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Common Core Algebra 2
Math Links
Common Core Algebra 2
Course Syllabus
Common Core Algebra 2 – Course Outline for Semester 1 and 2 (Revised June 2017)
Unit #1 – Review of Algebraic Ideas (Important Topics from Common Core Algebra I and Common Core Geometry Relating to Algebra) –
Summary: Includes but not limited to: Basic Review of Operations with Radicals, Review of Basic Terms and Vocabulary, Solving Linear Equations, Brief Exponent Review, Operations with Polynomials and Basic Calculator Work Using the TI-83Plus Graphing Calculator.
Specifics:
- Review of Operations with Radicals
o Adding, Subtracting, Multiplying, Dividing, Rationalizing, Simplifying (including square roots and nth roots)
- Review of Properties
o Properties of Real Numbers (Commutative, Associative, Distributive)
o Properties of Equalities (Addition and Multiplication)
o Properties of Inequalities (If time permits)
- Review of Linear Equations
o Analyzing linear equations to determine the number of real solutions (unique, identity, and inconsistent cases)
o Solving linear equations by recognizing applications of properties of real numbers and equalities
o Solving multi-step linear equations
o Solving fractional linear equations with emphasis on extraneous solutions (Cross multiply and Common Denominator technique)
- Review of Laws of Exponents with Monomial Expressions
o All power rules (multiplying, dividing, zero exponents, negative exponents, fractions raised to exponents, factors raised to an exponent, powers raised to an exponents, etc…)
o Simplifying monomial expressions (be sure to include expressions with variable bases and numerical bases)
- Review of Multiplying Polynomials
o Use an algebraic approach and a geometric approach (area array) to multiply binomials times binomials, binomials times trinomials, trinomials time trinomials, polynomials squared time polynomials, monomials times polynomials, etc…
o Determining the algebraic equivalence of expressions after multiplying polynomials and showing their equivalence by substituting values into the expressions and comparing.
o Application problems involving multiplying polynomials
- Review of Evaluating Expressions
o Review of GEMDAS
o Understanding how to use the variable and storage keys on the calculator to check evaluated expressions
o Introduction of a rational expression and how to use the fraction key, absolute value and square root function of a calculator and parentheses on a calculator to check the evaluated function.
- Review of the Exploration of other Features on the Graphing Calculator
o Using the calculator to find zeros of a function (CALC: ZERO, TABLE)
o Associating a zero with its appropriate factor to write equations of a function
o Other functions to review: y=, TABLE, VALUE, adjusting TBL SETTINGS, function notation on the home screen, WINDOW
o Briefly discuss Location Principle
o Relative and Absolute MINIMUM and MAXIMUM Points
o INTERSECT
Unit #2 – Intro to Functions
Summary: Includes but not limited to: Graphs of Functions and Important Ideas with the Graph of a Function (intervals of Increase/Decrease, Zero(s), y-intercepts, Maximum and Minimum (Absolute and Relative)), Definition of a Function, Function Notation, Evaluating Functions, Domain and Range of Functions, Composition of Functions, One to One Functions and Inverse Functions
Specifics:
- Intro to Vocabulary and Definition of a Function
o Independent, Dependent, Domain, Range, Codomain, Input, Output, x, y
o Relative vs. Function using multiple representations like mappings, equations, tables, graphs, charts, sets, etc…
o Function Notation
o Standard Form vs. Vertex Form for Functions
o Parent Functions
- Review of Completing the square with and without leading coefficients other than 1
- Review of 9 Parent Functions from Algebra 1 and Geometry and Respective Behaviors of those functions:
o Linear Function
o Quadratic Function
o Absolute Value Function
o Square Root Function
o Exponential Growth/Decay
o Cubic Function
o Cube Root Function
o Step Function (Greatest Integer Function)
o Circle (not a function, but good to review it here)
- Transforming Parent Functions
o Vertical and Horizontal Shifts
o Vertical Compressions and Stretches
o Reflections over the x-axis
- Evaluating Functions Algebraically using Function Notation
o Given Input, find output (evaluating functions)
o Given Output, find input
o Understanding that f(a) = b is another way to write the point (a, b)
o Given a restricted domain, find range.
- Evaluating Functions using Function Notation
o Using Graphs
o Using Tables
o Using Charts
- Finding the Domain of the following Functions:
o Polynomial, rational, square root, fractional equations with radicals in the denominator (linear only), exponential, absolute value, circles (not functions)
- Finding the Range of Functions:
o Linear, Exponential, Absolute Value, Square Root, Quadratic (standard and vertex form), circles
o Mixed Review of Domain and Range Questions with restricted domains and ranges, charts, tables, etc…
- Operations with Functions (Add, subtract, Multiply, and Divide)
- Composition of Functions
o Algebraically
o Graphically
o Using Tables/Charts
- One-to-One (1-1) Functions
o Horizontal Line Test, identifying 1-1 functions given equations, graphs, charts, etc…, restricting domains of functions, like quadratics, in order to make them 1-1
- Inverse Functions
o Notation
o Finding inverses algebraically and graphically
- Key Features of Functions (Algebraically and Using Other Methods Necessary, like the graphing calculator)
o Intercepts
o Zeros, Roots, Solutions, Answers, and x-intercepts
o Increasing, Decreasing, and Constant Functions
o Positive, Negative intervals of a function
o Relative Extrema
o Absolute Extrema
o End Behavior
Unit #3 – Linear Functions
Summary: Includes but not limited to: Direct Variation, Rate of Change, Various Forms of a Linear Equation, Modeling using linear functions, Inverses of Linear functions, Piecewise Equations/Graphing involving Linear Functions and Systems of Linear Equations (focus on Three Equations and Three Unknowns)
Specifics:
- Review of Terminology and Parts of a Linear Function
o Slope (rate of change), y-intercept
o Slope-Intercept form, Point-Slope form
o Graphing using the Table Method
o Graphing using the Slope-Intercept and Point-Slope method
- Vertical and Horizontal Lines
- Parallel and Perpendicular Lines
- Writing the equation of lines
- Average Rate of Change
- Linear Modeling
- Direct Variation and Indirect Variation
o Identifying Constant of Variation
o Identifying graphs of DV and IDV (linear and rectangular hyperbolas)
o Application problems and Charts for DV and IDV
- Systems of Linear Equations (2 x 2)
o Algebraically using Elimination Method and Substitution Method
o Graphically
- 3 x 3 Systems of Linear Equations Algebraically
- Piecewise Functions
Unit # 4 – Exponential Functions
Summary: Includes but not limited to: Exponents (integer and fractional), Review of the Rules of Exponents, Graph of Exponential Functions, Writing the Equation of an Exponential Function given the Base and Initial Value, Solving Exponential Equations with Common Bases, Modeling Exponential Functions (Growth and Decay)
Specifics:
- Rearranging Expressions Involving Exponents
o Rewrite expressions as a single power
o Rewrite a single power as multiple powers
o Evaluate expressions involving exponents
o Review of exponent laws
o Simplifying exponential expressions review (including scientific notation)
- Exponent Work with Function Notation, Manipulating Expressions involving Powers using Laws of Exponents
- Fractional Exponents
o Converting radical expression to an expression with a fractional exponent
o Converting a fractional exponent to a radical expression
o Simplifying expressions involving radicals and fractional exponents
- Solving Equations with Fractional Exponents
- Solving Exponential Equations with the same base and with an uncommon base
- Graphing Exponential Functions
o Making an appropriate table of values
o Understanding how to identify the equation of an asymptote
o Identifying intercepts, intervals of increase/decrease
o Exponential Growth/Decay
o Relationship between equations that are reflections of each other over the y-axis and x-axis
o Graphing exponential functions with a restricted domain
o Transforming exponential functions
- Writing the equation of exponential functions:
o Given “a” and a point
o Given “b” and a point
o Given two points
o Given a table
- Introduction to Exponential Word Problems
o Identifying initial amount, growth/decay factor, growth/decay rate (as a non-% and a %)
o General form(s) for exponential word problems
o Creating and Solving Exponential Word Problems
§ Find output given input
§ Find input given output
§ Write a model that best represents a given situation
§ Interpret the behavior of a given exponential model
§ Exponential Word Problems involving Money (Financial), Compounding “n” times a year
- Nominal vs. Effective Yearly Interest Rates
- Calculating the % of Growth/Decay within Various Periods of Time (Mindful Manipulations)
- Exponential Word Problems using base “e”
o Compounding Continuously
o Naturally Occurring Situations and Half-Life Problems
Unit # 5 – Logarithmic Functions
Summary: Definition of a Logarithm, Graphs of Logarithmic Functions, Rules of Logarithms, Solving Exponential Equations Using Logarithms, the Number e and the Natural Logarithm and Applications of Exponential Equations and Logarithmic Equations
Specifics:
- Introduction to Logs
o Understanding the inverse relationship between an exponential function and a logarithmic function
o Domain and Range of log functions (and their restrictions)
o Converting from exponential form to log form and vice versa
o Common log
o Inverse Property for Logs
o Evaluating log expressions
o Estimating between which two consecutive integers a log expression lies
- Solving Simple Log Equations
- Graphing Log Functions and Other Features of Log Graphs like:
o Domain, Range, Intervals of Increase/Decrease, Intervals of Positive/Negative, Intercepts, Asymptotes, End Behavior
o Finding an appropriate table of values for log graphs with knowledge of transformation shifts
o Finding intercepts, domain, and range of log graphs algebraically
o Graphing log graphs with restricted domains
o Finding the average rate of change over an interval of a log graph, finding ∆y given an interval of x
- Log Properties for Multiplication, Division, Powers
o Log Identity and Log Inverse Property
o Proving log identities using log properties only
o Expanding/Condensing log expressions
o Evaluating log expressions using log properties
- Manipulating Log Expressions
- Solving Log Equations
o Simple log equations (derive the change of base formula)
o Log equations with logs on one side where you have to use log condensing properties
o Log equations with logs on both sides where you have to get in the form logba = logbc and then drop the logs
- Log Application Word Problems
o Word problems given a log equation
o Word problems where you have to use logs to solve them
- Introduction to the Natural Log (ln)
o Ln rules and properties
o Mixed problems involving ln like, expanding/condensing expressions, evaluating expressions, manipulating expressions, etc…
o Ln application word problems
- Newton’s Law of Cooling
Unit # 6 – Sequences and Series
Summary: Includes but not limited to: Definition a Sequence, Arithmetic Sequences, Geometric Sequences, Sigma Notation (Summation Notation), Definition of a Series, Arithmetic Series, Geometric Series and Applications of Series
Specifics:
- Review of Sequences and Intro to Sigma Notation
o What is a sequence? What is the domain/range of a sequence? What types of sequences are there? Recursive vs. Explicit formulas? What is a series?
o Introduction to sigma notation and evaluating expressions that are in sigma notation
- Converting a series to Sigma Notation
- Generate sequences given explicit and recursive definitions (identify patterns where applicable)
- Given a sequence, write an explicit or recursive formula
- Arithmetic Sequences
o Identify common difference, d
o Derive and apply explicit formula
o Write recursive definitions
o Find a1, d, and an using a system of equations
o Other types of problems relating to arithmetic sequences
- Geometric Sequences
o Identify common ratio, r
o Derive and apply explicit formula
o Write recursive definitions
o Find a1, r, and an using a system of equations
o Other types of problems relating to geometric sequences
- Arithmetic and Geometric Series
o Derive and apply the formulas for arithmetic and geometric series.
o Find the nth partial sum of a series
- Mortgage Unit as it applies to Geometric Series
o Calculating the Amount Owed on a Mortgage
o Calculating the Number of Payments needed to pay off a loan
o Calculating the Monthly Payment
o Finding the monthly interest rate given the yearly interest rate
o Being able to solve word problems given equations involving the above unknowns
Unit #7 – Quadratic Functions
Summary: Includes but not limited to: Review of a Quadratic Equation (in one variable) and its Graph, Factoring (GCF, Factoring Completely, Difference of Perfect Squares (Conjugate Factors), Perfect Square Trinomials, Factoring Trinomials, Factoring by Grouping, Zero Product Property, Quadratic Inequalities in One Variable, Completing the Square, Vertex-Form of a Parabola, Horizontal and Vertical Shifts of a Parabola, Modeling with Quadratic Functions
Specifics:
- Factoring of All Types
o GCF
o Difference of Perfect Squares
o Sum and Difference of Perfect Cubes
o Trinomials with leading coefficients of 1 and coefficients other than 1
o Factor by grouping
o Factor using substitution
o Factoring Completely
- Solving Quadratic Equations
o Solving equations in standard form using Zero-Product Property Method (by Factoring)
o Solving equations in vertex form using Square Root Method
o Getting equations in vertex form by completing the square (then using the Square Root Method)
o Fractional Equations with and without extraneous solutions
- Solving Equations of a Higher Degree
- Quadratic Word Problems of All Types:
o Area, Perimeter, Ratio, Consecutive Integer, Volume, Systems, Proportions
- Quadratic Inequalities
o Solving Quadratic Inequalities Algebraically
- Modeling Quadratic Word Problems
o Building models for projectile motion in feet and meters
o Appropriate domain questions
o Intercept questions
o Vertex/Turning Point Questions
o Identifying the meaning of coefficients in a quadratic projectile model in standard form
o Identifying the meaning of numbers in a quadratic projectile model in vertex form
Unit #8 – Locus of a Circle and Parabola
Summary: Distance Formula, Equations of a Circle (Center-Radius and Expanded Form) and the Definition of a Parabolas as a Locus of Points Equidistant from a Point (Focus) and a Line (Directrix)
Specifics:
- Definition of a Circle as a locus of points
o Review of distance formula, midpoint formula, slope formula, Pythagorean theorem, center-radius form, slope/intercept and point/slope form of a line, and points of tangency
o Writing the equation of a circle in center-radius form given information that can find the center and radius of a circle
- Convert from standard form to Center-Radius Form by completing the square twice
- Systems Involving Circles Algebraically and Graphically
- Definition of a Parabola as a Locus of Points
o Define and identify focus and directrix
o Derive focus-directrix form of a parabola
o Mixed set of problems involving focus-directrix form
§ Find focus, vertex, directrix, p
§ Write focus-directrix form given information, convert focus-directrix form to standard or vertex form
§ Derive the focus-directrix equation of a parabola using the distance formula
Unit #9 – Transformations of Functions
Summary: Includes, but not limited to: Vertical and Horizontal Shifts of Various Functions, Reflections of a Parabola, Vertical and Horizontal Dilations of a Function (Stretching and Compressing) and Even & Odd Functions
Specifics:
- Transforming Functions (focus on answering questions without necessarily the use of a graph to read off of)
o Vertical and Horizontal Shifts
o Reflections over the x and y axes
o Vertical Stretches and Compressions
o Horizontal Stretches and Compressions
- Even and Odd Functions
o Algebraic Definition of an Even and Odd Function
o Graphically Representation of Even and Odd Functions
o Completing Tables given Even and Odd Functions
o Evaluating expressions given Even and Odd Functions
Unit #10 – Radicals and the Quadratic Formula, Complex Numbers
Summary: Includes but not limited to: Domain, Range and Graphs of Square Root Functions, Solving Square Root Equations (extraneous roots), revisit Fractional Exponents as a means of discussing roots other than square roots and Quadratic Formula, Definition of an Imaginary Number, Powers of I, Definition of Complex Number, Operations with Complex Numbers, Definition and Meaning of the Discriminant and Solving Quadratic Equations with Complex Roots
Specifics:
- Domain of Radical Equations
o Graphical representation
o Algebraic approach (include quadratic and higher degree equations under the radical)
- Solving Equations Involving Radicals
o Understanding inverse operations eliminate radicals
o Solving equations with one or two radical expressions within them and extraneous solutions
o Solving systems involving radical equations
- Introduction to “i” and the Complex Number System
o Visual Representation of the Set of Complex Numbers
o Definition of “i” (Complex number vs. Purely Imaginary or Purely Real Number)
o Cyclic Nature of “i”
o Powers of “i”
o Operations involving “i”
o Simplifying radical expressions involving “i” and/or negative radicands
- Properties of Complex Numbers
o Conjugates (the product of conjugates)
o Multiplicative and Additive Inverse
o Rationalizing expressions with monomial and polynomial imaginary terms in the denominator
- Solving Equations with Complex Roots
o Quadratic Formula
o Completing the Square (Square Root Method)
o Systems
- Discriminant Work
o Review the four cases for the discriminant
o Understand where it comes from and how it relates to the roots of an equation
o Find the value(s) of k such that….type questions
Unit #11 – Rational Functions (Depending on time, we will cover a portion of this unit)
Summary: Includes but not limited to: Simplifying Rational Expressions, Operations with Rational Expressions, Complex Fractions
Specifics:
- Simplifying Algebraic Fractions
o Mono over Mono
o Mono over Poly
o Poly over Mono
o Poly over Poly
o Different cases for cancelling binomial factors
- Multiplying and Dividing Algebraic Fractions
o Include Area and Volume word problems
- Complex Fractions
- Adding and Subtracting Algebraic Fractions
o Common Denominator and Uncommon Denominator
o Monomial and Polynomial Expressions in the Denominator
Assignments
Class Resources
Introduction to Calculus
Course Syllabus
Introduction to Calculus – Course Description
This course focuses on the foundations and analysis of the early material students would encounter in a calculus class in college. Specific topics include: Trigonometry, functions, the study of polynomials, limits (an algebraic and graphic approach), continuity, derivatives, and applied maximum and minimum problems.
I. More with Trigonometry –
Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function
Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent
Justify the Pythagorean identities
Solve trigonometric equations for all values of the variable from 0 to 360 degrees or 0 to 2π
Write the trigonometric function that is represented by a given periodic graph
Solve for an unknown side or angle, using the Law of Sines and/or the Law of Cosines
Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle
Determine the solution(s) from SSA situation - ambiguous case
Apply the angle sum and difference formula for trigonometric functions
Apply the double-angle and half-angle formulas for trigonometric functions
II. Polynomials
Nature and Number of Roots (including multiplicity of roots and maximum number of bends in a given polynomial function)
Writing a polynomial function given the roots (real and/or complex)
Descartes Rule of Signs
Finding all Rational Roots of a Polynomial
Upper and Lower Bound of a Zeros
III. Limits and Continuity
Graphing Various Functions - includes but not limited to: Multi-defined, rational, and greatest integer
Graphing Multi-Defined and Rational Expressions to Look at Limits Graphically - includes right-hand and left-hand limits
Looking at Limits Algebraically - Approaching Infinity, Negative Infinity, and a constant value of x
Vertical and Horizontal Asymptotes
Continuity - using the definition
Removable vs Essential Discontinuity
IV. Derivatives
Using the formal definition of a derivative
Writing an equation of a line tangent to a curve at x
Critical Points, Relative Maximums and Relative Minimums
Power Rule
Chain Rule
Product Rule
Quotient Rule
Applications of first derivative
** Implicit Differentiation
** Second Derivatives and Concavity
**Analyzing graphs - relationships between f(x) and f'(x), between f(x) and f''(x), and between f'(x) and f"(x)
** If time allows, we will discuss these topics.
Assignments
Class Resources
Calculus Resources
Classroom Resources
Website Resources
Emathinstruction
Geogebra
Interactive Graphing Calculator by Microsoft
Integral Calculator
Kahn Academy
Mastermathmentor
Math Bits Notebook
Oswego Regents Prep
Purple Math
Symbo Lab
Math 115
Course Syllabus
I. Basic Course Information
Course Title: College Algebra and Trigonometry
Dept. and Course Number:MAT 115
Instructor: Wendy Cohen/Jeannine Burkhardt
Phone: (845)657-2373
Email: wcohen@onteroa.k12.ny.us and jburkhardt@onteora.k12.ny.us
Prerequisites: Intermediate Algebra
II. General Course Goals
To provide the necessary background in Algebra for those students who will take Pre-Calculus.
III. Specific Objectives and Course Outline
UNIT I: Solving Equations and Inequalities
Part 1: Equations
A) 1. Solve linear equations with parentheses, fractions and decimals (including the use of a calculator).
2. Solve equations containing several variables.
3. Set up appropriate linear equations and solve word problems.
B) 1. Write a quadratic equation in standard form and solve by factoring.
2. Solve a quadratic equation by writing in standard form, and solve by factoring, by extracting the roots, by completing the square and by quadratic formula (including the use of a calculator).
3.Choose the most appropriate method for solving quadratics.
4. Solve certain types of word problems involving quadratic equations.
C) Solve second and higher degree equations in the complex number system.
D) Solve third and fourth degree equations by factoring, including factoring by grouping.
E) Solve equations containing either one or two radical expressions, checking to determine if there are extraneous solutions.
F) Solve equations involving absolute value notation.
Part 2: Inequalities
A) Understand open and closed interval notation and express solutions to inequalities using that notation.
B) Solve linear inequalities.
C) Solve quadratic and rational inequalities and inequalities or a higher degree by using critical numbers, test intervals and the sign chart approach.
D) Solve inequalities involving absolute value notation.
E) Express the solution to all sorts of inequalities graphically, in inequality form and in interval form.
F) Find the domain of a radical expression by solving an appropriate inequality, where needed.
UNIT II: Cartesian Coordinate System
A) Understand the rectangular or Cartesian coordinate system and graph ordered pairs of real numbers on graph paper.
B) Use the distance formula to find the distance between two points.
C) Find the midpoint of the line segment joining two points.
D) Determine whether three given points form a right triangle by using the distance formula and the Pythagorean Theorem.
E) Graph quadratic equations that are parabolas that are in standard form and vertex form.
1. Find whether it has a minimum or maximum point.
2. Find the vertex.
3. Find the y-intercept
4. Find the x-intercepts (roots).
5. Find the equation of the axis of symmetry.
6. Find the domain and the range.
F) Find x and y intercepts for given equations.
G) Find the slope of a line that passed through a given pair of points.
H) Graph a line passing through a given point and having a given slope.
I) Find the equation of a line under the given conditions:
1. given two points through which the line will pass,
2. given the slope and one point through which the line will pass,
3. given the slope and y-intercept of the line.
J) Determine whether two lines are parallel, perpendicular or neither under the following conditions:
1. given the slopes of the lines,
2. given pairs of points through which the lines will pass,
3. given the equations of the lines.
K) Write the equation of a line in slope-intercept form, point-slope form and general form.
L) Convert the equation of a line into slope-intercept form and then determine the slope and y-intercept of the line.
M) Write the equations of horizontal and vertical lines and determine their slopes.
N) Determine the intercepts for linear equations and construct their graphs.
O) Find the equation of a line that is parallel or perpendicular to a given line and passes through a given point.
P) Write the given equation of a circle in standard form, find the center and the radius and sketch the graph.
Q) Determine whether a given graph has symmetry to the x-axis, the y-axis, or the origin.
UNITI III: Functions
A) Understand the definition of “function” and determine whether a given relationship between two variables makes one variable a function of another.
B) Work with function notation and evaluate functions at specific values of the independent variable.
C) Find the domain of a function for a variety of types of functions
D) Use the vertical line test to determine whether a graph represents one variable as a function of another variable.
E) Given the graph of a function, determine;
1. the domain and range
2. the intervals for which the function is increasing, decreasing, or constant
3. what kind of symmetries are present
4. the intercepts, if any
F) Determine whether a given equation or graph represents a function that is even, odd or neither.
G) Graph functions of the form y=f(x) where f(x) is;
1. linear
2. quadratic
3. third degree
4. the absolute value of a linear expression
5. the square root of a linear expression
6. piecewise continuous
7. a rational expression with one vertical asymptote
H) Find the difference quotient for a given function
I) Use the idea of translations (shifting) and reflections of the graphs of simple functions as an aid in the construction of the graphs of more sophisticated functions, where appropriate.
J) Combine two functions by adding, subtracting multiplying or dividing the functions and understand the function notation involved.
K) Find the composition of two functions: (f o g)(x) and (g o f)(x)
L) Understand the definition of an exponential function and graph exponential functions that are either increasing or decreasing. Use shifting and reflecting, if needed.
M) Give the domain and range of exponential functions
N) Understand the exponential function 
and work problems involving compound interest where the compounding is done a finite number of times per year or is done continuously.
O) Use a calculator to do computations that are related to exponential functions and compound interest.
P) Know and apply the definition of a logarithm and convert given equations from exponential to logarithmic form and conversely.
Q) Graph logarithmic functions, using shifting and reflecting if needed. Give the domain and range.
R) Find the domain of a logarithmic function without the aid of a graph.
S) Understand and use the properties of logarithms to;
1. write logs of complicated expressions as sums and or differences of simpler expressions without the involvement of products, quotients and exponents (where possible)
2. write an expression containing two or more logs as a simple log with a coefficient of one
T) Use a calculator to evaluate common and natural logs of numbers.
U) Use the change of base formula and a calculator to evaluate logs to any appropriate base in terms of natural or common logs.
V) Solve log and exponential equations with the application of the properties of logs.
W) Solve simple word problems involving exponential growth/decay
UNIT IV: Trigonometry
A) Work with angles in both degrees and radians. Convert angles from degrees to radians, and conversely.
B) Construct angles in standard position and find reference angles.
C) Find the trigonometric functions of the acute angles in a right triangle when at least two sides are given.
D) Know the trig functions of the special acute angles: 30°, 60° and 45°.
E) Use a calculator to evaluate trig functions of angles where the angles are expressed in degrees or radians.
F) Solve right triangles for all missing angles and/or sides when certain sides or angles are given
G) Solve word problems that involve right triangles.
H) Find the trig functions of any angle in standard position, given a point on its terminal side.
I) Know which trig functions are positive and which are negative for standard position angles whose terminal sides may fall in any quadrant.
J) Construct any angle in standard position and evaluate its trig functions in terms of the reference angle involved.
K) Given the trig function of an angle in standard position and the quadrant involved, find the remaining trig functions of that angle.
L) Find the trig functions of quadrantal angles without using a calculator.
M) Find the trig functions of and angle in standard position, when the point on the terminal side of the angle lies on the unit circle.
N) Use the relationship between trig functions of real numbers and the unit circle to determine the domain and range of certain trig functions.
O) Recognize and use fundamental trig identities to help in evaluating trig functions of angles.
IV. Teaching and Evaluation of the Course
The above objectives of student learning will be assessed as follows:
1. Four quarters of instruction which will include regular exams, quizzes and hand-in assignments,
2. Mid-Term exam
3. Final exam
V. Statement on Academic Integrity
Students enrolled in MAT115, at Onteora High School are held to the same academic standard as those enrolled at UCCC. They are expected to complete all assignments in a timely manner, and pass all of the exams and quizzes. They are held accountable for attending class and risk failure if they are absent too frequently.
Their course grade is determined by averaging the 4 quarters and the final together. In addition the midterm is weighted as half a quarter. The students are expected to earn a grade of 65 or better in order to receive credit for the course.
The math department provides additional instructional support, outside of class time, to assist any students who are struggling and who want extra help.