| Concept | Detail |
|---|---|
| Number Sense and Operations | Strengthen understanding of numbers, number systems, place value, basic operations, fractions, decimals, and percentages. |
| Algebraic Expressions and Equations | Introduction to variables, expressions, simplifying algebraic expressions, solving linear equations and inequalities. |
| Functions | Explore various functions including quadratic, polynomial, rational functions. Study domain, range, function notation, graphing, and solving problems involving functions. |
| Geometry | Study geometric concepts such as points, lines, angles, triangles, quadrilaterals, polygons, circles, transformations (translations, rotations, reflections), congruence, similarity, and geometric proofs. |
| Data Analysis and Statistics | Learn data collection, organization, analysis using charts, tables, graphs. Study measures of central tendency, variability, and basic probability. |
| Ratios, Proportions, and Percents | Work with ratios, proportions, rates, and percents in various problem-solving scenarios. |
| Measurement | Explore measurement units, conversions, and apply them to perimeter, area, volume, and basic geometric measurements. |
| Mathematical Reasoning and Problem Solving | Develop critical thinking, logical reasoning, and problem-solving skills. Apply math to real-world situations. |
| Linear Equations and Systems | Study linear equations with multiple variables, solve them, explore systems of linear equations, inequalities, solving methods. |
| Probability and Statistics | Deepen understanding of probability, conditional probability, independent events, compound probability, data analysis, and statistics. |
| Right Triangle Trigonometry | Explore trigonometric ratios (sine, cosine, tangent), applications to right triangles, angles of elevation and depression. |
| Complex Numbers | Introduction to complex numbers, including the imaginary unit (i) and operations with complex numbers. |
| Sequences and Series | Explore arithmetic and geometric sequences, sum of terms, and convergence of infinite series. |
| Matrices and Matrix Operations | Introduction to matrices, operations, inverses, solving systems of linear equations using matrices. |
| Vectors | Introduction to vectors, operations, magnitude, direction, and applications in physics and geometry. |
| Probability Distributions | Study discrete and continuous probability distributions, probability density functions, and cumulative distribution functions. |
| Concept | Detail |
|---|---|
| Trigonometric Functions and Equations | Further exploration of trigonometric functions, including amplitude, period, phase shift, and solving trigonometric equations. |
| Circular Functions and their Graphs | Study of circular functions (sine, cosine, tangent), their graphs, transformations, and applications. |
| Law of Sines and Law of Cosines | Understanding and applying the Law of Sines and Law of Cosines to solve problems involving triangles. |
| Polar Coordinates and Complex Numbers | Introduction to polar coordinates, conversion between polar and rectangular coordinates, and complex numbers in polar form. |
| Probability and Statistics | Advanced techniques for data analysis and statistical inference, encompassing probability distributions, statistical sampling, hypothesis testing, regression analysis, analysis of variance (ANOVA), and non-linear regression. |
| Matrices and Systems of Equations | Advanced matrix operations, inverse matrices, solving systems of linear equations using matrices, and applications in real-world scenarios. |
| Sequences and Series | Further exploration of arithmetic and geometric sequences, sum of terms, infinite series, and applications. |
| Rational Functions and Partial Fractions | Study of rational functions, including partial fraction decomposition, graphing, and solving rational equations. |
| Conic Sections and Parametric Equations | Advanced study of conic sections, including parametric equations, polar equations, and applications. |
| Limits and Continuity | Introduction to limits, evaluating limits algebraically and graphically, and understanding continuity. |
| Derivatives and Applications | Basic concepts of derivatives, including rates of change, tangent lines, and applications of derivatives. |
| Integration and Applications | Basic concepts of integration, antiderivatives, definite and indefinite integrals, and applications of integration. |
| Advanced Algebra | Extensive study of advanced algebraic concepts, including polynomial and rational functions, exponential and logarithmic functions, matrices and determinants, complex numbers, sequences and series, and conic sections. |
| Trigonometry | In-depth exploration of trigonometric functions and their properties, covering the unit circle, trigonometric identities, inverse trigonometric functions, graphing trigonometric functions, solving trigonometric equations, and applications in triangles and circular motion. |
| Calculus | Comprehensive introduction to calculus, covering limits, continuity, derivatives, applications of derivatives (such as optimization and related rates), definite and indefinite integrals, and applications of integration (such as area, volume, and motion problems). |
| Geometry and Spatial Reasoning | Extends the study of geometric concepts, focusing on advanced topics such as proofs, transformations, advanced properties of triangles and quadrilaterals, circles, three-dimensional geometry, and vectors. |
| Mathematical Modeling | Engaging in advanced mathematical modeling, including the formulation of complex mathematical models, data analysis using statistical techniques, making predictions, and effectively communicating findings. |
| Concept | Detail |
|---|---|
| Introduction to Mathematical Modeling | Fundamentals of mathematical modeling, including problem formulation, data collection, mathematical representation, and model validation. |
| Linear Models | Using linear equations and functions to represent relationships, regression analysis, and prediction based on linear models. |
| Exponential and Logarithmic Models | Applications of exponential and logarithmic functions in modeling growth, decay, and related problems. |
| Systems of Equations and Inequalities | Modeling and solving systems of linear equations and inequalities, including applications in optimization and equilibrium analysis. |
| Discrete Models | Working with discrete structures like graphs, networks, and sequences for modeling and optimization. |
| Nonlinear Models | Modeling complex relationships using nonlinear equations, functions, regression, chaos theory, and dynamical systems. |
| Simulation and Optimization | Designing simulations and using optimization techniques for analyzing complex systems and finding optimal solutions. |
| Model Analysis and Validation | Techniques for analyzing, validating, and refining mathematical models, including sensitivity analysis and model calibration. |
| Advanced Mathematical Modeling | Further exploration of advanced techniques and applications in mathematical modeling, building upon the concepts from Math Modeling A. |
| Nonlinear Dynamics | Study of complex dynamical systems, chaos theory, bifurcation analysis, fractals, and attractors. |
| Optimization Models | Advanced optimization techniques, including linear programming, integer programming, nonlinear optimization, and constrained optimization. |
| Stochastic Models | Modeling randomness and uncertainty using probability theory, stochastic processes, Markov chains, and Monte Carlo simulations. |
| Differential Equations Models | Modeling using ordinary differential equations (ODEs) and partial differential equations (PDEs), including applications in physics, biology, economics, and engineering. |
| Agent-Based Models | Simulation and modeling of systems with individual agents or entities interacting with each other, incorporating behavior and decision-making processes. |
| Network Models | Modeling and analysis of complex systems using network theory, graph theory, social network analysis, and network dynamics. |
| Validation and Verification | Rigorous validation and verification techniques for mathematical models, including sensitivity analysis, parameter estimation, goodness-of-fit measures, and model calibration. |
| Functions and Graphs | Study of various types of functions, including linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions. Graphing functions, transformations, and understanding their properties. |
| Trigonometry | In-depth exploration of trigonometric functions, including the unit circle, trigonometric identities, graphing trigonometric functions, solving trigonometric equations, and applications of trigonometry. |
| Algebraic Expressions and Equations | Manipulating algebraic expressions, solving equations and inequalities, systems of equations, and applications involving algebraic reasoning. |
| Matrices and Vectors | Introduction to matrices, matrix operations, determinants, and vector operations. Applications of matrices and vectors in solving systems of equations and transformations. |
| Conic Sections | Study of conic sections, including circles, ellipses, hyperbolas, and parabolas. Analyzing their properties, graphing, and solving problems involving conic sections. |
| Sequences and Series | Investigation of arithmetic and geometric sequences and series, including sum formulas, convergence, and divergence. Applications involving sequences and series. |
| Limits and Continuity | Introduction to limits and continuity of functions. Evaluating limits algebraically, graphically, and using calculus techniques. |
| Rational Functions | Study of rational functions, including graphing, identifying asymptotes, and solving equations involving rational expressions. |
| Complex Numbers | Introduction to complex numbers, including complex arithmetic, operations, and applications involving complex numbers. |
| Trigonometric Identities | Exploring trigonometric identities, verifying trigonometric equations, and simplifying expressions using trigonometric identities. |
| Concept | Detail |
|---|---|
| Introduction to Mathematical Modeling | Fundamentals of mathematical modeling, including problem formulation, data collection, mathematical representation, and model validation. |
| Linear Models | Using linear equations and functions to represent relationships, regression analysis, and prediction based on linear models. |
| Exponential and Logarithmic Models | Applications of exponential and logarithmic functions in modeling growth, decay, and related problems. |
| Systems of Equations and Inequalities | Modeling and solving systems of linear equations and inequalities, including applications in optimization and equilibrium analysis. |
| Discrete Models | Working with discrete structures like graphs, networks, and sequences for modeling and optimization. |
| Nonlinear Models | Modeling complex relationships using nonlinear equations, functions, regression, chaos theory, and dynamical systems. |
| Simulation and Optimization | Designing simulations and using optimization techniques for analyzing complex systems and finding optimal solutions. |
| Model Analysis and Validation | Techniques for analyzing, validating, and refining mathematical models, including sensitivity analysis and model calibration. |
| Advanced Mathematical Modeling | Further exploration of advanced techniques and applications in mathematical modeling, building upon the concepts from Math Modeling A. |
| Nonlinear Dynamics | Study of complex dynamical systems, chaos theory, bifurcation analysis, fractals, and attractors. |
| Optimization Models | Advanced optimization techniques, including linear programming, integer programming, nonlinear optimization, and constrained optimization. |
| Stochastic Models | Modeling randomness and uncertainty using probability theory, stochastic processes, Markov chains, and Monte Carlo simulations. |
| Differential Equations Models | Modeling using ordinary differential equations (ODEs) and partial differential equations (PDEs), including applications in physics, biology, economics, and engineering. |
| Agent-Based Models | Simulation and modeling of systems with individual agents or entities interacting with each other, incorporating behavior and decision-making processes. |
| Network Models | Modeling and analysis of complex systems using network theory, graph theory, social network analysis, and network dynamics. |
| Validation and Verification | Rigorous validation and verification techniques for mathematical models, including sensitivity analysis, parameter estimation, goodness-of-fit measures, and model calibration. |
| Functions and Graphs | Study of various types of functions, including linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions. Graphing functions, transformations, and understanding their properties. |
| Trigonometry | In-depth exploration of trigonometric functions, including the unit circle, trigonometric identities, graphing trigonometric functions, solving trigonometric equations, and applications of trigonometry. |
| Algebraic Expressions and Equations | Manipulating algebraic expressions, solving equations and inequalities, systems of equations, and applications involving algebraic reasoning. |
| Matrices and Vectors | Introduction to matrices, matrix operations, determinants, and vector operations. Applications of matrices and vectors in solving systems of equations and transformations. |
| Conic Sections | Study of conic sections, including circles, ellipses, hyperbolas, and parabolas. Analyzing their properties, graphing, and solving problems involving conic sections. |
| Sequences and Series | Investigation of arithmetic and geometric sequences and series, including sum formulas, convergence, and divergence. Applications involving sequences and series. |
| Limits and Continuity | Introduction to limits and continuity of functions. Evaluating limits algebraically, graphically, and using calculus techniques. |
| Rational Functions | Study of rational functions, including graphing, identifying asymptotes, and solving equations involving rational expressions. |
| Complex Numbers | Introduction to complex numbers, including complex arithmetic, operations, and applications involving complex numbers. |
| Trigonometric Identities | Exploring trigonometric identities, verifying trigonometric equations, and simplifying expressions using trigonometric identities. |