Course Title: College Algebra and Trigonometry

ONTEORA HIGH SCHOOL 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: [email protected] [email protected]

Prerequisites: Intermediate Algebra

II. General Course Goals To provide the necessary background in Algebra for those students who will take Pre-Calculus.

II. 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 ° g)(x) and (g ° 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 y  e x 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.