IB Mathematics: Applications and Interpretation SL
Free IB Mathematics: Applications and Interpretation SL syllabus: clear theory, worked examples and IB exam questions with step-by-step solutions.
Block 1 · Number and algebra
Basic algebra and arithmetic
Basics for IB Applications and Interpretation SL: sets, rounding, standard form, percentage error, powers, logarithms, quadratics and currency.
- Sets, Venn diagrams and number sets
- Approximation, scientific notation and percentage error
- Integer exponents and logarithms
- Equations, inequalities and systems
- Currency exchange
- IB exam questions for topic 1
Arithmetic and geometric sequences
Arithmetic and geometric sequences for IB Applications and Interpretation SL: general term, sums, interest, depreciation, loans and worked IB exercises.
- Sequences, progressions and the nth term
- Sum of the first n terms of an arithmetic progression
- Sum of a geometric progression
- Simple and compound interest, depreciation and growth
- Annuities and amortization
- IB exam questions for topic 2
Block 2 · Geometry and trigonometry
Trigonometry
Trigonometry for IB Applications and Interpretation SL: right triangles, sine and cosine rules, area, elevation and depression, with IB exam questions.
- Prior knowledge: Pythagoras, similarity, arcs and sectors
- Trigonometric ratios in the right-angled triangle
- Solving any triangle: sine and cosine rules
- Area of a triangle
- IB exam questions for topic 3
2D geometry
Plane geometry for IB Applications SL: distance, midpoint, lines, parallel and perpendicular lines, point-to-line distance and Voronoi diagrams.
- Coordinates, distance between two points and midpoint
- Gradient and equations of a line
- Parallel and perpendicular lines
- Distance from a point to a line and perpendicular bisector
- Voronoi diagrams
- IB exam questions for topic 4
Geometry in 3D
3D geometry for IB Applications SL: coordinates, distance, midpoint, and the volumes and areas of prisms, pyramids, cones, cylinders and spheres.
- Coordinates, distance and midpoint in 3D
- Prisms and pyramids: volume, area and angles
- Cylinders, cones and spheres
- IB exam questions for topic 5
Block 3 · Functions and calculus
Functions
Functions for IB Applications and Interpretation SL: domain, range, linear, quadratic, inverse, exponential and circular models, with worked IB questions.
- Functions: domain, range and features of the graph
- Linear functions and linear models
- Quadratic functions and quadratic models
- Inverse function: how to find it and what it means
- Exponential functions and models of growth and decay
- Integer power functions and vertical and horizontal asymptotes
- Circular functions: sine, cosine, amplitude, period and periodic models
- IB exam questions for topic 6
Differential and integral calculus
Derivatives, tangent and normal lines, optimisation, antiderivatives, definite integrals and the trapezoidal rule, with worked IB exam questions.
- Limits and the concept of the derivative
- Tangent and normal lines
- Differentiation rules
- Increasing and decreasing, maxima and minima
- Optimisation: maxima and minima in context problems
- Antiderivatives of powers and indefinite integrals
- Definite integral, area under a curve and the trapezoidal rule
- IB exam questions for topic 7
Block 4 · Statistics and probability
Descriptive statistics
Frequency tables, graphs, measures of centre and spread, and worked IB exam questions for IB Applications and Interpretation SL.
- Data and frequency tables
- Graphical representations
- Measures of central tendency
- Quartiles and box-and-whisker diagrams
- Variance and standard deviation
- IB exam questions for topic 8
Regression and linear correlation
Scatter diagrams, Pearson and Spearman correlation, the regression line and worked IB exam questions for Applications and Interpretation SL.
- Bivariate distributions and scatter diagram
- Linear correlation and Pearson's correlation coefficient
- The regression line: fit, predictions and interpretation
- Spearman's rank correlation coefficient
- IB exam questions for topic 9
Probability
Events, probability, conditional probability, independence and tree diagrams for IB Applications and Interpretation SL, with worked IB exam questions.
- Sample space and events: union, intersection and Venn diagrams
- Probability and its properties: Laplace, complement and union
- Conditional probability and independence of events
- Compound experiments and tree diagrams
- IB exam questions for topic 10
Discrete random variables and the binomial distribution
Discrete random variables, probability distributions, expectation, variance and the binomial distribution for IB Applications SL, with worked exam questions.
- Discrete random variable and probability distribution
- Expected value, variance and standard deviation of a discrete variable
- The binomial distribution: probabilities, mean and variance
- IB exam questions for topic 11
Continuous random variable and normal distribution
Continuous random variables and the normal distribution for IB Applications SL: GDC probabilities, inverse calculations and worked IB exam questions.
- Continuous random variable and density function
- The normal distribution: mean, standard deviation and standardisation
- Normal distribution calculations: probabilities and inverse values
- IB exam questions for topic 12
χ² and t-tests
Hypothesis tests for IB Applications and Interpretation SL: chi-squared tests and the t-test, with worked IB exam questions.
3 sections · 9 worked examples · 44 IB exercisesThis is the syllabus for Mathematics: Applications and Interpretation, Standard Level of the International Baccalaureate (IB) Diploma Programme. Each topic has a short explanation with worked examples and a page with the IB exam questions for that topic, grouped by type and ordered from easiest to hardest, each with a step-by-step solution.
How it is organised
- Short, clear theory, with the key idea at the start and what the exam asks for.
- Worked examples step by step, from easiest to hardest.
- Common mistakes that come up again and again in the papers.
- IB exam questions grouped by type and by level (★ basic, ★★ medium, ★★★ hard), with the solution one click away.
The Applications and Interpretation SL exam
The external assessment has two papers, Paper 1 (short-response questions) and Paper 2 (extended-response questions), and a graphic display calculator (GDC) is allowed in both. That is why this course puts so much emphasis on knowing what to ask the GDC and how to interpret its answer. If you are preparing for the IB online, the academy also offers IB online classes.
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