Is the SL content included?

Yes. HL students sit the SL content too, so every SL syllabus point is here. Chapters only HL students need are tagged HL only.

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IB Diploma · Mathematics

IBDP Maths AA HL

IBDP Maths AA HL on Preppeo is a bank of 1,521 practice questions across 5 topics and 75 chapters, with worked solutions. Sign in and the whole course is free for 7 days.

questions: 1,521; questions
topics: 5; topics
chapters: 75; chapters
difficulty levels: 3; difficulty levels

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What you get

Syllabus: The current IB Mathematics: Analysis and Approaches guide (first exams 2021), all five topics, SL and HL content.
Questions: Written answers, in parts, with marks shown
Solutions: Mark-by-mark solutions in the IB style (M1, A1)
Progress: Your accuracy in every topic, so you know which one to practise next.

Three levels of difficulty

Start a chapter on basics and work up to exam-style questions.

Basics 693
Medium 553
Exam-style 275

Syllabus

5 topics, 75 chapters. Open a topic to see its chapters; numbers follow the official syllabus. The bar beside each chapter shows its mix of basics, medium and exam-style questions.

1Number and Algebra16 chapters · 346 questions

1.1Operations with numbers in the form a × 10^k (scientific notation)5
1.2Arithmetic sequences and seriesSum of finite series; sigma notation16
1.3Geometric sequences and seriesSum of finite/infinite series; sigma notation10
1.4Financial applicationsCompound interest, annual depreciation8
1.5Laws of exponents with integer exponentsIntroduction to logarithms11
1.6Simple deductive proof (numerical and algebraic)30
1.7Laws of exponents with rational exponentsLaws of logarithms (any base)46
1.8Sum of infinite convergent geometric series8
1.9Binomial theoremExpansion of (a+b)ⁿ for n ∈ ℤ⁺; use of nCr27
1.10Counting principlesHL onlyPermutations and combinations; extension of binomial theorem to rational n41
1.11Partial fractionsHL only4
1.12Complex numbersHL onlyCartesian form, modulus, argument, conjugate38
1.13Complex numbersHL onlyPolar form re^(iθ), Euler's formula11
1.14De Moivre's theoremHL onlyPowers and roots of complex numbers17
1.15Proof by mathematical induction, by contradiction, by counterexampleHL only36
1.16Systems of linear equations in 3 unknownsHL onlyUnique, infinite, no solution38

2Functions15 chapters · 287 questions

2.1Equations of straight linesGradient, intercept forms, parallel/perpendicular37
2.2Concept of functionDomain, range, inverse f⁻¹, identity, self-inverse10
2.4Key features of graphsFinding points of intersection3
2.5Composite functionsInverse function and its graph20
2.6Quadratic functionsGraph, vertex, axis of symmetry, intercepts, discriminant20
2.7Solution of quadratic equations and inequalitiesDiscriminant32
2.8Rational function f(x) = (ax+b)/(cx+d)Asymptotes4
2.9Exponential and logarithmic functionsGraphs and inverses32
2.10Solving equations analytically and graphically14
2.11Transformations of graphsTranslation, reflection, stretches31
2.12Polynomial functions, factor and remainder theorems, sum/product of rootsHL only47
2.13Rational functions with quadratic numerator or denominatorHL onlyOblique asymptotes9
2.14Modulus function |x|HL onlyModulus equations and inequalities14
2.15Solution of inequalities analytically and graphicallyHL only2
2.16Odd and even functionsHL onlyFinding inverse; restricting domain to make invertible12

3Geometry and Trigonometry17 chapters · 304 questions

3.1Distance in 3DVolume and surface area of 3D solids; angle between line and plane66
3.2Right-angled trigonometry (SOHCAHTOA)Sine rule; cosine rule; area = ½ab sin C47
3.3ApplicationsBearings, angles of elevation/depression17
3.4Arc length and sector area using radian measure27
3.5Unit circle definitions of sin, cos, tanExact values; quadrant relationships8
3.6Pythagorean identity sin²θ + cos²θ = 1Double-angle identities for sin and cos11
3.7Graphs of sin x, cos x, tan xDomain, range, period, amplitude; transformations20
3.8Solving trigonometric equations in a finite interval, analytically and graphically22
3.9Reciprocal trig ratios (sec, csc, cot)HL onlyInverse trig functions arcsin, arccos, arctan8
3.10Compound-angle identitiesHL onlyDouble-angle for tan; relationships between trig identities13
3.11Symmetric/periodic relationshipsHL onlyFurther trig equations and proofs of identities3
3.12Vectors in 2D and 3DHL onlyMagnitude, direction, addition, scalar multiplication; position vectors19
3.13Scalar (dot) productHL onlyAngle between vectors; perpendicular and parallel vectors15
3.14Vector equation of a line in 2D and 3DHL onlyParametric form; intersection of lines22
3.15Vector (cross) productHL onlyArea of parallelogram and triangle in 3D4
3.16Vector equation of a planeHL onlyAngles between line and plane, plane and plane1
3.17Intersections of planesHL onlyGeometric and algebraic solution1

4Statistics and Probability11 chapters · 235 questions

4.1SamplingPopulation vs sample, random sample, discrete vs continuous data, sampling bias25
4.2Presentation of dataFrequency tables, histograms, cumulative frequency, box plots14
4.3Measures of central tendency (mean, median, mode) and dispersion (range, IQR, SD, variance)34
4.4Linear correlationPearson's r, regression line, predictions29
4.5ProbabilityTheoretical, experimental, sample space, Venn diagrams, tree diagrams; complement38
4.6Combined eventsP(A∪B); mutually exclusive; conditional probability; independence19
4.7Discrete random variablesProbability distribution, expected value E(X)37
4.8Binomial distributionP(X=x), P(X≤x), mean, variance3
4.9Normal distributionProperties, standardization, inverse normal15
4.10Bayes' theorem for one or two intermediate eventsHL only7
4.11Continuous random variables and probability density functionsHL onlyE(X) and Var(X) for continuous; cumulative distribution function14

5Calculus16 chapters · 349 questions

5.1LimitsDerivative as rate of change; notation f'(x), dy/dx57
5.2Increasing/decreasing functionsSign of derivative5
5.3Differentiation of polynomials f(x) = axⁿ (n ∈ ℚ)Sums and constants6
5.4Tangents and normals at a given point8
5.5Introduction to integration as antidifferentiationIndefinite integral of axⁿ23
5.6Local maxima/minimaTesting critical points6
5.7Optimization problems in context18
5.8Definite integrationArea between a curve and the x-axis; area between two curves56
5.9KinematicsDisplacement, velocity, acceleration via differentiation and integration32
5.10Limits and l'Hôpital's ruleHL onlyDifferentiation of trig, exponential, logarithmic functions; chain rule, product rule, quotient rule47
5.11Implicit differentiationHL onlyRelated rates of change4
5.12Second derivativeHL onlyConcavity, points of inflection8
5.13Integration by substitutionHL onlyIntegration by parts; integration using partial fractions20
5.14Volume of revolution about the x-axis or y-axisHL only2
5.15First-order differential equationsHL onlySeparation of variables, integrating factor, Euler's method28
5.16Maclaurin seriesHL onlyTaylor series; using series for approximation29

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2.10 Solving equations analytically and graphically· Basics

Non-calculator

Solve each equation for $x \in R$ .

$x^{3} = 27$ [1 mark]
$x^{4} = 81$ [1 mark]
$2 x^{3} = - 54$ [1 mark]
$(x - 1)^{2} = 16$ [2 marks]
$x^{- 2} = \frac{1}{9}$ [2 marks]

See all 10 free questions

Questions

Is the SL content included?: Yes. HL students sit the SL content too, so every SL syllabus point is here. Chapters only HL students need are tagged HL only.
Are these IB past paper questions?: No. They are written by our teachers in the IB style, so you can practise without using up the past papers you will want for timed mocks.
What happens when the free week ends?: You keep your account and your scores. Courses you have not bought lock until you buy them. Nothing renews automatically, and you are never charged without choosing to pay.
How long can I buy a course for?: 1 month, 3 months, 6 months, 1 year or 2 years. Longer access costs less per month. If you buy again before your access ends, the new time is added on to the end.
How do I pay?: Through Razorpay, by UPI, card, net banking or wallet. Cards issued outside India work too.