Learning Outcomes for Precalculus
A. Testing Guidelines:
The following exams should be scheduled:
1. A one-hour exam at the end of the First Quarter.
2. A one session exam at the end of the Second Quarter.
3. A one-hour exam at the end of the Third Quarter.
4. A one session Final Examination.
B. Graphing calculators are required.
Learning Outcomes
For
MAT 1375/ MA 375 Precalculus
1. Students will be able to
• Find the distance and midpoint between two points.
• Determine the slope, intercept, and the equation of a line.
• Solve simple linear, quadratic and absolute value inequalities.
2. Students will be able to
• Determine the domain, and range of a given function.
• Find the sum, difference, product, quotient, and composition of functions.
• Determine the roots and relative extrema of polynomials
• Sketch the graph of polynomial, exponential and logarithmic functions with the
help of a graphing calculator
• Solve problems involving polynomial, exponential, and logarithmic functions.
• Find the amplitude, phase shift, and period of trigonometric functions.
• Students will know the domain and range of inverse trigonometric functions and
be able to calculate their values
corresponding to the special angles.
3. Students will be able to
• Write a complex number in the rectangular and polar forms.
• Multiply and divide two complex numbers.
• Use DeMoivre’s Theorem to find the nth root of a complex number.
• Find the magnitude, direction angle, horizontal, and vertical components of a
vector.
4. Students will be able identify and graph circles, parabolas, ellipses, and
hyperbolas.
5. Students will be able to find
• The nth term of arithmetic and geometric sequences.
• The nth partial sums of arithmetic and geometric sequences.
• Terms of a binomial expansion using the Binomial Theorem.
6. Students will be able to use a graphing calculator to assist in the above.
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MAT 1375 Mathematical Analysis Contemporary Precalculus: A Graphing Approach by T. Hungerford & D. J. Shaw 5th edition
| Session | Precalculus | Homework |
| 1 |
1.1 The Real Number System (pp. 2 – 13) 1.2A Special Topics: Absolute Value Equations (pp. 32 – 33) |
P. 13: 37 - 47 all, 123 - 134 all P. 33: 1 - 4 all |
| 2 |
4.6A Special Topics: Absolute Value Inequalities
(pp. 317 – 320) 2.1 Graphs (pp. 78 – 87) |
P. 320: 1 -6 all P. 89: 1 - 6 all, 9, 11, 15, 16, 19, 27 |
| 3
|
2.2 Solving Equations Graphically and Numerically
(pp. 92 – 99) 4.6 Polynomial and Rational Inequalities (pp. 308 – 315) |
P. 100: 7, 9, 21 - 27 odd P. 315: 2, 3 – 11 odd, 25-28 all Include inequalities of the form:  |
| 4
|
12.1
Sequences and Sums (pp. 826 ) Give the definition of a sequence on page 826 then go to section 12.2 12.2 Arithmetic Sequences (pp. 837 – 842) |
P. 842: 1, 6, 7, 17 , 25, 33, 37, 41,
45, 61, 63
|
| 5 | 12.3 Geometric Sequences (pp. 844 – 850) 12.3A Special Topics: Infinite Series (pp. 882 – 856) |
P. 850: 1 - 7 odd, 13, 15, 23, 33,
39-47 odd P. 856: 1 - 4 all, 7, 9, 10, 11, 13 |
| 6 | 1.3 The Coordinate Plane (pp. 39 – 48) | P. 48: 13 – 16 all, 27, 55 - 67 odd, 71 - 77 odd |
| 7 | First Examination | |
| 8 | 1.4 Lines (pp. 53 – 64) | P. 64: 2, 3, 5, 13-35 odd, 43-63 odd, 75,77 |
| 9 | 10.1 Circle and Ellipses (pp. 671 – 682) | P. 683: 1 - 6 all, 7 - 13 odd, 33 - 41 odd, 45, 47 |
| 10 | 10.2 Hyperbolas (pp. 686 – 697) | P. 697: 1 - 6 all, 11, 13, 15, 17, 25-31 odd |
| 11 | 10.3 Parabolas (pp. 700 – 708) | P. 710: 1 - 6 all, 17 - 25 odd, 35-39 odd, 55 - 61 odd |
| 12 |
3.1 Functions (pp. 142 – 148) 3.2 Functional Notation (pp. 151 – 158) |
P. 148: 1, 3, 11-17 odd, 23-27 all,
32, 34, 42-44 all P. 158: 1 - 5 odd, 13, 17, 21 |
| 13 |
3.2 Functional Notation 3.3A Special Topics: Graph Reading (pp. 168 – 169) |
P. 159: 27 - 31 all, 39, 41, 43 55,
57 P. 171: 12-21 all, 47, 50 |
| 14 |
3.4 Graphs and Transformations (pp. 179 – 186)
(optional) 3.5 Operations on Functions (pp. 195 – 201) |
P. 186: 1 - 8 all, 10, 12, 15, 23,
24, 26,28 P. 202: 3, 6, 11, 12-17 all, 19, 22, 25, 31-37 odd, 59 |
| 15 | Midterm Examination | |
| 16 |
4.2 Polynomial Functions (pp. 250 – 257) 4.2A Special Topics: Synthetic Division (pp. 259 – 261) |
P. 257: 11, 12, 18, 19, 23, 27,
39,41, 51, 53, 55, 56, 61 P. 262: 3, 5, 9, 10, 13, 15 |
| 17 | 4.3 Real Roots of Polynomials (pp. 262 – 268) | P. 268: 1, 3, 5, 17-19 all, 23, 25, 29, 31, 34 |
| 18 |
4.4 Graphs of Polynomial Functions (pp. 270 –
278) 4.8 Theory of Equations ( pp. 328 - 332) |
P. 278: 1 - 12 all, 19 – 24 all, 25,
29, 31, 43, 45 P. 332: 1, 3, 13, 17, 19, 21, 25, 26, 29, 30, 31, 45, 47 |
| 19 | 5.2 Exponential Functions (pp. 357 – 365) | P. 365: 1 - 5 all, 49, 51, 64, 67, 71, 72, 74 |
| 20 |
5.2A Special Topics: Compound Interest and the
Number e (pp. 369 – 373) |
P. 374: 3-9 odd, 11, 19, 23, 27, 28 |
| 21 |
5.3 Common and Natural Logarithmic Functions (pp.
375-382) 5.4 Properties of Logarithms (pp. 385 – 390) |
P. 383: 5, 9, 11, 15, 19, 23, 43, 45
57, 59, 77, 79 P. 390: 1 - 19 odd |
| 22 |
5.5 Algebraic Solutions of Exponential and
Logarithmic Equations (pp. 399– 406) |
P. 406: 1, 7 - 11 odd, 17, 19, 53 , 56 |
| 23 | Third Examination | |
| 24
|
6.4 Basic Graphs (pp. 466 – 474) (optional) 6.5 Periodic Graphs and Simple Harmonic Motion (pp. 477 – 486)
|
P. 474: 11 - 21 odd P. 486: In these problems modify the instructions to require that the graphs are plotted over one period:1, 2, 5, 6, 27, 28, 31, 32: Optional Problems: 15, 18, 23, 26 |
| 25 |
7.4 Inverse Trigonometric Functions (pp. 545 –
553) 9.1 The Complex Plane and Polar Form of Complex Numbers (pp. 626 – 630) |
P. 553: 1 - 17 odd P. 630: 1-5 odd, 9, 13, 25, 27, 37-45 odd, 53, 55, 59, 61 |
| 26 |
9.2
DeMoivre’s Theorem and nth Roots of Complex Numbers (pp. 632 – 638) |
P. 638: 1, 3, 13, 15, 19, 20, 23, 33,
41 |
| 27 | 9.3 Vectors in the Plane (pp. 639 – 650) | P. 651: 5, 11, 15, 17, 21,27-49 odd |
| 28 | 12.4 The Binomial Theorem (pp. 857 – 862) | P. 862: 3, 4, 7, 23, 24, 27, 37, 49, 51 |
| 29 | Final Examination Review | |
| 30 | Final Examination |