IB Math AI SL Syllabus
Complete breakdown of topics, assessment structure, and learning resources for IB Mathematics Applications & Interpretations Standard Level. Master practical mathematical applications with our expert video tutorials and comprehensive study materials.
Topic 1: 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 = n/2 (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 + r / (100k))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 − vE) / vE | × 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
Topic 2: 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
Topic 3: 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 = 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; cos C = (a2 + b2 − c2) / (2ab)
- Area of triangle: Area = 1/2 · 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 = 1/2 · 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
Topic 4: 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
Topic 5: 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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Syllabus Guide
Complete breakdown of the IB Math AI SL curriculum with learning objectives, assessment criteria, and topic weights
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IB Math AI SL covers 5 main topics: Topic 1 - Number and Algebra (financial mathematics, sequences, logarithms), Topic 2 - Functions (modeling, regression analysis, functions), Topic 3 - Geometry and Trigonometry (geometry, trigonometry, Voronoi diagrams), Topic 4 - Statistics and Probability (descriptive statistics, probability, normal distribution, hypothesis testing), and Topic 5 - Calculus (differential calculus, integration). The course emphasizes real-world applications and mathematical modeling.
IB Math AI SL assessment consists of three components: Paper 1 (40% of final grade, 90 minutes, calculator permitted) focuses on short and medium response questions. Paper 2 (40% of final grade, 90 minutes, calculator permitted) emphasizes extended response questions 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.
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. 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. AI SL has more statistics and real-world applications, while AA SL has more calculus content.
Start preparation 3-4 months before exams with consistent daily practice. Focus on understanding statistical concepts and real-world applications rather than just memorizing formulas. Practice past papers extensively - aim for at least 10 complete exam sets. Master your calculator's statistical and graphing functions as both papers allow calculators. Focus extra time on statistics and probability as they comprise a large portion of the exam content. Join study groups, seek help from teachers early, and maintain regular revision schedules rather than cramming.
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Yes, the IB Math AI SL Syllabus is periodically updated by the IB organization to reflect modern applications of mathematics. Students should always review the latest IB Math AI SL Syllabus to stay aligned with current topics and assessment requirements. Following the updated IB Math AI SL Syllabus helps learners focus on the right material, practice relevant problems, and prepare effectively without wasting time on outdated or unnecessary content.
The IB Math AI SL Syllabus is officially published by the International Baccalaureate (IB) and can be accessed through their website. Many schools also provide students with the IB Math AI SL Syllabus to ensure they understand the required topics, assessments, and exam structure. To prepare effectively, it’s important to study the IB Math AI SL Syllabus carefully, as it outlines all the key learning objectives and skills needed for success.