IB Maths: Analysis and Approaches, SL and HL
The DP course built on algebra, functions, calculus and proof — one-to-one, online or in person around Lisbon, with Paper 1 (no calculator) and the exploration in view from the start.
What this covers in detail
Number and algebra
Sequences and series, exponents and logarithms, the binomial theorem and proof. HL adds complex numbers, proof by induction and systems of equations.
Functions
Properties and transformations of functions, quadratic, rational, exponential and logarithmic functions. HL adds polynomial functions and further function properties.
Geometry and trigonometry
3D geometry, trigonometric functions, identities and equations. HL adds vectors, lines and planes.
Statistics and probability
Descriptive statistics, regression, probability, and the binomial and normal distributions. HL adds Bayes’ theorem and continuous random variables.
Calculus
Limits, differentiation and integration, with applications to kinematics and optimisation. HL adds further techniques, differential equations and Maclaurin series.
Analysis and Approaches is the DP maths course for students heading towards maths, physics, engineering and economics. It asks for fluent algebra, confident calculus and the ability to justify a result — part of it without a calculator. These lessons build exactly that, at SL or HL.
What this covers
Algebra that holds without a calculator
Paper 1 is calculator-free. Algebraic fluency is practised until manipulation stops costing marks.
The exploration, done properly
The internal assessment is a written mathematical exploration. Lessons help choose a workable topic and meet the criteria — the writing stays the student’s.
The right guide
The current course is examined for the last time in November 2028; revised courses start in August 2027. Lessons follow whichever guide the student is on.
Pricing
Choose the support that fits.
One-to-one tutoring, from a single session to consistent weekly progress.
Your first 30 minutes are free.
Start with a free 30-minute assessment. We will understand what the student needs and recommend the right plan.
Every plan includes live one-to-one lessons.
The Noktua practice platform is free with every account — even if you have not booked a lesson yet.
Lessons at the student's home carry an extra charge of €10/hour.
Common questions
Should I take SL or HL?
HL makes sense for maths-heavy university courses such as maths, physics or engineering. The assessment looks at current level and plans to help decide.
Should I switch to Applications and Interpretation?
Sometimes, but not always. AI is a different course, not an easier one. We can go through both syllabuses against your university plans.
Book your free 30-minute assessment
Tell us the year group and where it is going wrong. You will have a reply within 24 hours with a time.
Not ready to book? Create a free account and try the practice platform.