Mastering Quadratics: A Comprehensive Course
Course Summary:
This course provides an in-depth exploration of quadratic functions and equations, covering everything from their fundamental properties to advanced applications. Designed for students who want to build a solid foundation in algebra and understand how quadratics apply to real-world problems, this course progresses through five structured units. Each unit includes engaging activities, practical problem-solving, and assessments to reinforce learning. By the end of the course, students will confidently analyze, graph, solve, and apply quadratic functions in various contexts.
Course Units:
Introduction to Quadratic Functions
- Understand the definition, characteristics, and real-world relevance of quadratic functions. Explore parabolas and their key features like the vertex and axis of symmetry.
- Master graphing quadratics, including analyzing transformations, vertex form, and the relationship between roots and graphs. Solve practical problems using quadratic graphs.
- Learn various methods to solve quadratics: factoring, completing the square, and the quadratic formula. Analyze the discriminant and explore different root types.
- Apply quadratic concepts to real-world scenarios, such as projectile motion, profit optimization, and area problems. Use data modeling to derive quadratic equations.
Advanced Concepts in Quadratics
- Explore converting forms of quadratic equations, solving systems involving quadratics, quadratic inequalities, and equations with complex roots. Capstone projects integrate and showcase learning.
Key Features:
- Interactive problems and quizzes for practice.
- Real-world applications to connect quadratics with practical use.
- A final capstone project to consolidate learning and demonstrate mastery.
Enroll now to unlock the power of quadratics and gain the skills to tackle advanced algebra with confidence!
The Exponents course delves into the essential rules, properties, and applications of exponents, building a solid foundation for understanding exponential functions and their relevance in various fields. Through engaging lessons and real-world examples, students will master exponent concepts and develop skills to apply them effectively.
Units:
Laws of Exponents
Learn and apply the fundamental rules of exponents to simplify and solve mathematical expressions.Scientific Notation and Applications
Represent and work with very large and small numbers efficiently using scientific notation, with applications in real-world scenarios.Exponential Growth and Decay
Explore the behavior and applications of exponential growth and decay in areas such as population dynamics and financial modeling.Rational Exponents and Roots
Understand the connection between fractional exponents and roots, and simplify expressions involving rational exponents.Exponential Equations and Logarithms
Solve exponential equations and gain an introduction to logarithms as the inverse of exponents, with practical applications in technology and science.
This course equips students with the knowledge and tools to handle exponent-related problems and prepares them for advanced topics in mathematics and science.
Foundations of Math 12 Topics include:
- Statistics
- Logical Reasoning
- Probability
- Relations and Functions
- Sinusoidal Math
- Interest: simple and compound
- Set Theory
Content:
- Exploring Data
- Modeling Distributions of Data
- Describing Relationships
- Designing Studies
- Probability
- Random Variables
- Sampling Distributions
- Estimating With Confidence
- Testing a Claim
- Comparing Two Populations or Groups
- Inference for Distributions of Categorical Data
- More about Regression
Pre-cal 12 topics include:
- Function transformations
- Radical functions
- Exponential functions
- Functions and Inverses
- Logarithmic Functions
- Trigonometry and the Unit Circle
- Trigonometric Ratios and Special Angles
- Trigonometric Functions and graphs
- Polynomial Functions
- Rational Functions
- Function operations
- Function toolkit
- Limits
Options:
- Trigonometric Identities
- Permutations, combinations, and the binomial theorem
- Explorations:
- Elipses
- de Moivre Theorems
- Fast Fourier Transforms
- The Lagrangian
Content:
- Sequences and series
- Trigonometry
- Quadratics
- Quadratic equations
- Radical expressions and equations
- Rational expressions and equations
- Absolute value and reciprocal functions
- Systems of equations (linear and quadratic)
- Linear and quadratic inequalities
This course provides a comprehensive introduction to statistics, guiding students from foundational concepts to advanced applications. Through hands-on activities, real-world examples, and data analysis projects, students will develop the skills needed to collect, organize, interpret, and apply statistical data. The course fosters critical thinking and prepares students to make informed decisions based on data.
Course Topics:
- Types of data, levels of measurement, populations, samples, and variables.
Data Collection and Organization
- Methods of data collection, sampling techniques, frequency tables, and data visualization.
- Measures of central tendency and dispersion, shapes of distributions, and summary statistics.
Probability and Inferential Statistics
- Probability rules, sampling distributions, confidence intervals, and hypothesis testing.
- Correlation, regression, statistical significance, real-world applications, and ethical considerations.
This course equips students with essential statistical tools and techniques, empowering them to analyze data effectively and apply their knowledge in diverse fields such as business, healthcare, and environmental studies.