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Algebra II

Algebra II

Course Features

Course Duration: Full Year
Category: , ,
Prerequisite: Algebra I
Assessment: Lesson Practice, Unit Exams, Mid-Term Exam, Final Exam
Language: English

Course Details

Course Overview

Acellus Algebra II course builds on foundational algebraic skills, deepening students’ understanding of mathematical structures and their real-world applications. Students will explore advanced topics such as quadratic, polynomial, exponential, logarithmic, rational, and trigonometric functions, as well as conic sections, sequences, probability, statistics, and matrices. Through a combination of theoretical lessons, problem-solving activities, and modeling exercises, learners will develop proficiency in manipulating complex expressions, solving equations, analyzing functions, and interpreting data. The course emphasizes critical thinking, precision in calculations, and the ability to translate mathematical concepts into practical scenarios, preparing students for higher-level mathematics and STEM-related fields.

By the end of the course, students will have mastered a broad range of algebraic techniques, including factoring, solving systems of equations, working with complex numbers, and applying trigonometric identities. They will also gain skills in statistical analysis, probability, and matrix operations, enabling them to model and solve real-world problems. This course fosters a strong foundation for precalculus and calculus while cultivating an appreciation for the elegance and utility of mathematics in describing patterns and relationships in the world.

Sample Lesson - Algebraic Patterns

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This course was developed by the International Academy of Science. Learn More

Scope and Sequence

Unit 1 – Algebraic Expressions Students will explore the properties of real numbers, algebraic patterns, and sets of numbers, learning to evaluate and simplify expressions. They will solve linear equations, literal equations, and inequalities, including absolute value equations and inequalities, and represent solutions using interval notation and graphs. Through real-world modeling, students will apply these skills to practical scenarios, developing a strong foundation in algebraic manipulation. Unit 2 – Functions This unit introduces the concept of functions, focusing on linear and absolute value functions. Students will learn to represent functions using slope-intercept and point-slope forms, analyze direct variation, and calculate average rates of change. They will explore transformations, piece-wise functions, and inequalities in two variables, applying these concepts to linear models and real-world problems, enhancing their understanding of functional relationships. Unit 3 – Linear Systems Students will solve systems of linear equations using graphical, substitution, and elimination methods, addressing inconsistent and dependent systems. They will explore systems of inequalities, linear programming, and viable solutions, as well as systems in three variables using matrices. This unit equips students with tools to analyze multiple constraints and optimize solutions in practical contexts. Unit 4 – Quadratic Functions This unit covers quadratic functions in vertex and standard forms, including factoring techniques like greatest common factor, difference of squares, and perfect square trinomials. Students will solve quadratic equations using square roots, completing the square, and the quadratic formula, and work with complex numbers and inequalities. Through quadratic regression and real-world modeling, they will apply these concepts to parabolic phenomena. Unit 5 – Polynomials Students will study polynomial functions, performing operations like addition, subtraction, multiplication, and division using synthetic division. They will explore factoring techniques, the rational root theorem, Descartes’ rule of signs, and the fundamental theorem of algebra to solve polynomial equations. Graphing polynomials, binomial theorem applications, and polynomial regression will enable students to model complex relationships. Unit 6 – Radical Functions This unit focuses on radical functions, including properties of exponents and rational exponents. Students will solve radical equations, work with function composition, and find inverse functions using the horizontal line test. They will graph radical functions and apply these concepts to real-world modeling, developing skills in manipulating and analyzing non-linear relationships. Unit 7 – Exponential and Logarithmic Functions Students will explore exponential and logarithmic functions, learning to solve related equations and apply logarithmic identities. They will use the change of base formula, condense and expand logarithms, and model real-world scenarios like compound interest using future value and PERT formulas. This unit emphasizes the connection between exponential growth/decay and logarithmic scales. Unit 8 – Rational Functions This unit covers rational functions, including inverse and combined variation, reciprocal functions, and graphs with slant asymptotes. Students will perform operations on rational expressions, solve rational equations and inequalities, and analyze domain and end behavior. Through real-world modeling, they will apply rational functions to problems involving rates and proportions. Unit 9 – Sequences and Series Students will study arithmetic and geometric sequences and series, distinguishing between explicit and recursive definitions. They will calculate sums of finite and infinite geometric series and explore number theory concepts. Applications of geometric series will connect these ideas to financial and growth models, enhancing students’ understanding of patterned sequences. Unit 10 – Conic Sections This unit introduces conic sections, including parabolas, circles, ellipses, and hyperbolas. Students will learn to write and analyze equations for each conic, solve systems of conic equations, and work with general second-degree equations. This unit provides a geometric perspective on algebraic relationships, applicable to fields like engineering and astronomy. Unit 11 – Probability and Statistics Students will explore counting principles, permutations, combinations, and probability for independent and mutually exclusive events. They will analyze data using standard deviation, normal distributions, z-scores, and binomial distributions, and study sampling and margin of error. This unit equips students to interpret statistical models and make data-driven decisions. Unit 12 – Matrices This unit covers matrix operations, including addition, subtraction, scalar multiplication, and matrix multiplication. Students will calculate determinants, find inverses, and use matrices to solve systems of equations. They will also apply matrices to geometric transformations like rotations and reflections, connecting algebra to spatial reasoning. Unit 13 – Periodic Functions Students will study periodic functions, focusing on trigonometric functions like sine, cosine, and tangent. They will learn radian measure, arc length, and sector calculations, and explore transformations of trigonometric graphs. Modeling periodic phenomena will help students apply these concepts to real-world scenarios like waves and cycles. Unit 14 – Trigonometric Identities This unit introduces trigonometric identities, including the Pythagorean identity, and techniques for verifying identities. Students will solve trigonometric equations and work with inverse trigonometric functions. The unit emphasizes algebraic manipulation of trigonometric expressions, preparing students for advanced applications in calculus and physics.
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