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.
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 = n/2 (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(x/y) = logax − logay
- loga(xm) = m · logax
- Change of base: logax = logbx / logba
- Solving exponential equations using logarithms
1.8 Infinite Geometric Sequences
- Sum of infinite convergent sequences
- Formula: S∞ = a / (1 − 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 = −b / (2a)
- 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 ± √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
- 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 = opp / hyp
- cos θ = adj / hyp
- tan θ = opp / adj
- 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: 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 = 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:
- 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 (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) 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 − μ) / σ
- 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: 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 Polynomials
- f(x) = a · xn + b · xm → derivative: 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), 1/x, 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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Syllabus Guide
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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.