IB Math AA SL Syllabus
Complete breakdown of topics, assessment structure, and learning resources for IB Mathematics Analysis & Approaches Standard Level. Master complex mathematical concepts with our expert video tutorials and comprehensive study materials. The IB Math AA SL Syllabus provides a structured guide to mastering essential mathematical concepts while building problem-solving and analytical skills.
With clear explanations and targeted practice, students can confidently prepare for exams and strengthen their understanding. Designed to support effective learning, the IB Math AA SL Syllabus ensures students gain the knowledge and strategies needed to succeed.
IB Math AA SL Syllabus
Assessment Structure
40%
Paper 1
Non-calculator
40%
Paper 2
Calculator allowed
20%
Internal Assessment
Mathematical exploration
Topic 1: Number & Algebra
1.1 Operations with numbers in the form a × 10^k
Operations with numbers in the form a × 10^k, where 1 ≤ a < 10 and k is an integer
1.2 Arithmetic sequences and series
Use of the formulae for the nth term and the sum of the first n terms of the sequence
Use of sigma (Σ) notation for sums of arithmetic sequences
Applications: analysis, interpretation, and prediction where a model is not perfectly arithmetic in real life
1.3 Geometric sequences and series
Use of the formulae for the nth term and the sum of the first n terms of the sequence
Use of sigma (Σ) notation for the sums of geometric sequences
Applications of the topics mentioned above
1.4 Financial applications of geometric sequences and series
Compound interest: A = P(1 + r)^n
Annual depreciation
1.6 Simple deductive proof, numerical and algebraic
How to lay out a left-hand side (LHS) to right-hand side (RHS) proof
The symbols and notation for equality (=) and identity (≡)
1.7 Laws of exponents with rational exponents
Laws of logarithms:
log a (x y) = log a x + log a y
log a (x / y) = log a x − log a y
log a (x^m) = m · log a x
Change of base of a logarithm: log a x = log b x / log b a
Solving exponential equations, including using logarithms
1.8 Sum of infinite convergent geometric sequences
S = a / (1 − r) for |r| < 1
1.9 The binomial theorem
Expansion of (a + b)^n, n ∈ ℕ
Use of Pascal’s triangle and nCr
Topic 2: Functions
2.1 Different forms of equations of a straight line
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 as a reflection in y = x: f⁻¹(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 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) = a·x² + b·x + c, y-intercept (0, c), axis of symmetry
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 Solution of quadratic equations and inequalities
Quadratic formula: x = (−b ± √Δ)/(2a)
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) = 1/x, x ≠ 0, self-inverse nature
Rational: f(x) = (ax + b)/(cx + d), graphs, vertical and horizontal asymptotes
2.9 Exponential and logarithmic functions
Exponential: f(x) = a^x, f(x) = e^x
Logarithmic: f(x) = logₐx, f(x) = ln x
2.10 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
Sine rule: a / sin A = b / sin B = c / sin C
Cosine rule: c² = a² + b² − 2ab · cos C
Area of a triangle: 1/2 · a · b · sin C
3.3 Applications of trigonometry
Right-angled and non-right-angled problems, including Pythagoras’ theorem
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 = 1/2 · r² · θ
3.5 Unit circle definitions
cos θ and sin θ in terms of the unit circle
tan θ = sin θ / cos θ
Extension of the sine rule to the ambiguous case
3.6 Trigonometric identities
Pythagorean identity: sin² θ + cos² θ = 1
Double-angle formulas for sine and cosine
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 (b x + 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) and applications
4.8 Binomial distribution
Mean and variance of the binomial distribution
4.9 Normal distribution
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 definition)
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
z-values and inverse normal calculations when mean and standard deviation are unknown
Topic 5: Calculus
5.1 Introduction
Concept of a limit: lim x → 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 polynomial functions
f(x) = a · xⁿ + b · xᵐ → derivative: f′(x) = a · n · xⁿ⁻¹ + b · m · xᵐ⁻¹
5.4 Tangents and normals at a given point
Equations of tangent and normal lines
5.5 Introduction to integration
Anti-differentiation of functions: f(x) = a · xⁿ + b · xᵐ
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, e^x, ln x
Derivative of sums and multiples
Chain rule for composite functions: sin (3x − 1)
Product and quotient rules
5.7 Second derivative
Graphical behavior: relationships between f, f′, f″
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), 1/x, e^x, composites with linear functions a · x + b
Integration by inspection, reverse chain rule, or substitution
5.11 Definite integrals
Analytical approach: ∫ f(x) dx from a to b
Areas of regions enclosed by curves y = f(x) and x-axis (f(x) positive or negative)
Areas between curves
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IB Math AA SL Syllabus covers 5 main topics: Topic 1 - Number and Algebra (sequences, series, exponents, logarithms), Topic 2 - Functions (quadratic, exponential, rational functions and their graphs), Topic 3 - Geometry and Trigonometry (circular functions, triangles, vectors), Topic 4 - Statistics and Probability (descriptive statistics, probability distributions, hypothesis testing), and Topic 5 - Calculus (differentiation, integration, and their applications). Each topic builds foundational mathematical skills essential for higher education. For more advanced content, consider IB Math AA HL which includes additional calculus and complex numbers.
IB Math AA SL assessment consists of three components: Paper 1 (40% of final grade, 90 minutes, calculator not permitted) focuses on core mathematical skills and algebraic manipulation. Paper 2 (40% of final grade, 90 minutes, calculator permitted) emphasizes problem-solving and applications. The Internal Assessment (20% of final grade) is a mathematical exploration of 12-20 pages completed during the course. Final grades range from 1-7, with 4 being the minimum passing grade.
The Internal Assessment is a mathematical exploration worth 20% of your final grade. Students choose their own mathematical topic and investigate it in depth over 12-20 pages. The IA is assessed on 5 criteria: Engagement (how well you communicate your interest), Mathematical Communication (clarity and organization), Personal Engagement (your individual approach), Reflection (analysis of your process), and Use of Mathematics (appropriate mathematical techniques). Start early and choose a topic that genuinely interests you for the best results. Get expert help with our IA guidance resources.
Math AA SL (Analysis and Approaches) focuses on traditional mathematical methods with emphasis on algebraic manipulation, calculus, and theoretical understanding. It's ideal for students planning STEM careers. Math AI SL (Applications and Interpretations) emphasizes practical applications, statistics, modeling, and technology use. It's better suited for students interested in business, social sciences, or psychology. AA SL has more calculus content, while AI SL has more statistics and real-world applications. Compare with our detailed AI SL syllabus guide.
Start preparation 3-4 months before exams with consistent daily practice. Master fundamental concepts first, then practice past papers extensively - aim for at least 10 complete exam sets. Focus extra time on calculus and functions as they comprise 60-70% of exam content. Use your calculator efficiently for Paper 2 by learning all statistical and graphing functions. Create a formula sheet for Paper 1 (non-calculator) and memorize key formulas. Join study groups, seek help from teachers early, and maintain regular revision schedules rather than cramming.
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The IB Math AA SL Syllabus includes algebra, calculus, statistics, probability, and functions. By following the IB Math AA SL Syllabus, students gain a solid foundation in mathematical concepts and problem-solving.
The IB Math AA SL Syllabus is assessed through two written papers and an internal assessment. The IB Math AA SL Syllabus ensures students are tested on both theoretical understanding and applied skills.