Every subtopic of DP Mathematics: Analysis and Approaches, ready to teach.
Every subtopic of the DP Mathematics: Analysis and Approaches syllabus, structured around the key concepts, the assessment objectives, and rigorous mathematical inquiry.
One pack. Everything you need to teach the course.
83 topics, one coherent course.
Open any unit to see its topic map and the skills students build across SL and HL.
Unit 1Number, Algebra, and Logarithmic Functions
From laws of exponents and surds through sequences, logarithms, the binomial theorem, and — at HL — complex numbers in Cartesian and modulus-argument form.
This unit addresses the algebraic foundations of the AA syllabus across 15 lessons and 5 topics: number representation (exponents, surds, scientific notation), sequences & series (arithmetic and geometric), exponential and logarithmic relationships, the binomial theorem with combinatorics, and — for HL — complex numbers including De Moivre's theorem and modulus-argument form.
Skills & assessment. Lessons progress from procedural fluency with index and logarithm laws (AO1–AO2) to applying the binomial theorem and solving exponential equations (AO2–AO3). HL lessons on complex numbers develop the Representation and Relationships key concepts, with exam-style practice reflecting both Paper 1 (no technology) and Paper 2 expectations.
Unit 2Functions, Equations, and Graphical Analysis
Functions and their graphs — from quadratics and transformations through rational, exponential, logarithmic, and trigonometric functions, with technology-supported equation solving throughout.
Spanning 30 lessons across 10 topics, this unit builds a comprehensive treatment of functions: notation, domain, range, inverse and composite functions; graph transformations; quadratic functions and the discriminant; reciprocal and rational functions; exponential and logarithmic functions and their graphs; sinusoidal functions with amplitude, period and phase shift; and solving trigonometric equations over restricted domains.
Skills & assessment. The unit develops the Representation and Relationships key concepts systematically, moving from graphical interpretation (AO1–AO2) to modelling periodic and exponential phenomena (AO3–AO4). Technology use is embedded in topic 2.3, with GDC-based equation solving practised alongside analytic methods. Exam-style questions address both Paper 1 and Paper 2 formats.
Unit 3Geometry, Trigonometry, and Advanced Relationships
Trigonometric ratios and the unit circle extended to compound and double angle identities, reciprocal and inverse trigonometric functions, and formal proof of identities.
This 9-lesson, 3-topic unit moves from the six trigonometric ratios, exact values, and the unit circle definition through to HL-level compound and double angle identities — including formal proof — and the reciprocal trigonometric functions (secant, cosecant, cotangent) alongside inverse trigonometric functions with their restricted domains.
Skills & assessment. The Relationships key concept is central throughout, with students developing from evaluation and exact-value recall (AO1) to constructing and communicating rigorous proofs of trigonometric identities (AO3–AO4). Equation-solving with reciprocal and inverse functions prepares students for the analytical demands of Paper 1 HL questions.
Unit 4Probability Distributions and Random Variables
Discrete and continuous probability distributions — from expected value and variance through the binomial and normal distributions to confidence intervals, hypothesis testing, and HL statistical inference.
Across 21 lessons and 7 topics, this unit addresses the full probability and statistics strand: discrete random variables (probability distributions, expected value, variance); continuous random variables and probability density functions; the binomial distribution; the normal distribution; sampling distributions and the central limit theorem; confidence intervals for a population mean; and hypothesis testing including t-tests, z-tests, Type I and II errors, and p-values.
Skills & assessment. Key concepts of Representation, Validity, Approximation, and Quantity are woven through the unit as students move from constructing distributions (AO1–AO2) to evaluating statistical claims and interpreting inference in context (AO3–AO4). Technology use — GDC and statistical software — is embedded for normal probabilities, confidence intervals, and hypothesis tests, reflecting Paper 2 and Internal Assessment expectations.
Unit 5Differential Calculus and Differentiation Techniques
Differential calculus from first principles and the standard rules through curve analysis, optimisation, kinematics, and related rates of change.
This 15-lesson, 5-topic unit develops differentiation from the limit definition through the power, chain, product, and quotient rules; tangent and normal lines; increasing/decreasing functions; stationary points classified by the first and second derivative tests; points of inflection; and applications including optimisation, kinematics, and related rates of change.
Skills & assessment. The Change key concept frames all 15 lessons, with students progressing from procedural differentiation (AO1–AO2) to constructing and interpreting calculus-based arguments in applied contexts (AO3–AO4). Exam-style questions cover both non-calculator (Paper 1) and calculator-permitted (Paper 2) formats, with optimisation and kinematics tasks reflecting common Paper 2 demands.
Unit 8Definite Integrals and Area Under Curves
Definite integration using technology to find areas enclosed by curves and between functions, with careful attention to the interpretation of negative regions.
This focused 3-lesson unit addresses the use of the GDC to evaluate definite integrals, find areas enclosed between a curve and the axes — including the treatment of regions below the x-axis — and calculate areas between two curves.
Skills & assessment. Grounded in the Relationships key concept, lessons connect the definite integral to its geometric interpretation (AO1–AO2) and develop students' ability to set up and evaluate area problems correctly in context (AO3). Technology-based methods are emphasised, directly supporting Paper 2 question types.
Unit 12Probability, Statistics, and Real-World Applications
The Poisson distribution — from its derivation as a limiting case of the binomial through probability calculations and the modelling of rare events in real-world contexts.
This 3-lesson unit focuses on the Poisson distribution: its derivation from the binomial limiting case, the calculation of individual and cumulative Poisson probabilities, and its application as a model for rare or infrequent events in context.
Skills & assessment. The key concepts of Approximation, Generalisation, Relationships, and Modelling are all engaged as students move from understanding the theoretical basis of the distribution (AO1–AO2) to selecting, applying, and evaluating it as a statistical model (AO3–AO4). Questions reflect HL Paper 2 expectations and connect to actuarial and scientific contexts noted in the syllabus.
Unit 8Additional Core Topics
Skills & assessment.
A clear teaching arc in every lesson.
Built for the exams students will sit.
Walk into every lesson already prepared.
The entire DP Mathematics: Analysis and Approaches course, built to the current syllabus and ready to teach — so your time goes into the students in front of you, not into building resources from scratch.