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IB® Diploma Programme · Group 5

Applications & Interpretation
SL & HL Complete Course Modules

An applied-mathematics IB course. Builds modelling, statistics, and technology-driven problem solving for real-world exam contexts.

📘 5 core topic areas 🎯 SL + HL (full coverage) 🏁 Paper 1 · 2 · 3 ready
SL — all students HL — Higher Level only Practice & Exams
📐 Foundations
00
Prerequisites & Mathematical Toolkit SL
Algebra review, GDC usage, intro to the mathematical exploration (IA), the modelling process
→ Start
🔢 Number & Algebra
01
Numbers & Scientific Notation SL
Scientific notation (a × 10^k), approximation, significant figures, percentage error, estimation
→ Start
02
Sequences, Series & Financial Maths SL
Arithmetic/geometric sequences, sigma notation, amortization and annuities (with GDC)
→ Start
03
Logarithms & Rational Exponents HL
Laws of logarithms, rational exponents, sum of infinite geometric series
→ Start
04
Complex Numbers (Cartesian Form) HL
Complex numbers in Cartesian form, the four operations, solutions of quadratic equations
→ Start
05
Matrices & Applications HL
Matrix operations, determinant, inverse matrix, linear transformations, solving systems
→ Start
📊 Functions
06
Function Concepts & Graphing SL
Domain/range, function notation, functions as a modelling tool
→ Start
07
Modelling with Functions SL
Linear, quadratic, exponential growth/decay, logistic models; fitting and testing a model
→ Start
08
Advanced Modelling HL
Composite and inverse functions in context, cubic and sinusoidal models
→ Start
📏 Geometry & Trigonometry
09
3D Geometry & Volume Problems SL
Volume and surface area problems, real-world geometry contexts
→ Start
10
Trigonometry in Context SL
Sine/cosine rule, contextual applications, angles of elevation/depression
→ Start
11
Voronoi Diagrams SL
Nearest-neighbour interpolation, Voronoi cells, real-world location problems
→ Start
12
Vectors & Applications HL
Force and velocity problems with vectors, vector algebra
→ Start
13
Matrix Transformations in Geometry HL
Transformations with matrices, scaling, rotation, composite transformations
→ Start
📉 Statistics & Probability
14
Descriptive Statistics SL
Measures of central tendency and spread, data visualization
→ Start
15
Correlation & Regression SL
Linear and non-linear regression, correlation coefficient, interpretation
→ Start
16
Probability & Distributions SL
Probability fundamentals, binomial/normal distribution, expected value
→ Start
17
Hypothesis Testing & Chi-Square SL
Chi-square goodness-of-fit and independence tests, writing conclusions in context
→ Start
18
Poisson & Continuous Distributions HL
Poisson distribution, continuous random variables
→ Start
19
Markov Chains HL
Transition matrices, steady state, long-run behaviour
→ Start
∫ Calculus
20
Introduction to Derivatives SL
Rate of change, core differentiation rules, interpreting gradient
→ Start
21
Optimization Problems SL
Maximum/minimum problems, real-world optimization
→ Start
22
Integration & Area Under Curves SL
Definite integrals, area under a curve, numerical integration with GDC
→ Start
23
Differential Equations & Euler's Method HL
Separable differential equations, numerical solutions with Euler's method
→ Start
24
Kinematics & Second Derivatives HL
Motion problems, second-order derivatives, acceleration analysis
→ Start
✍️ Practice & Exams
25
SL Practice Problems
Solved questions in Paper 1 & Paper 2 format, with emphasis on GDC use
→ Start
26
HL Practice Problems
Includes HL-only topics, solved Paper 1 & Paper 2 questions
→ Start
27
Paper 3: Extended Investigations HL
Modelling-based investigative problems, multi-part scenarios
→ Start
28
Full-Length Mock Exams
Timed, IB-format full exams for SL and HL with answer keys
→ Start
29
Internal Assessment (IA) Guide
Mathematical exploration topic selection, data collection, assessment criteria
→ Start
🔁 Analysis & Approaches'a Geç ⊞ Matematik Araçları ☀ Teneffüs ✍ Eğitim Yazıları ? Sık Sorulan Sorular ⊕ Gizlilik Politikası