Brett Barwick
USC Department of Mathematics

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Spring 2009 - Math 115 - Precalculus - Section 002

 

Tentative Course Outline:

 

Date

Topics Covered

1/12

Introduction, Syllabus
P.1 - Real numbers, absolute value, exponents, order of operations, simplifying expressions.

1/13

P.2, P.3, P.5 - Negative exponents, rules for exponents, rational exponents, radicals (nth roots), polynomials, operations with polynomials.

1/14

P.5, P.6 – Conjugates, polynomial long division, factoring out common terms, factoring by grouping, factoring quadratic expressions, difference of squares, difference and sum of cubes.

1/15

P.6, P.7 - Factoring by polynomial long division, domain of a rational expression, reducing to lowest terms, multiplication and division of rational expressions, addition and subtraction of rational expressions, simplifying complex fractions.
Reminder: Tomorrow is the last day to change your class schedule without a grade of W being recorded.

1/19

Dr. Martin Luther King, Jr. Service Day – No Class.

1/20

1.1, 1.2, 1.3 – Solving linear equations, solving an equation involving rational expressions, solving absolute value equations, constructing formulas to model situations in real life, Cartesian coordinate system, plotting points.
Quiz #1 10:30am

1/21

1.3, 1.4 – Distance formula, midpoint formula, circles, center, radius, graphing a line by finding the intercepts, slope of a line, point-slope form, slope-intercept form, using the slope to graph a line,

1/22

1.4, 1.6 – Parallel lines, perpendicular lines, example of a linear function as a model, solving quadratic equations by factoring, completing the square, and the quadratic formula, the discriminant of a quadratic equation, application of quadratic equations.
Quiz #2 10:30am (Group)

1/26

1.7, 2.1 – Interval notation, solving a linear inequality, compound inequalities, absolute value inequalities, definition of a function, identifying a function given a set of relations, identifying a function using the vertical line test, determining the domain and range of a function, function notation.

1/27

2.1, 2.2 – Average rate of change of a function, calculating the difference quotient for a function, graphing common functions, semicircles, piecewise functions.
Quiz #3 10:30am

1/28

2.2, 2.3 – Determining when a function is increasing, decreasing, or constant, horizontal and vertical translations, reflections, stretching and shrinking.

1/29

2.3, 2.4, 2.5 – Even and odd functions, symmetry, solving inequalities by graphing, operations with functions, composition of functions, one-to-one (invertible) functions, the horizontal line test.
Quiz #4 10:30am (Group)

2/2

2.5, 2.6 – Computing inverse functions, domain and range of an inverse function, composing inverse functions, using symmetry to graph inverse functions, direct variation, inverse variation.

2/3

2.6 – Joint variation, combined variation.
Quiz #5 10:30am

2/4

Review

2/5

Exam #1

2/9

3.1 – Standard form of a quadratic function, vertex form of a quadratic function, opening, vertex, axis of symmetry, using the discriminant to determine the number of horizontal intercepts.

2/10

3.1, 3.2, 3.3 -  Solving quadratic inequalities, example of a quadratic maximization/minimization problem, Remainder Theorem, synthetic division, Factor Theorem, Fundamental Theorem of Algebra.
Quiz #6 10:30am

2/11

3.3 – Rational Roots Theorem, multiplicity, finding roots of a polynomial equation, Conjugate Pairs Theorem, Descartes’ Rule of Signs, finding bounds on the roots of a polynomial equation, example of using all of the theorems to determine the roots of a polynomial equation.

2/12

3.4, 3.5 – Solving higher degree equations, equations involving square roots, equations with rational exponents, equations in “quadratic form”, equations involving absolute value, applications, leading coefficient test to determine end behavior of a polynomial.
Quiz #7 10:30am (Group)

2/16

3.5, 3.6, 4.1 – Solving higher degree polynomial inequalities using the test point method, horizontal and vertical intercepts of a rational function, oblique asymptotes, solving rational inequalities, exponential functions, graphing exponential functions.

2/17

4.1, 4.2 – Solving exponential equations, compound interest, Euler’s number e, radioactive decay, logarithmic functions, graphing logarithmic functions, converting between logarithmic and exponential equations, solving logarithmic equations, solving for t in compound interest problems.
Quiz #8 10:30am

2/18

4.3, 4.4 – Rules of logarithms, inverse rules relating logarithms and exponential functions, expanding and contracting logarithmic expressions, base change formula.

2/19

4.4 – Solving more logarithmic and exponential equations, carbon dating, Newton’s law of cooling.  Review and Summary of Chapter 4.
Quiz #9 10:30am (Group)

2/23

5.1 – Degree measure of angles, coterminal angles, quadrants, converting degrees to dms, radian measure of angles, converting between degrees and radians, arc length.
Reminder: Today is the last day to drop the class without a grade of WF being recorded.

2/24

5.2, 5.3 – Sine and cosine, unit circle for evaluating standard values of sine and cosine, calculating sine and cosine using reference angles, Pythagorean identity, graph of sine, amplitude, period, frequency, phase shift, graph of cosine, vertical translation, graphing transformations of sine and cosine.
Quiz #10 10:30am

2/25

5.4, – Tangent, cotangent, secant, cosecant, evaluating these trigonometric functions at standard values on the unit circle, graphing these functions with transformations.

2/26

5.5, 5.6 – Inverse trigonometric functions, domains of inverse trigonometric functions, evaluating inverse trigonometric functions, finding the inverse of general sine and cosine functions, right triangles, trigonometric ratios, solving a right triangle, applications.
Quiz #11 10:30am (Group)

3/2

Review and Summary of Chapter 5.

3/3

Practice solving equations from Chapters 3 and 4.
Quiz #12 10:30am

3/4

Review

3/5

Exam #2

3/9

Spring Break – No Class.

3/10

Spring Break – No Class.

3/11

Spring Break – No Class.

3/12

Spring Break – No Class.

3/16

6.1 – Using trigonometric identities, even and odd identities, proving that an equation is not an identity by finding a counterexample.

3/17

6.2, 6.3 – Strategies for verifying trigonometric identities (proofs), sum and difference identities, cofunction identities.
Quiz #13 10:30am

3/18

6.4, 6.5 – Double-angle identities, half-angle identities, product-to-sum identities, sum-to-product identities.

3/19

6.6, 7.2 – Solving conditional trigonometric equations, oblique triangles.
Quiz #14 10:30am (Group)

3/23

7.1 – Law of Sines, area formula using the sine of a known included angle.

3/24

7.2, 7.6 – Law of Cosines, activity: finding the height of an object from a distance using trigonometry, Heron’s Formula.
Quiz #15 10:30am

3/25

7.6 – Introduction to polar coordinates, converting between rectangular and polar coordinates, converting equations between polar and rectangular form.

2/26

7.7 - Introduction to parametric equations, common examples, eliminating the parameter, writing a parametric equation for a line segment.
Quiz #16 10:30am (Group)

3/30

Summary and review of Chapters 6 and 7.

3/31

Practicing solving triangles and proving trigonometric identities.
Quiz #17 10:30am

4/1

Review

4/2

Exam #3

4/6

8.1 – Solving a system of linear equations in two variables by graphing, substitution, and elimination, independent systems, dependent systems, and inconsistent systems.

4/7

8.2 – Solving a system of two linear equations in three variables, three linear equations in three variables, solution sets as intersections of planes.
Quiz #18 10:30am

4/8

8.3, 8.4 – Solving nonlinear systems of equations, partial fraction decomposition of a rational function, linear factors, repeated linear factors, irreducible quadratic factors, repeated irreducible quadratic factors.

4/9

8.5 – Graphing linear inequalities using test points, graphing nonlinear inequalities using test points, solving systems of linear and nonlinear inequalities by graphing
Quiz #19 10:30am (Group)

4/13

8.6, 10.1 – Linear programming, using the corner points of a feasible region to maximize or minimize an objective function, geometric definition of a parabola, vertex, focus, directrix.

4/14

10.2, 10.3 – Geometric definition of an ellipse, foci, standard equations for an ellipse, graphing translations of ellipses, standard equation of a circle, finding the center and radius of a circle.
Quiz #20 10:30am

4/15

10.3, 11.1 – Geometric definition of a hyperbola, standard equations for a hyperbola, graphing hyperbolas, sequences, computing factorials, finding the general formula for a given sequence.

4/16

11.1, 11.2 – Recursive sequences, arithmetic sequences, sigma notation for a series, index of summation, evaluating finite sums, adjusting the starting index, arithmetic series, formula for the first n terms of an arithmetic series.
Quiz #21 10:30am (Group)

4/20

11.3 – Geometric sequences, geometric series, formula for the sum of a finite geometric series, infinite geometric series, formula for the sum of an infinite geometric series.

4/21

11.3 – Applications of series.
Quiz #22 10:30am

4/22

A look ahead – a brief overview of calculus (if time permits).
Final Exam Review

4/23

Final Exam Review

4/27

Final Exam Review

 

How to Get Help in the Course:

 

Math Labs and Private Tutoring:

USC provides students with many options for free help with math courses. The Leconte Math Lab in Leconte 105 is open Monday-Thursday from 11:00am-4:00pm and is staffed with graduate students who can answer your questions. You can find more information about these options at the Math Tutoring Center website. If you feel that you need more intensive and personalized help, you can also hire a private tutor either through a tutoring service or through the USC Math Department Private Tutor List.

 

Important Dates for Fall 2008:

  • Monday, January 12 - Classes begin.
  • Friday, January 16 - Last day to change a course schedule or drop a class without a grade of W being recorded.
  • Monday, January 19 - Dr. Martin Luther King, Jr. Service Day - No classes.
  • Monday, February 23 - Last day to drop a course or withdraw without a grade of WF being recorded.
  • Monday, March 2 - Midpoint in semester.
  • March 8-15 - Spring break - No classes.
  • Monday, April 27 - Last day of classes.
  • Tuesday, April 28 - Reading day.
  • Friday, May 1 - Cumulative final exam at 2:00pm in CSSC 004.

© 2011 Brett Barwick