Unit or Topic Skills

Chapter P - Prerequisites: Fundamental Concepts of Algebra:

Expressions and Mathematical Models

• I can evaluate an algebraic expression.

Intro to Number Sets

• I can describe the intersection or union of a set of data.

The Set of Real Numbers

• I can describe subsets of real numbers.

• I can evaluate absolute values.

• I can describe properties of real numbers.

• I can identify properties of real numbers and simplify expressions.

Exponent Rules and Scientific Notation

• I can describe the exponent rules and evaluate scientific notation.

Radicals

• I can describe rules for radicals and evaluate terms with radicals.

Polynomials

• I can perform operations with polynomials with one or many variables.

• I can factor a polynomial.

Chapter 1 - Equations and Inequalities:

Graphing

• I can plot points and interpret information given by graphs.

Linear Equations

• I can evaluate linear equations with one variable.

Linear Models and Applications

• I can solve real world problems and formulas for a variable.

Complex Numbers

• I can perform operations with complex numbers.

Quadratic Equations

• I can evaluate a quadratic equation.

• I can determine the roots/zeros of a quadratic equation.

• I can identify the nature of the roots of a quadratic equation by using the discriminant.

Other Types of Equations

• I can evaluate various types of equations.

Linear Inequalities

• I can evaluate a linear inequality and graph it on a number line.

• I can evaluate an absolute value equation and graph it on a number line.

Unit or Topic Skills

Chapter 2 - Functions and Graphs:

Basic Functions and Their Graphs

• I can determine if a relation is a function.

• I can find the domain and range of a function.

• I can describe the key features of a function from its graph.

• I can identify even or odd functions and recognize their symmetries.

• I can evaluate and graph a piecewise function.

Linear Functions and Slope

• I can calculate slope and graph lines from functions.

• I can write the equations of lines when given their slope.

Function Transformations

• I can perform various transformations on a function.

• I can identify a transformation on a function based on changes to the parent function.

Chapter 2:

Composite Functions

• I can find the domain of a function and create composite functions.

Inverse Functions

• I can find the inverse of a function.

• I can determine if two functions are inverses.

Distance and Midpoint Formulas; Circles

• I can find the midpoint between two points.

• I can calculate the distance between two points. 

• I can write the equation of a circle.

• I can graph a circle when given its equation.

Chapter 3 - Polynomials and Rational Functions:

Quadratic Functions

• I can recognize the characteristics of a quadratic function.

• I can find the vertex and intercepts of a quadratic function.

Polynomial Functions and Their Graphs

• I can recognize the characteristics of a polynomial function.

• I can determine the end behaviors of polynomial functions.

• I can find the zeros of a polynomial function.

Unit or Topic Skills

Chapter 3:

Dividing Polynomials and Synthetic Division

• I can use long division to divide polynomials.

• I can use synthetic division to divide polynomials.

Remainder and Factor Theorems

• I can determine if a binomial is a factor of a polynomial.

• I can factor a polynomial completely.

• I can evaluate the zeros of polynomials.

Graphs of Rational Polynomials

• I can identify asymptotes of a rational function.

• I can sketch a graph of a rational function from its zeros and asymptotes.

• I can solve polynomial and rational inequalities.

Modeling Using Variation

• I can solve various types of variation problems.

Chapter 4 - Exponential and Logarithmic Functions:

Exponential Functions

• I evaluate exponential and compounding interest functions.

Logarithmic Functions

• I can evaluate common and natural logarithms.

• I can graph common and natural logarithms.

Chapter 4:

Properties of Logarithms

• I can apply properties of logarithms to expand and condense logarithmic expressions.

• I can use logarithmic properties to evaluate exponential and logarithmic equations.

Exponential Growth/Decay

• I can evaluate exponential growth and decay using natural logarithms.

• I can evaluate logistic growth and decay problems.

Chapter 5 - Trigonometric Functions:

Angles and Radian Measures

• I can use degree and radian measure and convert between them.

• I can draw angles of rotational measure in radians and degrees.

Unit or Topic Skills

Chapter 5:

Linear and Angular Speed

• I can find coterminal angles and find the length of a circular arc.

• I can determine linear and angular speed.

• I can use linear and angular speed to describe motion on a circular path

Right Angle Trigonometry

• I can use right triangles to evaluate trigonometric functions.

• I can find function values for special angles.

• I can recognize and use fundamental and Pythagorean Identities.

• I can evaluate trigonometric functions with a calculator.

• I can solve real world problems using right triangle trigonometry.

Trigonometric Functions of Any Angle and Reference Angles

• I can use the definitions of trigonometric functions of any angle.

• I can use the signs of trigonometric functions to evaluate other trigonometric functions.

• I can find reference angles and use them to evaluate trigonometric functions.

Trigonometric Functions of Real Numbers and Periodic Functions

• I can use the unit circle to define trigonometric functions of real numbers.

• I can recognize the domain and range of sine and cosine functions.

• I can use even and odd trig functions.

• I can define and use periodic properties.

Graphs of Sine and Cosine

• I can define the amplitude, period and phase shift for various sine and cosine functions.

• I can graph various sine and cosine curves given changes to their function.

Chapter 5:

Periodic Behavior

• I can model periodic behavior.

• I can write trigonometric functions based on period behavior.

Graphs of Tangent, Cotangent, Secant and Cosecant

• I can graph various tangent, cotangent, secant and cosecant curves.

Inverse Trigonometric Functions

• I can understand and use inverse trig functions.

• I can evaluate the composition of functions involving inverse trigonometric functions.

Solving Right Triangles

• I can solve a right triangle by finding the missing angles and side lengths.

• I can solve real world problems using trigonometric functions and properties.

Final Exam Review