MAT 123 - College Mathematics I: Precalculus

Objectives

1. Know the development of the binomial theorem; solve problems using binomial coefficients.
2. Understand and use Pascal's triangle.
3. Solve inequalities (linear, nonlinear, absolute value).
4. Graph the solutions of inequalities using open, closed, half-open, and infinite interval notation.
5. Find the distance between two given points.
6. Recognize the equation of a circle, find the coordinates of the center, and determine the radius (and diameter).
7. Develop the midpoint formula. Use it to find the mid-point coordinates of a well-defined line segment.
8. Make an accurate graph of a given equation in x and y. Use symmetry tests.
9. Discuss the meaning of variable and domain of a variable.
10. Explain the meaning of function in terms of domain, range, and one-to-one relation.
11. know the meaning of identity function, constant function, even function, and odd function.
12. Given the graph of a function, state the interval(s) on which it is increasing, decreasing, and constant.
13. Graph a given function.
14. Know to shift a graph horizontally and vertically.
15. Know how to reflect and/or stretch a graph.
16. Recognize the equation of a linear function.
17. Know the meaning of, and how to determine, the slope of a line.
18. Write the standard form of a given linear equation in x and y.
19. Find the equation of a line using point-slope and slope-intercept forms.
20. Know how to add, subtract, multiply, and divide functions.
21. Determine the specified composite function of two given functions.
22. Determine the inverse function of a given 1-1 function.
23. Determine if a given function is one-to-one.
24. Know the form of an equation of a quadratic function.
25. Graph a given quadratic function.
26. Find the maximum or minimum value of a given quadratic function.
27. sketch the graph, including all intercepts and linear asymptotes, of a given rational function.
28. Sketch the graph of a given exponential function.
29. Become familiar with the natural exponential function (ex) and some of the applications of this function.
30. Sketch the graph of a given logarithmic function.
31. Know and be able to use the major properties of logarithms.
32. Become familiar with common and natural logarithms.

Optional

1. Express in equation form a stated variation between two variable expressions.
2. Understand and use the intermediate value theorem.
3. Understand and use the remainder and factor theorems.
4. Understand the fundamental theorem of algebra.
5. Understand the meaning of the division algorithm for polynomials.
6. Know the meaning of multiplicity of a zero of a polynomial.
7. Know how to determine the number of zeros of a polynomial.
8. Use Descartes' rule of signs.
9. Understand upper and lower bounds for solutions of an equation.
10. Determine the rational zeros of a given polynomial function.
11. Recognize the equation of a conic section and sketch the graph.

Back to the top

Syllabus

Back to the top