**TEXT: Precalculus, 3 ^{rd} Edition, by Faires and DeFranza
NOTE: A graphing calculator is required for this course. The TI-86 should be
recommended for students who must purchase a new calculator for the course.
Students
who already own a graphing calculator should be encouraged to use the one they
have.
The main objective of this course is to prepare students to take MA 1713
Calculus I. The
course focuses on the specific pre-calculus concepts that are needed in Calculus
I in the
context and at the level of mathematical maturity normally encountered in
calculus.
Additionally, students will be taught the effective use of a graphing
calculator. The
terminology, level of exposition, and use of the calculator in the course should
closely match
what is commonly encountered in Calculus I. At least three graphing calculator
projects
that emphasize mathematical correctness and quality of presentation should be
assigned
and should reflect in the final grade. At least one of these should be a group
project.**

- know the properties of inequality and the definition and properties of absolute value.

- be able to find the solution set of linear and non-linear inequalities in one variable

using analytical and graphical methods.

- know how to represent intervals graphically and using set and interval notation.

- know the distance and midpoint formulas for two points in the coordinate plane.

- know how to put the equation of a circle in standard form by completing the square,

find the coordinates of the center and the radius, and graph the circle.

- know the difference in an equation and an identity.

- be able to determine the intercepts and symmetries of an equation in two variables and

graph the equation without (or with a graphing calculator, as needed).

- be able to use the

calculator, as needed.

- know the definitions of function, domain, range, value of a function, odd function and

even function.

- be able to evaluate functions analytically and by using their graphs.

- be able to find the domain of algebraic functions.

- know the definitions of linear and quadratic functions and how to find their intercepts.

- be able to find the slope and y-intercept of a linear function, the critical number of a

quadratic function, the extreme value of a quadratic function and to write linear and

quadratic functions in standard form.

- be able to determine whether lines are parallel or perpendicular to a given line.

- be able to write the equations of lines in point-slope, slope-intercept and general form.s

Section | Suggested minimum course Assignment |

1.2 1.3 1.4 1.5 1.6 1.7 1.8 |
p. 12:
1,2,5,7,9,12,16,19,27-35(odd),38,41,43,49,53,55,58,60,61 p. 19: 6,9,12,13,17,19,21,34,42,43,45,49,51,55,61,63 p. 25: 1-8,11,13,21,25,28,30,33,35,37,38-43 p. 32: 1bc,3bd,4,5,8,9,12 p. 46: 1acg,2h,3cde,4,5,7-15,17,20,21,23-31,37,41-51(odd), 52-55,57,61,68,69,71 p.58: 3,7,11,13,15,16,17bd,19,20,22,23-31(odd),35,37 p. 69: 3,7,11,13,20,21,23,28,29,31,33b,34,37,41 |

11 hours |

**Chapter 2, Sections 2.1 – 2.5: **After completing Chapter 2,
a student should:

- know the properties of, the domain and range, and be able to sketch the graphs

the absolute value function, the square root function, the cube root function,

and the greatest integer function.

- be able to graph more complicated functions from simpler functions by

understanding the algebra that produces horizontal or vertical shifts,
dilations,

or compressions in the graph.

- know the definitions o sum, difference, product, quotient and composition of

two functions and the inverse of a function.

- be able to find the domain of various combinations of algebraic functions.

- know the properties of inverse functions and how to make the graph of

of its inverse from the graph of a one-to-one function.

- understand the significance of the vertical and horizontal line tests as
applied to

a graph and whether or not the defining function is one-to-one.

Section | Suggested minimum course assignment |

2.2 2.3 2.4 2.5 |
p. 86: 3,13,16,17ace,18a,19,22,25,27,30,33a-h p. 95: 3,6,7,11,14,18,19,21,23,25 p. 104: 1,3,5,8,10,13,16,17,20,21a,22,28,29,33,37 p. 114: 1-10,13,17,19,23,25,28,30,32,33,37,39 |

4 hours |

**Chapter 3, Sections 3.1 – 3.6:** After completing Chapter 3,
a student should :

- be able to define polynomial, rational and irrational function.

- be able to find intercepts and the behavior of the function as x → ∞ (or −∞ ).

- be able to use a graphing calculator to graph the polynomial and to find
critical

numbers and relative extreme values.

- know the Intermediate Value Theorem, the Division Algorithm, the Factor

Theorem, the Rational Zero Theorem, Descartes’ Rule of Signs and the

Fundamental Theorem of Algebra and how to apply them in solving polynomial

equations and finding the zeros of polynomial functions.

- be able to find the domain, intercepts, vertical, horizontal and slant
asymptotes

of rational functions and sketch their graphs with the help of a graphing

calculator.

- be able to find the domain and asymptotes, if they
exist, and sketch the graph

of irrational functions with the help of a graphing calculator.

- know how to perform complex arithmetic and determine complex roots of

polynomial equations.

Section | Suggested minimum course assignment |

3.2 3.3. 3.4. 3.5. 3.6 |
p. 134: 1,3,4,5,7,11,13,15,23,2
6,33,34,35,39,41,43,47 p. 144 5,9,15,17,21,25,29,33,35,38,39 p. 157: 1-7,9,12,13,16,17,20,23,27,31,34,35,37,39,43 p. 163: 1,3,9,11,13,19,25,31 p. 172: 2,5,8,13,16,18,19,21,23,25,26,28,37,41,43,47,48,51,55: |

8 hours |

**Chapter 4, Sections 4.1 – 4.9: **After completing Chapter 3,
a student should:

- be able to define radian measure.

- be able to convert between degree and radian measure.

- know the definition of sine of t and cosine of t, where t is a real number and

that they are bounded, periodic functions.

- know that sine is an odd function and cosine is even.

- know the sine and cosine of the special angles (in radians) and the quadrantal

angles.

- be able to use reference angles to find the sine and cosine.

- be able to determine the amplitude, period and phase shift of sine and cosine

functions and sketch their graphs.

- know the definitions of the tangent, cotangent, secant and cosecant functions

in terms of sine and cosine, be able to determine their values for the

special and quadrantal angles, know their periods,aand be able to sketch their

graphs.

- know the Pythagorean identities and the sum, difference and double angle

identities for sine and cosine.

- know the half-angle identities and their derivation for sine and cosine,

i.e.,
.

- be able to state and apply the trigonometric identities that commonly arise in

calculus and use them to solve problems.

- be able to solve applications using right-triangle trigonometry.

- be able to restrict the domain of trigonometric functions to produce

trigonometric functions that are invertible.

- be able to define the inverse trigonometric functions and give their domains,

ranges, and sketch their graphs.

- be able to work problems that involve inverse trigonometric functions.

- know the Law of Sines and the Law of Cosines and understand the

ambiguous case of the Law of Sines.

- be able to apply the Law of Sines and Law of Cosines to applications

involving oblique triangles.

- know how to add sine and cosine functions with the same argument to produce

a single sine (or cosine) function.

- know and be able to apply Heron’s formula and to find the area of a

triangle, given two sides and an included angle.

Section | Suggested minimum course assignment |

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 |
p. 187: 1-9,
11-17(odd),18,21,24,25,29,31,33,34,35,38,40 p. 200: 1,2,3,5,6ab,7-53(odd) p. 210: 1-8,13,16,19,23-35(odd),36,37,40 p. 219: 1-9, 9-17(odd), 21,23,29,31,35,39,41 p. 231: 1-53(odd) p. 237: 1-17(odd) p. 246: 1-43(odd) p. 260: 1,5,9,13,15,17,19,22,23,25 |

12 days |

**Chapter 5, Sections 5.1 – 5.4:** After completing Chapter 5,
a student should:

- know the definition of e, how to approximate e, the definition of the natural

exponential function, its properties, and how to work problems involving

compound interest, and exponential growth or decay.

- know the definition of logarithm and natural logarithm and the properties of

logarithmic functions.

- be able to graph exponential and logarithmic functions and know the change of

base formulas for both exponential and logarithmic functions.

- be able to solve exponential and logarithmic equations in exact form and to

approximate solutions using a calculator.

Section | Suggested minimum course assignment |

5.2 5.3 5.4 |
p. 282: 1,3,5,7,11,15,17,19,21,24,25,30,32a,38 p. 292: 1,5,9,13,17,21,25,29,32,33,37,39,53,57,61,65 p. 298: 1,5,7,9,13,17,19,22: |

3 days |

Other Pertinent Information for Instructors

1. The fall and spring semesters normally contain 45 class hours on a MWF

schedule; however, in the 2003-2004 academic year they contained 42 hours, only.
The summer

terms typically contain 42 hours. Sections 6.1 through 6.4 should be viewed as

optional.

The Course Outline suggests 38 hours of lecture. Three or four scheduled onehour

tests should be administered each semester in addition to a comprehensive

final examination.

2. Instructors are expected to teach their students how to use their calculators
wisely

and well.

3. Instructors are expected to use a graphing calculator
for the purpose of

enhancement and clarification of material in the course and for speed and

accuracy in calculation. They should teach students to give exact answers, when

possible, and to resort to calculator approximations at the appropriate stage in

their calculations.

4. Instructors should be aware of the symbolic manipulation capabilities of
certain

calculators (e.g. TI-89) and should exercise care in the construction of exams
so

that students using such calculators do not have an unfair advantage.

5. Calculators should be used on all scheduled tests and on the final
examination.

6. If time allows, students should be introduced to coordinate transformations

involving translations and rotations in the context of conic sections.

7. Instructors should take advantage of computer graded homework assignments
that

are available on the ILRN website of Brooks/Cole Publishing.

8. Instructors should assign at least three calculator projects during the
course of the

semester. The project reports should be graded for correctness, grammar,
spelling

and clarity of exposition. Graphs contained in the report should be neat, axes

should be labeled and tick marks should be labeled with appropriate units.