IB Math AA 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 AA SL is right for you? AA focuses on algebraic methods, exact reasoning, and symbolic manipulation. AI focuses on interpretation, technology use, statistics, and modelling. Both come in SL and HL. See the full comparison between all four IB Math courses →
Number & Algebra
1.1 Operations with Numbers
- Operations with numbers in the form a × 10k
- Where 1 ≤ a < 10 and k is an integer
1.2 Arithmetic Sequences
- Formulae for the 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 and prediction in real models
1.3 Geometric Sequences
- Formulae for the nth term: un = u1 rn−1
- Sum of first n terms: Sn = u1(rn − 1)r − 1
- Use of sigma (Σ) notation for sums
- Applications of the topics mentioned above
1.4 Financial Applications
- Compound interest formula: A = P(1 + r)n
- Annual depreciation calculations
1.6 Proofs
- Simple deductive proof: numerical and algebraic
- Layout of LHS to RHS proof
- Symbols: equality (=) and identity (≡)
1.7 Exponents & Logarithms
- Laws of exponents with rational exponents
- Laws of logarithms:
- loga(xy) = logax + logay
- loga(xy) = logax − logay
- loga(xm) = m · logax
- Change of base: logax = logbxlogba
- Solving exponential equations using logarithms
1.8 Infinite Geometric Sequences
- Sum of infinite convergent sequences
- Formula: S∞ = a1 − r where |r| < 1
1.9 The Binomial Theorem
- Expansion of (a + b)n, where n ∈ ℕ
- General term formula: nCr an−r br
- Use of Pascal’s triangle and nCr values
Functions
2.1 Equations of a Straight Line
- Equation: y = mx + c
- Lines with gradients m1 and m2:
- Parallel: m1 = m2
- Perpendicular: m1 × m2 = −1
2.2 Concept of a Function
- Domain, range, and graph
- Function notation: f(x), v(t)
- Concept of a function as a mathematical model
- Inverse function f−1(x) as a reflection in y = x
2.3 The Graph of a Function
- Equation y = f(x)
- Creating a sketch from given information or a context
- Using technology to graph functions, including sums and differences
2.4 Key Features of Graphs
- Determine key features of graphs
- Finding intersections of two curves or lines using technology
2.5 Composite Functions
- (f ∘ g)(x) = f(g(x))
- Identity function and inverse function: f−1(x), (f ∘ f−1)(x) = x
2.6 The Quadratic Function
- Standard form: f(x) = ax2 + bx + c, y-intercept (0, c), axis of symmetry x = −b2a
- Factor form: f(x) = a(x − p)(x − q), x-intercepts (p, 0) and (q, 0)
- Vertex form: f(x) = a(x − h)2 + k, vertex (h, k)
2.7 Quadratic Equations
- Solution of quadratic equations and inequalities
- Quadratic formula: x = −b ± √Δ2a
- Discriminant: Δ = b2 − 4ac
- Nature of roots: two distinct real roots, two equal real roots, or no real roots
2.8 Reciprocal and Rational Functions
- Reciprocal: f(x) = 1x, x ≠ 0, self-inverse nature
- Rational: f(x) = ax + bcx + d, graphs, vertical and horizontal asymptotes
2.9 Exponential and Logarithmic
- Exponential: f(x) = ax, f(x) = ex
- Logarithmic: f(x) = logax, f(x) = ln x
2.10 Solving Equations
- Solving equations graphically and analytically, use of technology
- Applications to real-life situations
2.11 Transformations of Graphs
- Translations: y = f(x) + b, y = f(x − a)
- Reflections: y = −f(x), y = f(−x)
- Vertical stretch: y = p·f(x), horizontal stretch: y = f(qx)
- Composite transformations
Geometry & Trigonometry
3.1 3D Geometry
- Volume and surface area of three-dimensional solids, including right pyramids, cones, spheres, hemispheres, and combinations of these solids
- Size of an angle between two intersecting lines or between a line and a plane
3.2 Trigonometry in Right-Angled Triangles
- Use of sine, cosine, and tangent ratios to find sides and angles:
- 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
- Area of a triangle: 12 · a · b · sin C
3.3 Applications of Trigonometry
- Right-angled and non-right-angled problems, including Pythagoras’ theorem: a2 + b2 = c2
- Angles of elevation and depression
- Construction of labelled diagrams from written statements
3.4 The Circle
- Radian measure of angles
- Length of an arc: s = r · θ
- Area of a sector: A = 12 · r2 · θ
3.5 Unit Circle Definitions
- cos θ and sin θ in terms of the unit circle
- tan θ = sin θcos θ
- Extension of the sine rule to the ambiguous case
3.6 Trigonometric Identities
- Pythagorean identity: sin2 θ + cos2 θ = 1
- Double-angle formulas:
- sin 2θ = 2 sin θ cos θ
- cos 2θ = cos2 θ − sin2 θ
- cos 2θ = 2cos2 θ − 1
- cos 2θ = 1 − 2sin2 θ
- Relationships between trigonometric ratios
3.7 Circular Functions
- sin x, cos x, tan x, amplitude, periodic nature, and graphs
- Composite functions: f(x) = a · sin (bx + c) + d
- Transformations and real-life contexts
3.8 Solving Trigonometric Equations
- Graphically and analytically in finite intervals
- Equations leading to quadratic equations in sin x, cos x, or tan x
Statistics & Probability
4.1 Concepts of Data
- Population, sample, random sample, discrete and continuous data
- Reliability of data sources and bias in sampling
- Interpreting outliers, sampling techniques
4.2 Presentation of Data
- Frequency distributions, histograms
- Cumulative frequency and cumulative frequency graphs
- Using graphs to find median, quartiles, percentiles, range, and interquartile range (IQR)
- Box-and-whisker diagrams
4.3 Measures of Central Tendency
- Mean, median, and mode
- Estimation of mean from grouped data
- Modal class
- Measures of dispersion: IQR, standard deviation, variance
- Effect of constant changes on original data
- Quartiles of discrete data
4.4 Linear Correlation of Bivariate Data
- Pearson’s correlation coefficient r
- Scatter diagrams, lines of best fit by eye through mean point
- Regression line of y on x: y = a · x + b, interpretation of a and b
4.5 Probability Concepts
- Trial, outcome, equally likely outcomes, sample space U, and event
- Probability of event A: P(A) = n(A)n(U)
- Complementary events: A and A′
- Expected number of occurrences
4.6 Using Diagrams for Probability
- Venn diagrams, tree diagrams, sample space diagrams, and tables of outcomes
- Combined events: P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
- Mutually exclusive events: 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) and applications
4.8 Binomial Distribution
- General notation: X ~ B(n, p)
- Mean and variance of the binomial distribution
4.9 Normal Distribution
- General notation: X ~ N(μ, σ2)
- Properties and diagrammatic representation
- Normal probability calculations and inverse normal calculations
4.10 Regression Line of x on y
- Use for prediction purposes
4.11 Conditional Probability (Formal)
- P(A|B) = P(A ∩ B)P(B) for conditional probabilities
- Independent events: P(A|B) = P(A) = P(A|B′)
4.12 Standardization of Normal Variables
- Formula: z = x − μσ
- z-values and inverse normal calculations when mean and standard deviation are unknown
Calculus
5.1 Introduction to Calculus
- Concept of a limit: limx → a f(x)
- Derivative 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 Polynomials
- f(x) = a · xn + b · xm ⇒ f′(x) = a · n · xn−1 + b · m · xm−1
5.4 Tangents and Normals
- Equations of tangent and normal lines at a given point
5.5 Introduction to Integration
- Anti-differentiation of functions: ∫ (a · xn + b · xm) dx
- Anti-differentiation with boundary condition to determine constant
- Definite integrals using technology: area under y = f(x), f(x) ≥ 0
5.6 Derivatives of Elementary Functions
- xn, sin x, cos x, ex, ln x
- Derivative of sums and multiples
- Chain rule for composite functions: e.g. sin(3x − 1) or ln(2x + 5)
- Product and quotient rules
5.7 Second Derivative
- Graphical behavior: relationships between f(x), f′(x), f″(x)
5.8 Local Maxima and Minima
- Testing for maxima and minima, optimization
- Points of inflection: zero and non-zero gradient
5.9 Kinematics Problems
- Displacement (s), velocity (v), acceleration (a)
- Total distance traveled
5.10 Indefinite Integrals
- xn (n rational), 1x, ex
- Composites with linear functions: ∫ f(ax + b) dx
- Integration by inspection (e.g. ∫ cos(3x) dx), reverse chain rule, or substitution
5.11 Definite Integrals
- Analytical approach: ∫ab f(x) dx
- Areas of regions enclosed by curves y = f(x) and x-axis (f(x) positive or negative)
- Areas between curves: ∫ab (f(x) − g(x)) dx
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Where AA SL Students Lose Marks
AA SL rewards precision. Students often understand the method but lose marks through poor presentation, algebraic slips, or misreading what the question actually asks for.
What Separates a 5 from a 7 in AA SL
Understands the topic but loses marks on execution. Can differentiate a function but forgets the chain rule on composites. Knows the quadratic formula but misreads the discriminant condition. Starts integration questions correctly but makes sign errors or forgets the constant.
Does what the examiner expects at every step. States the formula before substituting. Shows the derivative before evaluating. Writes “therefore” before the conclusion. The mathematics is the same. The difference is how clearly the working is communicated under timed conditions.
Most students who improve from a 5 to a 7 do not learn new content. They learn how to present what they already know in the format examiners actually mark for.
How Tutoring Helps in AA SL
AA SL covers a lot of ground across five topics. Students who fall behind on one area often find it affects others, because the syllabus builds on itself. Work is adapted to each student and adjusted as weak points improve.
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See student results →Frequently Asked Questions
Common questions about the IB Math AA SL course, exams, and preparation.
AA SL covers five topics: Number and Algebra (sequences, series, exponents, logarithms), Functions (quadratic, exponential, rational functions and their graphs), Geometry and Trigonometry (circular functions, identities, triangle rules), Statistics and Probability (distributions, correlation, conditional probability), and Calculus (differentiation, integration, and their applications). Each topic builds on the others, so gaps in one area tend to affect performance across the paper.
Assessment consists of two written papers and an Internal Assessment. Paper 1 is 90 minutes with no calculator and carries 40% of the final grade. It focuses on algebraic manipulation and exact working. Paper 2 is 90 minutes with a calculator allowed and also carries 40%. The Internal Assessment is a mathematical exploration worth 20%, marked against five criteria.
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. The IA is assessed on five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection, and Use of Mathematics. Starting early and choosing a topic you find interesting makes a noticeable difference in the final result. See the full IA criteria breakdown.
AA SL focuses on algebraic methods, exact reasoning, and symbolic manipulation. It has more calculus content and a non-calculator paper. AI SL focuses on interpretation, real-world applications, statistics, and technology use. AA SL suits students heading towards mathematics, engineering, or the physical sciences. AI SL suits students heading towards business, social sciences, or fields that use data and modelling. See the full comparison between all four IB Math courses.
Start past paper practice three to four months before exams and work through at least ten full sets. Focus extra time on calculus and functions, which together carry the majority of marks. For Paper 1, practise algebraic manipulation without a calculator until it feels automatic. For Paper 2, learn your calculator’s statistical and graphing functions so you are not wasting time on mechanics. Consistent weekly revision works better than last-minute cramming.
Paper 2 allows a graphic display calculator (GDC). The most commonly used models are the TI-84 and the TI-Nspire. Paper 1 does not allow any calculator at all, which is why strong algebraic skills matter so much in AA. Students should practise with their specific GDC model well before the exam so that calculator operations feel automatic under timed conditions.
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