IB Maths: Analysis and Approaches HL, marked to the mark scheme.

Practise every topic on the HL specification and get each answer checked against the published scheme, point by point — with the wording that would have earned the marks you missed.

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Built for HL, not adapted to it.

IB Maths: Analysis and Approaches HL spans 5 topics, from Number and algebra to Calculus, and Exaim covers all 83 subtopics — with practice written for the HL specification rather than adapted from another board's.

Maths is marked on method as much as outcome: working that is right earns marks even when the last line is wrong, and a right answer with no working earns fewer than you would think. Exaim marks your written answers the way HL's own examiners do, one marking point at a time, so every question shows you where a real mark was won or lost.

What you get with every HL Maths course.

The same thing in every subject: real exam questions, marked properly, and a clear next step.

Marked like an examiner would

Write the answer in full and get it checked against your board’s published scheme, point by point, with the wording that would have earned each mark.

Built for your exact board

Not a generic summary written for everyone. Questions, notes and mark schemes all follow the specification you are actually sitting.

Practice, papers and timed mocks

Topic questions when you are learning something, full papers under exam conditions when you are ready to find out.

Handwritten work included

Photograph a written answer or a diagram and it is marked the same way — so you can revise on paper if that is how you work.

A plan that reorders itself

Every mark you drop becomes scheduled practice, so the weakest topic is always next and you never open the app wondering what to do.

How HL Maths practice actually works.

Not a video you watch. A question you answer, marked the way an examiner would.

  1. 01

    Answer a real exam question

    Type it, write it on paper and photograph it, or draw the diagram. Full sentences, the way you would in the exam.

  2. 02

    It is marked point by point

    Checked against your board’s published mark scheme, one mark point at a time — with the wording that would have earned the ones you missed.

  3. 03

    Your plan moves

    Every mark you drop becomes scheduled practice. The weakest topic is next, so you never open it wondering what to do.

Every HL Maths topic.

The whole IB specification, broken into the subtopics you actually revise and get tested on.

Number and algebra

16
  • Scientific notation
  • Arithmetic sequences and series
  • Geometric sequences and series
  • Financial applications of geometric sequences
  • Laws of exponents and introduction to logarithms
  • Simple deductive proof
  • Rational exponents, laws of logarithms and exponential equations
  • Infinite geometric series
  • The binomial theorem
  • Counting principles and extended binomial theorem
  • Partial fractions
  • Complex numbers in Cartesian form
  • Modulus–argument and Euler form
  • Polynomial roots, De Moivre's theorem, powers and roots
  • Proof by induction, contradiction and counterexample
  • Systems of linear equations

Functions

16
  • Equations of straight lines
  • Functions, domain, range and inverse
  • The graph of a function
  • Key features of graphs
  • Composite and inverse functions
  • The quadratic function
  • Quadratic equations, inequalities and the discriminant
  • Reciprocal and simple rational functions
  • Exponential and logarithmic functions
  • Solving equations graphically and analytically
  • Transformations of graphs
  • Polynomial functions
  • Further rational functions
  • Odd and even functions; inverse with domain restriction
  • Solving inequalities
  • Modulus and further transformed graphs

Geometry and trigonometry

18
  • Three-dimensional geometry
  • Right-angled and non-right-angled trigonometry
  • Applications of trigonometry
  • Radians, arcs and sectors
  • The unit circle and exact values
  • Trigonometric identities
  • Circular functions and their graphs
  • Solving trigonometric equations
  • Reciprocal and inverse trigonometric functions
  • Compound angle identities
  • Symmetry properties of trigonometric graphs
  • Vectors: concepts and algebra
  • The scalar product
  • Vector equation of a line
  • Relationships between lines
  • The vector product
  • Equations of a plane
  • Intersections and angles of lines and planes

Statistics and probability

14
  • Populations, samples and data collection
  • Presentation of data
  • Measures of central tendency and dispersion
  • Correlation and regression of y on x
  • Basic probability
  • Combined, conditional and independent events
  • Discrete random variables
  • The binomial distribution
  • The normal distribution
  • Regression line of x on y
  • Formal conditional probability and independence
  • Standardisation and inverse normal with unknown parameters
  • Bayes' theorem
  • Discrete and continuous random variables

Calculus

19
  • Limits and the derivative
  • Increasing and decreasing functions
  • Differentiating polynomials
  • Tangents and normals
  • Introduction to integration
  • Further differentiation rules
  • The second derivative
  • Stationary points, optimisation and inflexion
  • Kinematics
  • Indefinite integrals and substitution
  • Definite integrals and areas
  • Continuity, differentiability and first principles
  • Limits and l'Hôpital's rule
  • Implicit differentiation, related rates and optimisation
  • Further derivatives and integrals
  • Integration by substitution and by parts
  • Areas with the y-axis and volumes of revolution
  • Differential equations
  • Maclaurin series

Studying the other level?

Maths is covered at both SL and HL. The specifications differ, so the practice does too.

SL Maths

Common questions.

How is IB Maths: Analysis and Approaches HL marked on Exaim?

You write a real exam-style answer and it is marked against HL's published mark scheme, point by point — the same marking points an examiner uses. You see exactly which points you earned, which you missed, and the wording that would have earned them.

How many topics does IB Maths: Analysis and Approaches HL cover?

The whole specification: 5 topics, from Number and algebra to Calculus, broken into 83 subtopics you revise and get tested on. Every one has practice, and the full list is on this page.

Is this built for HL, or a generic maths course?

Built for HL. The questions, the topics and the marking all follow the HL specification — not one generic maths course with a different level name on the front.

Can I try IB Maths: Analysis and Approaches HL for free?

Yes — start free with no card. You can practise Maths questions and see exactly how the marking works before you decide anything.

I sit a different level — is Maths covered for others?

Yes. IB Maths is covered for SL too, each built for that level's own specification. The links are further up this page.

Start IB Maths: Analysis and Approaches HL free.

Practise a few questions and see how the marking works before you decide anything.

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