NHTI Concord s Community College 31 College Drive Concord, NH 03301-7412 603) 271-6484; FAX 603-271-7734 COURSE OUTLINE & INFORMATION SHEET PROGRAM COURSE NO. COURSE TITLE CREDIT HOURS CRN# Math (NHTI) MT134 Pre-Calculus 4 20338 & 20409 Math (CCA) PRECAL(DC) Pre-Calculus 1 INSTRUCTOR: CCA: James Schofield; (603) 228-8888; e-mail: jwschofield@concordchristian.org COURSE DESCRIPTION: Topics include: complex numbers; polynomial and rational functions and their graphs; trigonometric identities and equations; non-linear systems and inequalities; conic sections; sequences and series; counting methods; binomial theorem; limits and continuity. A graphing calculator is required. GENERAL COURSE OBJECTIVES: 1) The student will apply knowledge of mathematical topics (listed in the catalog description) in analyzing specific "real-world" problems. 2) The student will demonstrate problem-solving skills based on logical thinking and systematic application of mathematical tools. PREREQUISITE: Algebra II MEETING TIMES: Room 210 - CCA M-F 11:15-12:07 CCA Concord Christian Academy 37 Regional Dr Concord, NH 03301 (603) 228-8888 Class cancellations due to weather will be will be notified via One Call Now CANCELLATION/DELAYED START OF CLASSES: When the Principal deems it prudent to cancel all classes at the school, the announcement will be made on WMUR-TV, Channel 9. In addition, the announcement will be made on local radio stations and via a One Call Now notificatio. Occasionally, the Principal will opt for a delayed start to classes. IF CLASSES ARE CANCELLED ON THE DAY AN EXAM IS SCHEDULED, THE INSTRUCTOR WILL NOTIFY YOU WHAT DATE THE EXAM WILL BE RESCHEDULED TO.
ATTENDANCE POLICY AND MISSED WORK Any student who misses more than 4 hours of classes (for any reason) and has a grade of C or below, or who has missed all classes for any two-week period (without instructor contact), will be eligible for termination from the course with a failing grade of AF. A student who misses class is still required to complete homework assignments with the expectation that the student will take each exam when scheduled. (See Exams for more information.) MATERIALS REQUIRED: Text: PreCalculus, 5/e; Blitzer; Pearson/Prentice Hall, 2014. ISBN: 9780321199911 or the e-book Graphing Calculator: TI-83+ or TI 84+. No other calculator will be supported during class GRADING POLICY: A. NHTI: Exam and course grades are assigned on the following basis, where the indicated quality points are the minimum needed to achieve the assigned letter grade: 100-93 A 4.0 92-90 A- 3.7 89-87 B+ 3.3 79-77 C+ 2.3 69-67 D+ 1.3 86-83 B 3.0 76-73 C 2.0 66-63 D 1.0 82-80 B- 2.7 72-70 C- 1.7 62-60 D- 0.7 <60 F 0.0 CCA: Exam and course grades are assigned on the following basis, where the indicated quality points are the minimum needed to achieve the assigned letter grade: 100-95 A 4.0 94-93 A- 3.9 92-90 B+ 3.7 84-82 C+ 2.7 74-73 D+ 1.7 89-87 B 3.3 81-78 C 2.3 72-71 D 1.3 86-85 B- 3.0 77-75 C- 2.0 70 D- 1.0 <70 F 0.0 The following definitions describe the significance of the above grade levels: A or A- B+, B, or B- C+, C, or C- D+, D, or D- represents achievement of a level of understanding and ability which is excellent and distinctive. represents achievement of a level of understanding and ability of consistent high quality. represents achievement of a level of understanding consistent with those required for successful entry into the student s chosen field. represents some evidence of achievement, but substantially below the level required for successful entry into the student s chosen career field. F represents negligible academic achievement. B. NHTI/CCA: Your grade for the course will be determined based on the following: Each quarter grade (Two quarters per semester) determined by: Tests Homework Participation Preparation 65% of quarter grade 20% of quarter grade 5% of quarter grade 5% of quarter grade
Assignment Timeliness 5% of quarter grade Final Exam 20% of overall semester grade C. When any course work is not completed by its due date, grade credit is reduced for whatever work remains undone this includes exams not taken at their scheduled times. In any case, no work will be accepted after two days late. NOTE: A grade of Incomplete will only be considered by the instructor if the student has been missing consecutive assignments or tests for an extended time period, due to, for example, an extended illness or other unusual circumstance. D. Each student is assumed to be earnestly working to the best of his or her ability in the course. If well into the course student performance is averaging less than C, the instructor and student should discuss an action plan with a goal towards assuring the student the best possible success in the course. GRADE REPORTING: NHTI: Faculty submit grades electronically to the Registrar s Office within a few days following the end of each final exam period. FINAL GRADES ARE NOT MAILED to students. It is the student s responsibility to review his/her final grades via the Student Information System as soon as grades are available. Students who receive an I (Incomplete) grade should coordinate with the instructor to complete the remaining coursework as soon as possible. Unresolved I grades may affect (i.e., delay or reduce) financial aid awards and will convert to an F (Failing) grade after a specified time period. Consult the NHTI catalog for the full Incomplete Grade Policy. CCA: Faculty submits grades electronically to the Student Information System within a few days following the end of each final exam period. Final grades are mailed to students. It is the student s responsibility to review his/her final grades via the Student Information System as soon as grades are available. ASSIGNMENTS: Since 80% of the semester grade comes from exams, the remaining 20% of your end grade will be based on homework exercises from the textbook and additional handouts prepared by the instructor (sometimes to be completed in class and at other times due at a later date). The quantity and quality of the work you complete determine how much of the 20 percentage points you earn. EXAMS/TESTS: Exams will be administered after the end of each chapter. Normally, only one hour is available to students for test-taking. I WILL CALL FOR ALL TESTS TO BE HANDED IN by the end of the class period--even though not all questions have been answered! However, extended time for exams may be an option for those who qualify. PLEASE NOTE: If a class should be cancelled on the day an exam is scheduled, all students are to assume that the test will be given at the very next meeting time of the course MAKE-UP WORK POLICY: A missed test/exam can be considered for make-up only if the instructor has been notified prior or during the day the exam is given that the student can not take the exam as scheduled. You are NOT guaranteed makeup of tests/exam; individual circumstances will dictate whether or not you are allowed makeup. Work not completed by the designated time does mean a reduction in grade credit, but could also mean no credit at all. If you expect to get some credit for work completed after the time indicated in the assignment schedule, then you need to discuss with the instructor your extenuating circumstances. If there is no valid
reason for being late with assignments, then late work cannot be made up. Students are expected to attend all lectures and, in any case, are responsible for making up missed work. A student who misses more than 4 classes for any reason may be terminated from the course with a failing grade (see Student Handbook). Make-up tests are allowed only in extenuating circumstances. If makeup is allowed, it must be taken upon the student's first return to class after an absence. Also, make-up of a missed exam can occur only if the instructor has been notified, prior or during the day the exam is given. IF MORE THAN THREE EXAMS ARE NOT TAKEN, A PASSING GRADE WILL NOT BE GIVEN regardless of the average of tests taken. Performance Objectives I. Polynomial and Rational Functions 1. Add and subtract complex numbers. 2. Multiply complex numbers. 3. Divide complex numbers. 4. Perform operations with square roots of negative numbers. 5. Solve quadratic equations with complex imaginary solutions. 6. Recognize characteristics of parabolas. 7. Graph parabolas. 8. Determine a quadratic function s minimum or maximum value. 9. Solve problems involving a quadratic function s minimum or maximum value. 10. Identify polynomial functions. 11. Recognize characteristics of graphs of polynomial functions. 12. Determine end behavior. 13. Use factoring to find zeros of polynomial functions. 14. Identify zeros and their multiplicities. 15. Use the Intermediate Value Theorem. 16. Understand the relationship between degree and turning points. 17. Graph polynomial functions. 18. Use long division to divide polynomials. 19. Use synthetic division to divide polynomials. 20. Evaluate a polynomial using the Remainder Theorem. 21. Use the Factor Theorem to solve a polynomial equation. 22. Use the Rational Zero Theorem to find possible rational zeros. 23. Find zeros of a polynomial function. 24. Solve polynomial equations. 25. Use the Linear Factorization Theorem to find polynomials with given zeros. 26. Use Descartes s Rule of Signs. 27. Find the domain of rational functions. 28. Use arrow notation. 29. Identify vertical asymptotes. 30. Identify horizontal asymptotes. 31. Use transformations to graph rational functions. 32. Graph rational functions. 33. Identify slant asymptotes. 34. Solve applied problems involving rational functions. 35. Solve polynomial inequalities. 36. Solve rational inequalities. 37. Solve problems modeled by polynomial or rational inequalities. 38. Solve direct variation problems. 39. Solve inverse variation problems. 40. Solve combined variation problems. 41. Solve problems involving joint variation.
II. Analytic Trigonometry 1. Use the fundamental trigonometric identities to verify identities. 2. Use the formula for the cosine of the difference of two angles. 3. Use sum and difference formulas for cosines and sines. 4. Use sum and difference formulas for tangents. 5. Use the double-angle formulas. 6. Use the power-reducing formulas. 7. Use the half-angle formulas. 8. Use the product-to-sum formulas. 9. Use the sum-to-product formulas. 10. Find all solutions of a trigonometric equation. 11. Solve equations with multiple angles. 12. Solve trigonometric equations quadratic in form. 13. Use factoring to separate different function in trigonometric equations. 14. Use identities to solve trigonometric equations. 15. Use a calculator to solve trigonometric equations. III. Systems of Equations and Inequalities 1. Recognize systems of nonlinear equations in two variables. 2. Solve nonlinear systems by substitution. 3. Solve nonlinear systems by addition. 4. Solve problems using systems of nonlinear equations. 5. Graph a linear inequality in two variables. 6. Graph a nonlinear inequality in two variables. 7. Use Mathematical models involving linear inequalities. 8. Graph a system of inequalities. 9. Write an objective function describing a quantity that must be maximized or minimized. 10. Use inequalities to describe limitations in a situation. 11. Use linear programming to solve problems. IV. Conic Sections and Analytic Geometry 1. Graph ellipses centered at the origin. 2. Write equations of ellipses in standard form. 3. Graph ellipses not centered at the origin. 4. Solve applied problems involving ellipses. 5. Locate a hyperbola s vertices and foci. 6. Write equations of hyperbolas in standard form. 7. Graph hyperbolas centered at the origin. 8. Graph hyperbolas not centered at the origin. 9. Solve applied problems involving hyperbolas. 10. Graph parabolas with vertices at the origin. 11. Write equations of parabolas in standard form. 12. Graph parabolas with vertices not at the origin. 13. Solve applied problems involving parabolas. 14. Identify conics without completing the square. 15. Use rotation of axes formulas. 16. Write equations of rotated conics in standard form. 17. Identify conics without rotating axes. V. Sequences, Induction, and Probability 1. Find particular terms of a sequence from the general term.
2. Use recursion formulas. 3. Use factorial notation. 4. Use summation notation. 5. Find the common difference for an arithmetic sequence. 6. Write terms of an arithmetic sequence. 7. Use the formula for the general term of an arithmetic sequence. 8. Use the formula for the sum of the first n terms of an arithmetic sequence. 9. Find the common ratio of a geometric sequence. 10. Write terms of a geometric sequence. 11. Use the formula for the general term of a geometric sequence. 12. Use the formula for the sum of the first n terms of a geometric sequence. 13. Find the value of an annuity. 14. Use the formula for the sum of an infinite geometric series. 15. Understand the principle of mathematical induction and prove statements using mathematical induction. (time permitting) 16. Evaluate a binomial coefficient. 17. Expand a binomial raised to a power. 18. Find a particular term in a binomial expansion. 19. Use the fundamental counting principle. 20. Use the permutations formula. 21. Distinguish between permutation problems and combination problems. 22. Use the combinations formula. 23. Compute empirical probability.* 24. Compute theoretical probability.* 25. Find the probability that an event will not occur.* 26. Find the probability of one event or a second event occurring.* 27. Find the probability of one event and a second event occurring.* VI. Introduction to Calculus 1. Understand limit notation. 2. Find limits using tables. 3. Find limits using graphs. 4. Find one-sided limits and use them to determine if a limit exists. 5. Find limits of constant functions and the identity function. 6. Find limits using properties of limits. 7. Find one-sided limits using properties of limits. 8. Find limits of fractional expressions in which the limit of the denominator is zero. 9. Determine whether a function is continuous at a number. 10. Determine for what numbers a function is discontinuous. 11. Find slopes and equations of tangent lines. 12. Find the derivative of a function. 13. Find average and instantaneous rates of change. 14. Find instantaneous velocity. * Time permitting
PRECALCULUS MT134, COURSE SCHEDULE Week 1 1/20-1/24 (No School 1/20 Civil Rights Day) Week 2 1/27-1/31 WK Sec. Topics 2.1 2.2 2.3 2.4 2.5 Complex Numbers Quadratic Functions Polynomial Functions and Their Graphs Dividing Polynomials; Remainder and the Factor Theorems Zeros of Polynomial Functions Week 3 2/3-2/7 (No School 2/6 Parent/Teacher Conf) (No School 2/7 Granite State Conf) Week 4 2/10-2/14 Week 5 2/17-2/21 (Winter Break 2/24-2/28) Week 6 3/3-3/7 Week 7 3/10-3/14 Week 8 3/17-3/21 Week 9 3/24-3/28 Week 10 3/25-3/28 Week 11 3/31-4/4 Week 12 4/7-4/11 (Community Service Week 4/14-4/17) (No Classes 4/18 Good Friday) (Spring Break 4/21-4/25) Week 13 4/28-5/2 2.6 2.7 2.8 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 5.5 7.4 7.5 7.6 9.1 9.2 9.3 9.4 10.1 10.2 10.3 10.5 Rational Functions and Their Graphs Polynomial and Rational Inequalities Modeling Using Variation Exam 1: Sections 2.1 2.8 Angles and Radian Measure Trigonometric Functions: The Unit Circle Right Triangle Trigonometry Trigonometric Functions of Any Angle Verifying Trigonometric Identities Sum and Difference Formulas Double-Angle, Power-Reducing, and Half-Angle Formulas Product-to-Sum and Sum-to-Product Formulas Trigonometric Equations Exam 2: Sections 5.1 5.5 Systems of Nonlinear Equations in Two Variables Systems of Inequalities Linear Programming The Ellipse The Hyperbola The Parabola Rotation of Axes Exam 3: Sections 7.4 7.6, 9.1 9.4 Sequences and Summation Notation Arithmetic Sequences Geometric Sequences and Series The Binomial Theorem Week 14 5/5-5/9 (No Classes 5/9 Leadercast Conf) Week 15 5/12-5/16 Week 16 5/19-5/23 (Senior Trip 5/22-5/23) Week 17 5/26-5/30 (No School 5/26 Memorial Day) Week 18 6/2-6/6 (Final Exam Week) 10.6 Counting Principles, Permutations, and Combinations Exam 4: Sections 10.1 10.3, 10.5 10.6 11.1 11.2 11.3 Finding Limits Using Tables and Graphs Finding Limits Using Properties of Limits Limits and Continuity 11.4 Introduction to Derivatives Exam 5: Sections 11.1-11.4 Final Review FINAL EXAM