IB Mathematics Applications and Interpretations SL Study Guide

General Information

• Available at www.ib-academy.nl
• Author: Alex Barancova
• Version: MathAISL.2.1.210726
• Published under Creative Commons BY-NC-ND 4.0 License
• Feedback is encouraged to improve the guide.
• Material is collaborative, involving students and teachers.

Study Guide Approach

• Compiled by teachers for easy revision.
• Step-by-step approach to learning.
• Includes TI-Nspire instructions transferable to other GDC models.
• Encourages studying with partners for better retention.

Key Topics Covered

Prior Learning

1. Approximation

   • Rounding rules based on digit value.
   • Rounding for decimal places and significant figures.

2. Standard Form

   • Also known as scientific notation.
   • Express numbers as a x 10^k where 1 <= a < 10.

3. Sets

   • Basic set notation and operations (intersection, union).
   • Number sets (N, Z, Q, R) and Venn diagrams.

4. Algebra and Equations

   • Solving equations and inequalities.
   • Absolute values and their interpretations.
   • Ratios and percentages.

5. Geometry and Trigonometry

   • Calculating lengths, areas, and volumes of geometric shapes.

Number and Algebra

1. Exponents and Logarithms

   • Laws of exponents and logarithms.
   • Solving equations with logarithms.

2. Sequences and Series

   • Arithmetic and geometric sequences.
   • Sigma notation for summation.

3. Finance

   • Concepts of simple and compound interest.
   • Annuities and amortization.

4. Estimation and Error

   • Calculating errors and percentage errors.

5. Simultaneous Equations

   • Solving systems of equations using elimination and substitution.

Functions

1. Basic Concepts

   • Domain and range of functions.
   • Inverse functions and graph sketching.

2. Linear Models

   • Slope, y-intercept, and finding equations of lines.
   • Intersection and parallel/perpendicular lines.

3. Quadratic Models

   • Parabolas, vertex, and axis of symmetry.
   • Solving quadratic equations by factorization.

4. Polynomials

   • Polynomial functions and solving polynomial equations.

5. Exponential Models

   • Solving exponential functions and understanding asymptotes.

6. Sinusoidal Models

   • Understanding sine and cosine functions, their transformations.

Geometry and Trigonometry

1. Lengths, Areas, and Volumes

   • Calculating surface area and volume for various shapes.

2. Right-angled Triangles

   • Pythagorean theorem and trigonometric ratios.

3. Non-right-angled Triangles

   • Sine and cosine rules.

4. Circles

   • Formulas for arc length and area of a sector.

5. Voronoi Diagrams

   • Concepts of sites, cells, edges, and vertices.

Calculus

1. Differentiation

   • Differentiating polynomials.
   • Tangents, normals, and turning points.

2. Integration

   • Indefinite and definite integrals.
   • Trapezoidal rule for approximating areas.

Probability

1. Single Events

   • Venn diagrams and probability basics.

2. Multiple Events

   • Tree diagrams for successive events.

3. Probability Distributions

   • Discrete random variables and binomial distribution.
   • Normal distribution and its applications.

Statistics

1. Basic Statistical Concepts

   • Population, sample, and types of data.

2. Descriptive Statistics

   • Measures of central tendency and dispersion.
   • Quartiles and box plots.

3. Bivariate Statistics

   • Correlation and regression analysis.

4. Chi-squared Test

   • Testing independence and goodness of fit.

5. T-test

   • Comparing means using one-tailed and two-tailed tests.

This guide provides a comprehensive overview of topics critical to IB Mathematics Applications and Interpretations SL, offering theoretical explanations and practical problem-solving strategies.