Algebra A Syllabus

Algebra A is an exciting, engaging course designed for students who have completed Pre-Algebra or 7th grade integrated math, and are ready to tackle more advanced algebraic concepts. Aligned with the Common Core Standards for Algebra 1, this course covers solving systems of equations, graphing linear and quadratic equations and inequalities, identifying special factorizations, and exploring irrational numbers. Through engaging problem-solving exercises, logic puzzles, and friendly competition-style challenges, students will deepen their understanding and enjoy the thrill of discovery in math. Perfect for young learners looking to build a strong algebra foundation and stay inspired along the way!

Required Textbook: Art of Problem Solving: Introduction to Algebra

Required for: Algebra B and Geometry

Concepts, skills, and learning tools students see in this course include, but are not limited to:

• Algebraic Foundations and Variable Isolation: Develop fluency with formal algebraic rules, focusing on techniques for isolating variables.
• Functions and Equation Analysis: Explore linear, quadratic, polynomial, and exponential functions, analyzing linear and quadratic equations through factoring, graphing, and various equation forms.
• Introduction to Sequences and Series: Gain a foundational understanding of sequences and series and their applications.
• Problem-solving skills, logic puzzles, algebraic and geometric thinking, competition-style problems

Upon completing the course, students will be able to:

• Manipulate Expressions and Equations: Rewrite rational expressions, solve rational and radical equations (identifying extraneous solutions), and rearrange formulas to highlight specific quantities.
• Solve and Graph Equations: Solve systems of linear equations, translate word problems into equations/inequalities, and graph linear and quadratic functions.
• Analyze Functions: Interpret graphs of linear and quadratic functions and factor quadratic expressions to identify zeros.
• Apply Constraints and Solutions: Represent and interpret constraints in equations, inequalities, and systems to determine viable solutions.

Students registering for this course should be comfortable with the following Math:‍

• Strong Arithmetic Skills: Confident with positive and negative numbers, exponents, radicals, and arithmetic up to six-digit numbers, including converting between fractions, decimals, and percentages.
• Basic Algebra Foundations: Comfortable with arithmetic operations involving variables.
• Graphing Proficiency: Able to draw and graph points on a Cartesian plane.
• Pre-Algebra or Equivalent

• Foundations of Algebra (8 weeks): Review advanced operations, exponents, radicals, and linear equations. Study fractions, ratios, percents, and proportions, and learn how to graph linear equations and slopes.
• Systems of Equations and Inequalities (7 weeks): Solve systems using substitution and elimination, graph inequalities, and explore optimization using graphs. This section introduces inequalities and explores various methods for comparing lines.
• Quadratic Functions and Factoring (8 weeks): Explore quadratics, including factoring, graphing, and solving quadratic equations. Cover special cases like completing the square and applying the quadratic formula.
• Function Analysis and Transformations (9 weeks): Examine functions in-depth, including composition, transformations, and inverse functions. This section also introduces exponential functions, transformations, and higher-order polynomials.
• Advanced Topics and Applications (6 weeks): Learn about sequences, series, and circle equations. Conclude with applications of functions and transformations, including polynomial functions and exponential transformations.