard deviation
ProbabilityVenn diagrams, combined/mutually-exclusive events, conditional probability, independent events, Bayes’ theorem, probability distributions, probability density functions, mean/mode/median/variance/standard deviation, binomial/poisson/normal distributions
3TrigonometryRadian, arc length, sector area, the unit circle and trigonometric identities, special angles, Pythagorean identities, compound angle identities, double angle identities, cosine rule
Trigonometric functionsTrigonometric composite/inverse functions, solving trigonometric equations
VectorsVector addition/subtraction, scalar/vector product, vector equation of a line/plane, intersections of lines and planes
4Limits and derivativesLimits, continuity and convergence, derivative of a function, tangents and normals, higher order derivatives, derivatives of different functions, product/quotient rules, chain rules for composite functions, related rates of change, implicit differentiation, maxima and minima, optimisation, relationship between derivatives
IntegrationAntiderivatives, indefinite and definite integrals, area of regions enclosed by curves, volume of revolution, kinematics, integration by substitution/parts

Request for a Math trial class

We will get back to you within 24 hours


By submitting this form, I agree to Prep Zone Academy’s Privacy Policy and Terms of Use.

IB Subjects

Prep Zone Academy offers a range of IB subject preparation courses. You are invited to a free trial class with one of our IB certified trainers for any subjects of your choice!