ALGEBRA II

Course Overview
This course is built on the mathematical topics and problem-solving techniques of Algebra I.
After some review of the standard topics of Algebra I, this course will take students deeper into
solving 1st and 2nd degree equations, solving quadratic equations by factoring, completing the
square, and the quadratic formula. We will also study irrational and complex numbers; and
direct, inverse, joint variation, and combined variation. Solving systems of equations by the
methods of substitution, linear combinations, and matrices (Cramer’s Rule) is an important part
of Algebra II. Analytic Geometry starts the study of conic sections (circles, ellipses, hyperbolas,
and parabolas) and ties algebra together with geometry. Other topics deal with exponential
growth (you would like to have your savings account grow exponentially) and with logarithmic
functions, which have a big name but are really just exponents disguised. Sequences and series,
which are fundamental to the understanding of the concept of a limit and can also help you find
shortcuts to counting things that are hard or too time-consuming to count. Trigonometry
(triangle measurement) using sine, cosine, etc. is also woven into the lessons. Also included in
the text are statistics, probability, and using matrices (arrays of numbers)

Units of Instruction
 Foundations for Functions
 Linear Functions
– Linear Systems
– Matrices
– Quadratic Functions
– Polynomial Functions
– Exponential & Logarithmic Functions
– Rational and Radical Functions
 Properties and Attributes of Functions
 Conic Sections
– Probability & Statistics
 Sequences and Series
– Trigonometric Functions

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ALGEBRA I

Key points usually covered in an Algebra 1 syllabus:

  • Number Systems:Understanding different types of real numbers (integers, rational, irrational) and their operations (addition, subtraction, multiplication, division).
  • Algebraic Expressions:Writing, simplifying, and evaluating expressions with variables, including order of operations.
  • Linear Equations:Solving one-step, two-step, and multi-step linear equations, including equations with variables on both sides.
  • Graphing Linear Equations:Plotting points and graphing linear equations using slope-intercept form (y = mx + b)
  • Inequalities:Solving and graphing linear inequalities, including compound inequalities
  • Functions:Concept of a function, function notation, finding domain and range, and analyzing graphs of functions
  • Systems of Linear Equations:Solving systems of equations using substitution, elimination, and graphical methods
  • Polynomials:Adding, subtracting, multiplying polynomials, and understanding the concept of degree
  • Factoring:Factoring polynomials using different techniques (greatest common factor, difference of squares, trinomial factoring)
  • Exponents:Properties of exponents, solving exponential equations
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