Algebra B Syllabus

Algebra B is an advanced course for students who have completed Algebra A (or Algebra 1) and are ready to expand their algebraic skills. Aligned with Common Core Standards for Algebra 2, this course covers conic sections, roots of quadratics and higher-order polynomials, a range of functions, including polynomial, exponential, and logarithmic, and sequences and series. The course incorporates interactive problem-solving, logic puzzles, and competition-style challenges to build confidence and mastery in advanced algebra.

Required Textbook: Art of Problem Solving: Intermediate Algebra

Required for: Pre-Calculus

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

• Elementary functions: polynomials, exponents & logarithms, quadratics and conics, trigonometric
• Graphing and manipulations of functions: polynomial division, polynomial roots, factoring multivariable polynomials, piecewise functions
• Number theory: complex numbers, sequences & series, binomial theorem
• Problem-solving skills, logic puzzles, algebraic and geometric thinking, competition-style problems

Upon completing the course, students will be able to:

• Expression and Equation Mastery: Write, manipulate, and solve expressions and equations in equivalent forms, including polynomial arithmetic.
• Polynomial and Function Analysis: Understand zeros, factors, and identities of polynomials; define, evaluate, and compare functions.
• Exponents, Logarithms, and Systems: Solve equations involving exponents and logarithms, and tackle both linear and nonlinear systems.
• Graphing and Real-World Applications: Represent equations and inequalities graphically and solve volume problems for cylinders, cones, and spheres.

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

• Algebra Basics: Completed Algebra 1 or equivalent, with skills in solving linear equations and systems.
• Arithmetic Proficiency: Confident with positive/negative numbers, fractions, decimals, and large-number calculations.
• Algebraic Operations: Skilled in working with variables, factoring quadratics, and manipulating exponents and radicals.
• Graphing Skills: Able to plot and interpret points on a Cartesian plane.

• Functions and Complex Numbers (8 weeks): Explore function basics, inverses, and compositions, then dive into complex numbers, including arithmetic, graphing, and applications in the complex plane.
• Quadratics and Conics (8 weeks): Review quadratics with factoring, the quadratic formula, and inequalities, and study conic sections like parabolas, ellipses, and hyperbolas, including max/min problems.
• Polynomials, Sequences, and Series (8 weeks): Learn polynomial operations, synthetic division, and roots; cover sequences, series, sigma notation, and the Binomial Theorem.
• Exponentials, Logarithms, and Advanced Functions (9 weeks): Work with exponential and logarithmic functions, identities, natural logs, and rational functions, and introduce piecewise, absolute value, floor, and ceiling functions.
• Introduction to Trigonometry (5 weeks): Study right triangles, trig ratios, the unit circle, radians, and graphing basic trigonometric functions, leading into inverse trig functions.