Unit 1 - Equations, Graphs, & Functions
Objectives
I. Language and operations with algebra
1. Use the order of operations to simplify expressions.
2. Evaluate algebraic expressions.
3. Translate verbal statements into algebra.
II. Equations in one variable and problem-solving
4. Solve a linear equation in one variable.
5. Solve a literal equation or formula for a particular variable.
6. Solve applications: mark up/down, geometry, interest calculations, number
relationships
III. Graphs and Functions
7. Graph equations in two variables by plotting points.
8. Graph linear equations by finding the intercepts.
9. Use function notation.
10. Identify the domain, range, and function values from a graph.
IV. Lines and Linear Functions
11. Calculate the slope of a line through two points.
12. Graph lines using the slope and y-intercept.
13. De termine if two linear equations represent parallel or perpendicular lines.
14. Write equations for lines that
(a) pass through two given points.
(b) have a specified slope through a given point.
(c) are parallel or perpendicular to a given line through a specific point.
(d) are horizontal or vertical through a given point.
15. Solve applications involving linear relationships.
Unit 2 - Equations, Inequalities and Linear Systems
Objectives
I. Equations
1. Solve equations graphically by the intersect method or by the x- intercept
method .
2. Solve absolute value equations in one variable.
II. Inequalities in 1 Variable
3. Solve inequalities and compound inequalities in one
variable.
4. Graph the solution on a number line.
5. Write solutions in interval notation.
III. Systems of Linear Equations
6. Solve systems of linear equations by graphing, substitution, or elimination.
7. Identify the solution to a dependent or inconsistent linear system.
8. Use systems of linear equations to solve applications.
IV. Inequalities in 2 Variables
9. Graph inequalities in 2 variables on the Cartesian plane.
10. Graph systems of inequalities in 2 variables on the Cartesian plane.
Unit 3 - Exponents, Polynomial operations, and Factoring
Objectives
I. Exponents & scientific Notation
1. Use the properties of exponents to simplify expressions.
2. Write large/small numbers in scientific notation.
3. Expand scientific notation to write large/small numbers.
II. Polynomial Operations
4. Be able to use function notation with polynomials.
5. Add or subtract polynomials by combining like terms .
6. Perform multiplication of polynomials using the distributive property and
special product
patterns.
7. Factor polynomials completely.
III. Applications of Factoring
8. Zero-Factor Property
(a) Solve polynomial equations by applying the zero-factor property.
(b) Form polynomial equations by identifying the zeros from the graph and
applying the
zero-factor property in reverse.
9. Rational Expressions (fractions)
(a) Express the domain of a rational expression in inequality or interval
notation.
(b) Simplify rational expressions dividing out common factors .
(c) Multiply or divide rational expressions by defining the operation, factoring
and simpli-
fying.
Unit 4 - Rational Expressions & Equations
Objectives
I. Addition, Subtraction and Complex Fractions
1. Perform addition or subtraction with like or unlike denominators
2. Simplify complex rational expressions
II. Polynomial Division
3. Divide a polynomial by a monomial
4. Use long division to divide a polynomial by a binomial (or higher degree
polynomial)
5. Use synthetic division to divide a polynomial by a binomial of the form (x -
c)
6. Use the remainder theorem to determine P(c) for a given c
III. Solving Rational Equations
7. Solve rational equations by clearing denominators.
8. Identify extraneous solutions.
IV. Applications
9. Solve work/rate applications.
10. Write variation equations for direct, inverse, and joint variation
situations.
11. Determine the constant of variation.
12. Solve variation applications.
Unit 5 - Rational Exponents, Radicals, Complex Numbers and
Equation Solving
Objectives
I. Rational Exponents and Radicals
1. Simplify expressions with rational exponents.
2. Convert between radical and rational exponent form.
3. Use the product and quotient properties to simplify radicals.
II. Radicals | Operations and Equations
4. Add/subtract radical expressions.
5. Multiply radical expressions involving more than one term.
6. Rationalize expressions with radical denominators.
7. Solving Radical equations ( square or cube roots .
8. Graph radical function, identify domain, & evaluate.
9. Find the exact (and approximate) distance between two points in the Cartesian
plane.
III. Complex Numbers & Quadratic Equations
10. Rewrite even roots of negative values as complex numbers.
11. Perform operations (+, - , ×, ÷) on complex numbers.
12. Solve quadratic equations by taking square roots, completing the square, and
by the Quadratic
formula.
13. Analyze the nature of quadratic solutions by examining the discriminant of
the quadratic
formula.
14. Solve applications modeled by quadratics. [Pythagorean Theorem models in
particular]
