List of Math Topics Taught in K-12

1. Number Sense and Operations

• Counting and Cardinality

• Addition, Subtraction, Multiplication, Division

• Place Value and Number Representation

• Fractions, Decimals, and Percentages

• Prime Numbers and Factors

• Negative Numbers and Absolute Value

• Ratios and Proportions

• Integers and Rational Numbers

2. Algebra

• Expressions, Equations, and Inequalities

  • Simplifying Expressions

  • Solving Linear Equations and Inequalities

  • Systems of Equations and Inequalities

  • Quadratic Equations and Functions

  • Polynomials and Factoring

  • Exponential and Logarithmic Functions

  • Rational Expressions and Equations

• Functions and Graphs

  • Understanding Functions

  • Linear, Quadratic, Polynomial, Rational, Exponential, and Logarithmic Functions

  • Graphing Functions and Analyzing Graphs

  • Transformations of Functions

  • Piecewise and Step Functions

• Advanced Algebra Topics

  • Complex Numbers

  • Matrices and Determinants

  • Sequences and Series

  • Binomial Theorem

3. Geometry

• Basic Geometric Shapes and Properties

  • Points, Lines, and Angles

  • Parallel and Perpendicular Lines

  • Triangles, Quadrilaterals, and Polygons

  • Circles and Their Properties

• Measurement and Dimension

  • Perimeter, Area, and Volume

  • Surface Area and Volume of Solids

  • Units of Measurement and Conversion

• Transformations and Congruence

  • Reflections, Rotations, Translations, and Dilations

  • Congruent Figures and Proofs

  • Similarity and Scale Factor

• Coordinate Geometry

  • Graphing Points and Lines

  • Distance and Midpoint Formulas

  • Equations of Lines and Conic Sections

4. Trigonometry

• Trigonometric Ratios and Functions

  • Sine, Cosine, Tangent

  • Reciprocal Trigonometric Functions

  • Unit Circle and Radian Measure

  • Graphs of Trigonometric Functions

• Trigonometric Identities and Equations

  • Pythagorean Identity

  • Sum and Difference Formulas

  • Double-Angle and Half-Angle Formulas

  • Solving Trigonometric Equations

• Applications of Trigonometry

  • Right Triangle Trigonometry

  • Law of Sines and Law of Cosines

  • Trigonometric Applications in Real-World Problems

5. Calculus

• Limits and Continuity

  • Understanding Limits

  • Limit Laws and Theorems

  • Continuity of Functions

• Derivatives and Their Applications

  • Definition and Interpretation of Derivatives

  • Rules of Differentiation

  • Applications of Derivatives (e.g., motion, optimization)

  • Related Rates

• Integrals and Their Applications

  • Definite and Indefinite Integrals

  • Fundamental Theorem of Calculus

  • Techniques of Integration

  • Applications of Integrals (e.g., area, volume)

• Series and Sequences

  • Arithmetic and Geometric Sequences

  • Infinite Series and Convergence Tests

  • Power Series and Taylor Series

6. Statistics and Probability

• Descriptive Statistics

  • Measures of Central Tendency (Mean, Median, Mode)

  • Measures of Dispersion (Range, Variance, Standard Deviation)

  • Data Representation (Graphs, Charts)

• Probability

  • Basic Probability Concepts

  • Conditional Probability and Independence

  • Probability Distributions (Binomial, Normal, etc.)

  • Counting Principles (Permutations and Combinations)

• Inferential Statistics

  • Sampling Methods and Data Collection

  • Hypothesis Testing and Confidence Intervals

  • Correlation and Regression Analysis

7. Discrete Mathematics

• Logic and Proof

  • Statements and Logical Connectives

  • Truth Tables and Logical Equivalences

  • Direct and Indirect Proofs

• Combinatorics

  • Counting Techniques

  • Permutations and Combinations

  • Binomial Theorem

• Graph Theory

  • Graphs and Their Properties

  • Paths, Circuits, and Trees

  • Applications of Graph Theory

8. Mathematical Modeling and Applications

• Real-World Problem Solving

• Creating and Interpreting Mathematical Models

• Using Technology in Mathematical Modeling (e.g., graphing calculators, software)

• Applications in Sciences, Engineering, Economics, and Other Fields

These topics encompass a comprehensive range of mathematical concepts and skills that students typically encounter throughout their K-12 education.