IB Math AI SL Syllabus (2026)
Complete topic outline with assessment structure, expanded formulas, and where students consistently lose marks. Built from 6,500+ hours of teaching this course.
Need help this term? Apply for tutoring →Assessment Structure
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 →
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
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
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
- Right-angled triangles (sine, cosine, tangent):
- 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
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
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
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Where AI SL Students Lose Marks
AI SL is not the easy option. The course tests whether students can interpret mathematics in context, choose the right model, and explain what their results actually mean. That is harder than it sounds under exam conditions.
What Separates a 5 from a 7 in AI SL
Can run the right test on the calculator but writes a weak conclusion. Gets the regression equation but cannot explain what the gradient means in context. Sets up a chi-square table correctly but confuses the expected frequencies. Knows the method but loses marks through vague interpretation.
Writes every conclusion in context. States what the correlation means for the actual variables, not just “strong positive.” Justifies model choice with reference to the data shape and residuals. Links the hypothesis test result back to the original question. The statistics are the same. The difference is interpretation.
Most students who improve from a 5 to a 7 do not learn new content. They learn to write about their results the way examiners expect.
How Tutoring Helps in AI SL
AI SL students often lose marks not because they cannot do the maths, 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.
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See student results →Frequently Asked Questions
Common questions about the IB Math AI SL course, exams, and preparation.
AI SL covers five topics: Number and Algebra (financial maths, 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 and focuses on short and medium response questions. Paper 2 is 90 minutes and features extended response questions with more emphasis on applications and modelling. Both papers allow a calculator. The Internal Assessment is a mathematical exploration worth 20% of the final grade, marked against five criteria.
The IA is a mathematical exploration of 12 to 20 pages, worth 20% of the final grade. Students choose a topic and investigate it using mathematics from the course. In AI SL, strong IAs often involve collecting real data and applying statistical or modelling techniques to answer a genuine question. The exploration is assessed on five criteria including personal engagement, mathematical communication, and reflection. See the full IA criteria breakdown.
AI SL focuses on practical applications, statistics, modelling, and using technology to solve problems. Both papers allow a calculator. AA SL focuses on algebraic manipulation, exact reasoning, and symbolic working, and has a non-calculator paper. AI SL has more statistics content and hypothesis testing. AA SL has more calculus and pure algebra. AI SL tends to suit students heading towards business, social sciences, or psychology. AA SL suits students heading towards engineering, physical sciences, or mathematics. See the full comparison between all four courses.
Focus on understanding what questions are really asking for, not just which buttons to press. Statistics and probability carry a large share of the marks, so give those topics extra time. Practise writing conclusions in context rather than just stating numbers. Work through at least ten full past papers under timed conditions. Learn your calculator inside out, especially the statistics, regression, and distribution functions. Regular weekly revision is far more effective than cramming before the exam.
Not exactly. AI SL has less abstract algebra and no non-calculator paper, which some students find more accessible. But it requires strong statistical reasoning, the ability to interpret results in context, and clear written communication of findings. Many students underestimate how many marks depend on interpretation rather than calculation. The courses are different, not ranked by difficulty. The right choice depends on your strengths and what you plan to study after the IB.
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