COURSE TITLE: Algebra II-Trigonometry
COURSE DESCRIPTION: Algebra II-Trigonometry reinforces and extends the skills developed in Algebra I. Concepts developed include linear functions, rational functions, quadratic functions, complex numbers, right triangle trigonometry, circular functions and series and sequences. This is a college preparatory course.
Prerequisite: Geometry and a grade of "B" or above in both semesters of Algebra I.
COURSE REQUIREMENTS/REQUIRED MATERIALS:
A. Text: Algebra 2, Holliday, Cuevas, Marks, Casey, Moore-Harris,
Day, Carter, Hayek. Copyright 2005 by McGraw-Hill, and cover.
B. A 3-ring binder, looseleaf, notebook
C. Pencils, erasers
D. Graphing calculator (TI 83 or TI84), scientific calculator
E. Red Pen.
COURSE OBJECTIVE/STUDENT OUTCOMES:
A. Students will become familiar with solving and graphing
equations and inequalities.
Upon completing this goal the student will be able to
* use the order of operations to evaluate expressions
* use formulas
* determine the sets of numbers to which a number belongs
* use the properties of real numbers to
simplify expressions
* solve equations using the properties of equality
* evaluate expressions using a graphing calculator
* use equations to solve problems
* solve problems by making lists
* solve absolute value equations
* solve an inequality and graph the solution set
* use inequalities to solve problems
* solve compound sentences using and/or
* solve absolute value inequalities and graph the solutions
B. Students will understand the concepts of linear relations and
functions.
Upon completing this goal students will be able to
* graph a relation, state its domain and range, and
determine if the relation is a function
* identify equations that are linear and graph them
* graph linear equations on a graphing calculator
* write linear equations in standard form
* solve a problem by identifying the pattern and using it
to find the missing information
* determine the slopes and intercepts of a line
* use the slopes and intercepts to graph a line
* determine if two lines are parallel, perpendicular,
or neither
* write the slope-intercept and standard form of an
equation given the slope and a point or two points
* write the equation of a line that is parallel or
perpendicular to the graph of a given equation
* draw a scatter plot and find the prediction equation
* solve problems using prediction equation
* graph lines of regression on a graphing calculator
* identify and graph special functions
* draw graphs of inequalities in two variables
* write an inequality to solve problems
C. Students will develop skills in solving and graphing systems
of equations.
Upon completing this goal the student will be able to
* graph and solve systems of equations on a
graphing calculator
* solve a system of equations by graphing
* use substitution and elimination to solve a
system of equations
* find the value of a second order determinant
* solve a systems of equations using Cramer's Rule
* graph and solve a system of inequalities
* solve a system of equations in three variables
D. Students will acquire an understanding of polynomials
Upon completing this goal the student will be able to:
* multiply monomials and powers of monomials
* represent numbers in scientific notation
* divide monomials
* divide expressions written in scientific notation
* solve problems using a diagram
* add, subtract, and multiply polynomials
* factor polynomials
* divide polynomials using factoring, long division,
and synthetic division
* add, subtract, multiply, and divide rational
polynomial expressions
E. Students will become familiar with all the operations of irrational and complex numbers.
Upon completing this goal the student will be able to:
* simplify radicals having various indices
* use a calculator to estimate roots of numbers
* simplify radical expressions using multiplication
and division
* rationalize the denominator of a fraction containing
a radical expression
* add, subtract, multiply and divide radical expressions
* write expressions with rational exponents in simplest
radical form and vice versa
* evaluate expressions in either exponential
or radical form
* simplify expressions containing rational exponents
* solve equations containing radicals
* simplify radicals containing negative radicands
* multiply pure imaginary numbers
* solve quadratic equations that have pure
imaginary solutions
* add, subtract, multiply, and divide complex numbers
F. Students will develop skills in solving quadratic equations.
Upon completing this goal the student will be able to:
* solve quadratic equations by graphing, factoring, and
completing the square
* derive the quadratic formula and use it to
solve equations
* graph and solve quadratic equations on a
graphing calculator
* use the discriminate to determine the nature of the roots
of a quadratic equation
* find the sum and product of the roots of a quadratic
equation without solving it
* find all possible integral roots of a quadratic function
* find a quadratic equation to fit a given condition
G. Students will gain an understanding of sequences and series.
Upon completing this goal the student will be able to:
* distinguish sequences which are arithmetic, geometric,
or neither
* find the nth term of arithmetic, geometric,
and other sequences
* find the sum of n terms of a given sequence
* distinguish between sequences that are convergent
or divergent
H. Students will learn about trigonometric functions.
Upon completing this goal the student will be able to:
* change radian measure to degree measure and vice versa
* identify coterminal angles
* find the least positive angle that is coterminal to a
given angle
* find the values of expressions involving sine and cosine
* find the values of other trig functions
* find the values of expressions involving trig functions
* use a calculator to find the values of trig functions
* use right triangles to find trig values
* solve problems involving right triangles using right
triangle trig
* solve triangles, using the Law of Sines and Cosines
I. Students will become adept at graphing trig equations,
verifying identities, and solving trigonometric equations.
Upon completing this goal the student will be able to:
* graph trig functions
* write equations of trig functions given the graph
* use trig identities to simplify or evaluate expressions
* verify trig identities involving sum and
difference formulas
* find values and verify identities involving sum and
difference formulas
* find values and verify identities using double and half
angle formulas
* solve trig equations
COURSE OUTLINE:
I. Equations and Inequalities
A. Expressions and formulas
B. Solve equations and inequalities
C. Solve absolute value equations and inequalities
D. Use equations and inequalities to solve word problems
II. Linear Relations and Functions
A. Graph relations and functions using the graphing calculator
B. Graph linear equations using slopes and intercepts
C. Write equations of lines
D. Use scatter plots and prediction equations
E. Graph special functions, i.e., greatest integer, absolute value
F. Graph linear inequalities
III. Systems of Equations and Inequalities
A. Graph systems and use the graphing calculator to check
these solutions
B. Solve systems algebraically
C. Solve systems using Cramer's Rule
D. Graph systems of inequalities
E. Linear programming
IV. Polynomials
A. Monomials
B. Polynomials
C. Factoring
D. Long and synthetic division
E. Rational Polynomial Expressions
V. Irrational and Complex Numbers
A. Roots of real numbers
B. Products and Quotients of radicals
C. Computations with radicals
D. Rational exponents
E. Pure imaginary numbers
F. Complex numbers
VI. Quadratic Equations
A. Solve quadratic equations by graphing, factoring,
and completing the square
B. Derive and use the quadratic formula
C. Use the discriminate to tell the nature of roots
D. Find the sum and product of the roots
E. Use quadratic techniques to solve polynomial equations
VII. Sequences and Series
A. Arithmetic sequences
B. Arithmetic series
C. Geometric sequences
D. Geometric series
E. Infinite geometric series
F. Binomial Theorem
VIII. Trigonometric Functions
A. Angles and the unit circle
B. Sine and cosine functions
C. Tangent, cotangent, secant and cosecant functions
D. Inverse trigonometric functions
E. Find values of trig functions
F. Solve right triangles
G. Applications of right triangles
H. Law of sines and cosines
IX. Trigonometric Graphs, Identities, and Equations
A. Use the graphing calculator to explore trig functions
B. Graph all trig functions using amplitude, period,
phase and vertical shift
C. Verify trig identities
D. Use sum and difference formulas
E. Use double and half-angle formulas
F. Solve trig equations
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