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IB Mathematics Specialist

IB Math AI SL Syllabus (2026)

Complete topic outline with assessment structure, expanded formulas, and where students consistently lose marks. Built from 7,000+ IB Math lessons.

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Assessment Structure

  • 40%
    Paper 1
    90 minutes
    Calculator allowed
  • 40%
    Paper 2
    90 minutes
    Calculator allowed
  • 20%
    Internal Assessment
    12–20 pages
    Mathematical exploration

The Internal Assessment is a mathematical exploration worth 20% of the final grade. It is marked against five criteria that most students misunderstand without guidance.

Not sure if AI SL is right for you? AI focuses on real-world applications, statistics, modelling, and technology use. AA focuses on algebraic methods, exact reasoning, and symbolic manipulation. Both come in SL and HL. See the full comparison between all four IB Math courses

See common AI SL challenges and how I help

IB Math AI SL Topics

This is the official IB Math AI SL syllabus. I have expanded some points to be clearer and more specific, from years of teaching AI SL. Every subtopic shows the exact formulas, notation, and depth you need to know, so you know exactly what the IB expects at each point.

Topic 1 Number & Algebra

1.1 Operations with Numbers

  • Numbers in the form a × 10k
  • Where 1 ≤ a < 10 and k is an integer

1.2 Arithmetic Sequences and Series

  • Formulae for nth term: un = u1 + (n − 1)d
  • Sum of first n terms: Sn = n2(2u1 + (n − 1)d)
  • Use of sigma (Σ) notation, e.g. Σk=1n (3k + 2)
  • Applications: analysis, interpretation, prediction when models are not perfectly arithmetic

1.3 Geometric Sequences and Series

  • Formulae for nth term: un = u1 rn−1
  • Sum of first n terms: Sn = u1(rn − 1)r − 1
  • Sigma notation for sums of geometric sequences
  • Identify first term and ratio; applications

1.4 Financial Applications

  • Compound interest: FV = PV × (1 + r100k)nk
  • Annual depreciation

1.5 Laws of Exponents and Logarithms

  • Laws of exponents with integer exponents
  • Introduction to logarithms: log10 x and ln x
  • Numerical evaluation using technology

1.6 Approximation

  • Decimal places and significant figures
  • Upper and lower bounds of rounded numbers
  • Percentage errors: ε = | vA − vEvE | × 100%, estimation

1.7 Amortization and Annuities

  • Use of technology to calculate payments and balances

1.8 Solving Equations with Technology

  • Systems of linear equations (up to 3 variables)
  • Polynomial equations

Topic 2 Functions

2.1 Equations of a Straight Line

  • Different forms: gradient, intercepts
  • Parallel lines: m1 = m2
  • Perpendicular lines: m1 × m2 = −1

2.2 Concept of a Function

  • Domain, range, graph, notation (f(x), v(t), C(n))
  • Inverse function as reflection in y = x, notation f−1(x)

2.3 Graphing Functions

  • Sketch from context or data; transfer from screen to paper
  • Graph sums and differences using technology

2.4 Key Features of Graphs

  • Determine points of intersection of curves/lines using technology

2.5 Modelling with Functions

  • Linear: f(x) = mx + c
  • Quadratic: f(x) = ax2 + bx + c, a ≠ 0; axis, vertex, zeros, intercepts
  • Exponential: f(x) = k · ax + c, f(x) = k · erx + c; horizontal asymptote
  • Direct/inverse variation: f(x) = a · xn, n ∈ ℤ
  • Cubic: f(x) = ax3 + bx2 + cx + d
  • Sinusoidal: f(x) = a sin(bx) + d, f(x) = a cos(bx) + d

2.6 Modelling Skills

  • Develop, fit, test, reflect, and use models
  • Select a reasonable domain
  • Justify the choice of a model based on data, curve shape, and context

Topic 3 Geometry & Trigonometry

3.1 Distance, Midpoint, and Solids

  • Distance between two points: d = √((x2−x1)2 + (y2−y1)2 + (z2−z1)2)
  • Midpoint: M = ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
  • Volume and surface area: right pyramid, right cone, sphere, hemisphere, and combinations
  • Angle between two intersecting lines or between a line and a plane

3.2 Trigonometry in Triangles

  • Use of sine, cosine, and tangent ratios to find sides and angles of right-angled triangles:
    • sin θ = opphyp, cos θ = adjhyp, tan θ = oppadj
  • Sine rule: asin A = bsin B = csin C
  • Cosine rule: c2 = a2 + b2 − 2ab cos C; cos C = a2 + b2 − c22ab
  • Area of triangle: Area = 12 · a · b · sin C

3.3 Applications of Trigonometry

  • Applications of right and non-right triangle including Pythagoras’ theorem: a2 + b2 = c2
  • Angles of elevation and depression
  • Constructing labelled diagrams from statements

3.4 The Circle

  • Radian measure of angles
  • Length of an arc: L = r · θ
  • Area of a sector: A = 12 · r2 · θ

3.5 Equations of Perpendicular Bisectors

  • Find perpendicular bisector of a line segment
  • Given two points or the equation of a line segment, calculate midpoint
  • Determine slope of perpendicular bisector
  • Equation using point-slope form: y − y0 = m(x − x0)

3.6 Voronoi Diagrams

  • Sites, vertices, edges, cells
  • Adding a site to an existing diagram
  • Nearest neighbour interpolation
  • Applications such as the “toxic waste dump” problem

Topic 4 Statistics & Probability

4.1 Population and Sampling

  • Concepts of population, sample, random sample, discrete and continuous data
  • Reliability of data sources and bias in sampling
  • Interpretation of outliers
  • Sampling techniques and their effectiveness

4.2 Presentation of Data

  • Frequency distributions (tables) for discrete and continuous data
  • Histograms
  • Cumulative frequency and cumulative frequency graphs; find median, quartiles, percentiles, range, interquartile range (IQR)
  • Box-and-whisker diagrams

4.3 Measures of Central Tendency

  • Mean, median, mode
  • Estimation of mean from grouped data
  • Modal class
  • Interquartile range (IQR), standard deviation, variance
  • Effect of constant changes on data

4.4 Linear Correlation

  • Scatter diagrams; lines of best fit (by eye through mean point)
  • Pearson’s correlation coefficient r
  • Regression line of y on x: y = ax + b; interpret parameters a and b
  • Use of regression for prediction

4.5 Probability – Basic Concepts

  • Trial, outcome, equally likely outcomes, relative frequency, sample space U, event
  • Probability: P(A) = n(A)n(U)
  • Complementary events: P(A′) = 1 − P(A)
  • Expected number of occurrences

4.6 Probability – Diagrams and Rules

  • Venn diagrams, tree diagrams, sample space diagrams, tables of outcomes
  • Combined events: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
  • Mutually exclusive: P(A ∩ B) = 0
  • Conditional probability: P(A|B) = P(A ∩ B)P(B)
  • Independent events: P(A ∩ B) = P(A) · P(B)

4.7 Discrete Random Variables

  • Probability distributions
  • Expected value (mean) E(X)
  • Applications

4.8 Binomial Distribution

  • General notation: X ~ B(n, p)
  • Mean formula: μ = np
  • Variance formula: σ2 = np(1 − p)

4.9 Normal Distribution

  • General notation: X ~ N(μ, σ2)
  • Properties of normal curve and diagrammatic representation
  • Normal probability calculations using technology
  • Inverse normal calculations

4.10 Spearman’s Rank Correlation

  • Spearman’s rank correlation coefficient rs
  • Awareness of Pearson vs Spearman correlation
  • Effect of outliers

4.11 Hypothesis Testing

  • Null and alternative hypotheses: H0 and H1
  • Significance levels, p-values
  • Chi-square test (χ2): independence, goodness of fit
  • t-test: comparing two population means
  • One-tailed and two-tailed tests

Topic 5 Calculus

5.1 Introduction to Limits and Derivatives

  • Concept of a limit
  • Derivative interpreted as gradient function and rate of change

5.2 Increasing and Decreasing Functions

  • Graphical interpretation: f′(x) > 0, f′(x) = 0, f′(x) < 0

5.3 Derivatives of Polynomial Functions

  • f(x) = axn ⇒ f′(x) = anxn−1, n ∈ ℤ
  • Derivative of f(x) = axn + bxm + …, all integer exponents

5.4 Tangents and Normals

  • Tangent and normal lines at a given point
  • Equations of tangents and normals

5.5 Introduction to Integration

  • Anti-differentiation of f(x) = axn + bxm + …, n ∈ ℤ, n ≠ −1
  • Notation: ∫ f(x) dx
  • Anti-differentiation with boundary condition
  • Definite integrals using technology
  • Area of a region enclosed by y = f(x) and the x-axis where f(x) > 0

5.6 Stationary Points

  • Values of x where gradient is zero: f′(x) = 0
  • Local maximum and minimum points

5.7 Optimisation Problems

  • Solving context-based optimisation problems

5.8 Approximating Areas

  • Trapezoidal rule for approximating areas under curves

Where AI SL Students Lose Marks

AI SL rewards clear interpretation. Students often reach the right answer but lose marks by not explaining what it means in context, or by misreading what a worded question is actually asking.

  • Giving a numerical answer without interpreting what it means in the real-world context the question describes
  • Choosing the wrong statistical test, or running a chi-squared or t-test without checking its conditions first
  • Misreading multi-part worded questions and missing what is actually being asked for in each section
  • Relying on the calculator for statistics without understanding what the output actually represents
  • Setting up models incorrectly, or failing to define variables clearly before applying a function
  • Losing communication marks by not writing conclusions in full sentences that answer the question directly

What Separates a 5 from a 7 in AI SL

  • Grade 5

    Can run the calculation but stops at the number. Finds the regression equation but does not interpret the gradient. Completes the hypothesis test but does not state a clear conclusion in context. Understands the method but leaves the interpretation marks on the table.

  • Grade 7

    Turns every answer into a statement about the real-world situation. Interprets the gradient as a rate of change. States what the hypothesis test result means for the original question. The calculation is the same. The difference is explaining what the mathematics tells you.

Most students who improve from a 5 to a 7 do not learn new content. They learn to interpret their results and communicate them the way examiners actually mark for.

How Tutoring Helps in AI SL

AI SL students often lose marks not because they cannot do the math, but because they do not write about it the way examiners want. Sessions focus on building the interpretation and modelling skills that separate a solid understanding from a top grade.

  • A study plan built around your exam date, your school’s teaching order, and the topics where you need the most support
  • Regular past paper practice marked against the real scheme, with direct feedback on where interpretation and communication marks were lost
  • Focused work on statistics and modelling, which carry significant weight across both papers in AI SL
  • Practice writing clear conclusions in context, so you capture the communication marks that many students miss

See how I structure AI SL tutoring sessions

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Frequently Asked Questions

Common questions about the IB Math AI SL course, exams, and preparation.

AI SL covers five topics: Number and Algebra (financial math, sequences, logarithms, approximation), Functions (modelling with linear, quadratic, exponential, and sinusoidal functions), Geometry and Trigonometry (triangle rules, Voronoi diagrams, perpendicular bisectors), Statistics and Probability (descriptive stats, distributions, hypothesis testing, Spearman’s rank), and Calculus (differentiation, integration, optimisation, trapezoidal rule). The course is built around real-world applications rather than abstract theory.

Assessment consists of two written papers and an Internal Assessment. Paper 1 is 90 minutes with a calculator allowed and carries 40% of the final grade. Paper 2 is also 90 minutes with a calculator and carries 40%. Both papers are set in real-world contexts. The Internal Assessment is a mathematical exploration worth 20%, marked against five criteria. AI SL has no non-calculator paper.

The Internal Assessment is a mathematical exploration of 12 to 20 pages, worth 20% of the final grade. Students choose their own topic and investigate it in depth, usually using real-world data or a statistical model. The IA is assessed on five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection, and Use of Mathematics. Choosing a topic with genuine data makes the exploration far stronger. See the full IA criteria breakdown.

AI SL focuses on real-world applications, statistics, and modelling, with a calculator allowed on both papers. AA SL focuses on algebraic methods, exact reasoning, and has a non-calculator paper with more calculus. AI SL suits students heading towards business, social sciences, design, or fields that use data. AA SL suits students heading towards mathematics, engineering, or the physical sciences. See the full comparison between all four IB Math courses.

Start past paper practice three to four months before exams. Focus on interpreting results in context, not just calculating them, because that is where AI SL marks are won and lost. Learn your calculator’s statistical functions thoroughly, since both papers allow one. Practise writing conclusions in full sentences that answer the question directly. Consistent weekly revision works better than last-minute cramming.

Both papers allow a graphic display calculator (GDC). The most commonly used models are the TI-84 and the TI-Nspire. Because AI SL has no non-calculator paper, being fluent with your GDC is essential. Students should practise with their specific model well before the exam so that statistical tests, graphing, and regression functions feel automatic under timed conditions.

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