Math 130 - Pre-Calculus

Credits: 3

Course Description: Preparation for first-year calculus. Covers symmetry, graphs, functions, lines, parabolas and max-min problems, exponential and logarithm functions, exponential growth, and the trigonometric functions and their inverses.

Pre-Requisites: A suitable score on the Math placement test B only.

Note: No student receives graduation credits for MATH 130 if it is taken after successful completion of any higher math course. Students who have successfully completed MATH 130 may not subsequently take MATH 129 for credit. Students may take MATH 130 after MATH 129 only with explicit permission of the department, and then only for two credits.

Frequency:

Current Textbook: Precalculus Mathematics, Fifth Edition, by Max A. Sobel and Norbert Lerner, published by Prentice Hall, 1995. Check with your instructor to make sure this is the textbook used for your section.

Chapter 2:

2.1 Function: domain, range, piecewise-defined and function graph.
2.2 Lines: slope of segment, concept of line, and slope of line.
2.3 x and y intercepts formula.
2.4 Piecewise-linear functions: absolute value, step functions, etc.
2.6 Quadratic functions: graph parabolas, translations, concavity, increasing/decreasing, symmetry, graphs and vertical line functions test.
2.7 Graph quadratic formula, the discriminant, solutions as graph intercepts.
2.8 Quadratic function: extrema, max-min word problems.

Chapter 3:

3.1 Techniques for graphing: symmetry, odd-even, translation, stretch; slope between two parabola points.
3.2 Rational graphs, asymptotes and holes.

Chapter 4:

4.1 Distance formula and circles.
4.4 Functions: arithmetic and composition; notation.
4.5 Function inversion.

Chapter 5:

5.1 Exponential functions.
5.2 Logarithmic functions; graphs and asymptotes.
5.3 Logarithm laws; change of base formula.
5.4 Natural log and exponential functions: base and graphs.
5.5 Exponential growth: function and lines.

Chapter 6:

6.1 Angle measure, radians, angular speed.
6.2 Trigonometric functions: sine and cosine, fractions, quadrants and standard position angle.
6.3 Graph sine and cosine; period, amplitude and phase.
6.4 Graph trig functions and vertical asymptotes.
6.5 Inverse trig functions: domain, range, graphs, symmetries, special value and radical form.

Chapter 7:

7.1 Sine, etc., as ratios, for acute angles and special values.
7.2 Right triangle trigonometry; solving right triangles.
7.3 Identities involving Pythagoras and the trig function definitions.
7.4 Addition Laws for sin, cases for sin and cos.
7.5 Double and half angle formulae.
7.6 Solving trig equations; the corresponding graph intersections.

Chapter 8:

8.1 The Law of Cosines.