MATH 138 - Precalculus

1. Perform arithmetic operations, including conjugation, on complex numbers. Identify
complex solutions of equations.
2. Solve equations, including absolute value, radical, rational, rational exponent, exponential, and logarithmic. Solve equations that are quadratic in form.
3. Solve inequalities, including absolute value, polynomials of degree greater than 1, and
rational.
4. Find the equation of a circle by completing the square. Find the equations for the upper, lower, right, and left halves of a circle.
5. Find and simplify the difference quotient of algebraic functions.
6. Identify even and odd functions. Identify and sketch transformations of algebraic and
trigonometric functions.
7. Sketch algebraic functions, including piecewise and absolute value.
8. Find characteristics of a parabola, including the vertex, intercepts, axis of symmetry, and concavity.
9. Find the sum, difference, product, quotient, and composition of two or more functions.
10. Determine if a relation is a function and if a function is one-to-one. Find inverse functions by graphical and algebraic methods.
11. Construct and sketch exponential and logarithmic functions, including base e. Use laws of logarithms to manipulate expressions and solve equations. Solve exponential growth and decay problems.
12. Locate zeros of polynomial functions with degree greater than two using the Rational Zero Theorem, Intermediate Value Theorem, Remainder Theorem, Factor Theorem, and division. Sketch polynomial functions, including using end behavior.
13. Perform calculations using degrees and radians. Find arc length, circumference of a circle, area of a circular sector, and angular and linear speeds.
14. Solve right triangles using the six trigonometric ratios.
15. Know special angles in the unit circle. Find trigonometric values of angles in standard
position. Use reference angles to find values of trigonometric functions.

16. Use basic trigonometric identities to derive other identities, including addition, subtraction, multiple-angle, and half-angle. Verify and solve trigonometric equations using identities.
17. State the domain and range of algebraic and trigonometric functions and their inverses.
18. Use the law of sines and cosines to solve oblique triangles. Find the area of triangles using various methods, including Heron's formula.
19. Solve systems of linear and nonlinear equations by graphing, substitution, and elimination.
20. Write equations of circles, parabolas, ellipses, and hyperbolas in standard form. Sketch conics by identifying attributes including foci, directrix, vertices, axes, asymptotes,
horizontal and vertical orientations, and centers.
21. Perform vector operations including addition, subtraction, scalar multiplication, and dot product.
22. Convert between rectangular and polar coordinate systems. Sketch polar coordinates and equations.
23. Solve applied problems in the above areas.
24. Use technology as appropriate to enhance course objectives.

COURSE CONTENT: Topical areas of study include - ● Radicals and rational expressions
● Graphs of equations and functions
● Rational functions
● Exponential and logarithmic functions
● Quadratic, polynomial, rational, radical, and absolute value equations and inequalities
● Complex numbers
● Angles and trigonometric functions
● Right and oblique triangles
● Graphs of trigonometric functions
● Trigonometric equations and identities
● Conics