IB Math AA SL Topics (2026)
Topic 1
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
Topic 2
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
Topic 3
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
Topic 4
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
Topic 5
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