.Prerequisites for MATH 2413 – Calculus I
In order to succeed in calculus, students need to have taken a trigonometry course and a precalculus course and to have current knowledge of the material in those courses.
If you have forgotten the material in those courses, this sheet can serve as a study guide to remind you of what you need to review. By the time you go to your first calculus class, you should be able to do at least 14 of the problems in Part I and 7 of the problems in Part II. Many instructors will test you on this material at the beginning of your calculus course and that test will be part of your grade in the course.
If you cannot work enough of the problems correctly in each part below, you should take a trigonometry course and/or a precalculus course before you register for calculus.
Part I.
1. Write the equation of a line through (2,-3) and perpendicular to .
2. For 
, calculate 
, 
, and 
.
3. State the domain of each function:
4. For 
and 
, find 
.
5. For f(x) = 2x + 3, find the inverse function of f.
In problems 6 – 9, solve for x:
6. 
7. 
8. 
9. 
10. Simplify: 
11. Find all rational roots of 
.
In 12-18, sketch the graph without using a graphing calculator or computer software. In each, you should be able to describe the general shape and then plot a few crucial points to sketch it.
12. 
13. 
14. 
15. 
16. 
17. 
18. 
Part II.
1. Graph: 
In 2 – 5, evaluate:
2. 
3. 
4. 
5. 
6. Solve: 
In 7 – 10, convert each of the expressions on the left to the one on the right using trigonometric identities.
7. 
,
8. 
, 
9. 
, 
10. 
, 
Answers:
1. 
2. 
, 
, 
3. f has domain all real numbers, g: 
, h has domain all positive real numbers except 2, j has domain all real numbers except 0 or 1.
4. 
5. 
6. 
7. 
or 
8. 
9. -3
10. 
11. -2, 3
12. parabola, open to the right, vertex (0,0). See graph.
13.
14. hyperbola, asymptotes at 
, foci 
15. ellipse, center (4, -2)
16.
17.
18. ellipse, center (3, 0)
Part II.
1. Amplitude 5, horizontal shift 
, period 
.
2. 
3. undefined
4. 
5. 1
6. 
| where n is an integer}
7. and 8. Use the basic trig identities
9. use the formula for 
10. One possible solution:
