This is the fourth year of mathematics for students in the ECHA program or for students who are pursuing college. Units include: Equations and Inequalities, Functions and Graphs, Polynomial and Rational Functions, Exponential and Logarithmic Functions, and Trigonometry. (A scientific calculator is required).
Quarter 1
Sep - Nov
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.
Quarter 2
Nov - Jan
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.
Quarter 3
Jan - Apr
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.
Quarter 4
Apr - Jun
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