IB Diploma Programme · Mathematics: Analysis and Approaches Resource Hub
DP Mathematics: Analysis and Approaches, ready to teach.
Lesson plans, worksheets and mark schemes for DP Mathematics: Analysis and Approaches — written against the 2021 guide and structured around the key concepts, the assessment objectives, and rigorous mathematical inquiry.
136Lessons
5Units · 74 topics
SL · HLBoth levels
AssessmentObjectives aligned
What's included
One pack. Everything you need to teach the course.
136
Lesson plans
A full plan for every topic in the hub — objectives, timings, and a clear teaching arc.
136
Student worksheets
Structured practice tasks ready to print or assign.
136
Mark schemes
Full mark schemes aligned to the assessment objectives.
✓
Interactive digital lessons
Self-paced lessons for in-class or independent study.
5
Units · 74 topics
136 lessons across 5 units and 74 topics.
✓
Exam-style-aligned
Exam-style questions and full mark schemes, written against the assessment objectives of the current guide.
The units
74 topics, one coherent course.
Open any unit to see its topic map and the skills students build.
Unit 1Number and algebra
RepresentationRelationshipsGeneralisationGeneralization
14 topics
Arithmetic and geometric sequences and seriesSigma notation for seriesSurds, exponents and scientific notationDirect proof, proof by contrapositive, and counter-exampleInfinite geometric series — sum to infinity and convergence conditionsCounting principles and the binomial theoremArgand diagrams: plotting, loci and geometric interpretationComplex numbers and De Moivre's theoremRoots of complex numbers and nth roots of unityConjugate roots of polynomials with real coefficientsProof by contradiction and direct proofProof by mathematical inductionRelationships between exponential and logarithmic functionsSum and product of roots of polynomial equations
Skills & assessment.
Unit 2Functions
RepresentationRelationshipsModelling
15 topics
Functions: domain, range, composition and inversesQuadratic functions and equationsReciprocal and rational functionsExponential functions and modelsLogarithmic functions and equationsSolving equations using technologySolving exponential and logarithmic equationsGraph transformations — explicit coverage of y = fTransformations of graphsPolynomial functions: factor and remainder theorems, and divisionRational functions — sketching graphs with oblique asymptotes and holesInequalities — solving and representing linear, quadratic and rationalAbsolute valueSinusoidal functions and periodic modelsSolving trigonometric equations
Skills & assessment.
Unit 3Geometry and trigonometry
RelationshipsRepresentationEquivalenceSpace
11 topics
Three-dimensional coordinate geometry and distanceArea of a triangle using ½ab sinCGeometric applications — 3D trigonometry, angle between line and planeThree-dimensional trigonometry: angles of elevation and depressionRadian measure, arc length, and sector areaTrigonometric ratios and the unit circleReciprocal and inverse trigonometric functionsCompound and double angle identitiesVectors — vector algebra, scalarVector equations of lines in 2D and 3DVector cross product and equations of planes
Skills & assessment.
Unit 4Statistics and probability
RepresentationRelationshipsApproximationValidity
15 topics
Sampling distributions and unbiased estimatesFrequency histograms, cumulative frequency graphs and stem-and-leaf diagramsDescriptive statistics — measures of central tendency and spreadMeasures of central tendency for grouped dataLinear regression and Pearson's correlation coefficientBasic probability: sample spaces, complementary and mutually exclusive eventsDiscrete random variables and expected valueThe binomial distributionThe normal distributionConfidence intervals for the meanHypothesis testing for the meanHypothesis testing: one-tailed vs two-tailed tests and critical regionsBayes' theorem and conditional probability from tablesContinuous random variables — uniform and other named distributionsContinuous random variables and probability density functions
Skills & assessment.
Unit 5Calculus
ChangeApproximationRelationshipsRepresentation
19 topics
Partial fractions and integration of rational functionsLimits and continuity — formal concept of a limitIntroduction to differentiationTangents, normals and increasing/decreasing functionsAntiderivatives and indefinite integrationProduct, quotient and chain rulesStationary points, inflection and concavityKinematics using integrationOptimisation, kinematics and related ratesIntegration of 1Definite integrals and areas using technologyDefinite integration as area and the Fundamental Theorem of CalculusL'Hôpital's rule for indeterminate formsDerivatives of inverse trigonometric functions and further derivativesIntegration by substitutionDifferential equations — separable variables and generalNumerical methods for solving DEsSlope fieldsMaclaurin series and Taylor polynomials
Skills & assessment.
How the lessons work
A clear teaching arc in every lesson.
01
Hook
Surface prior thinking and frame the inquiry.
02
Develop
Guided development of the theory and key concepts.
03
Practise
Structured practice on the worksheet tasks.
04
Apply
An applied or evaluative task that lifts thinking.
Explicit learning objectivesCommand-term focusATL skill linksDifferentiation support
Assessment-ready
Built for the exams students will sit.
01
Exam-style questions
Exam-style tasks in every worksheet, each showing the marks it carries.
02
Full mark schemes
A complete mark scheme for every worksheet — what earns each mark, and why.
03
The assessment objectives
Written against the objectives set out in the current subject guide.
04
Command terms
Tasks use the command terms the guide defines, in the sense it defines them.
Why DP Mathematics: Analysis and Approaches teachers choose this hub
Walk into every lesson already prepared.
Written against the current DP Mathematics: Analysis and Approaches guide and ready to teach — so your time goes into the students in front of you, not into building resources from scratch.
01
Aligned to the current DP guide
Written against the current DP guide and framed by the key concepts and the inquiry approach.
02
The planning, already done
136 lesson plans, worksheets and mark schemes with a consistent teaching arc — teach as-is or adapt.
03
Exam confidence built in
Exam-style questions and full mark schemes, written against the assessment objectives and command terms of the current guide.
Available per subject, or added to a whole-school license bundle.