Mathematics 2121-01
Calculus for Life Sciences I
Fall 02
Dr. A. Shlapentokh
Study Guide for Test #1

1. Which of the following statements is correct ?
(a)
(b)
(c)
(d)
2. Let . What is ?
3. Let . What is ?
4. Graph .
5. Which of the following graphs can be the graph of ?

(a)
(b)
(c)
6. Find the domain of .
7. Solve: .
8. Solve: .
9. Find the domain of .
10. Find the domain of .
11. Find the slope of the line passing through the points and .
12. Which of the following lines do not have slope ?
(a) Line passing through the points (1,2) and (1,3).
(b) Line passing through the points (1,2) and (2,3).
(c) Line passing through the points (1,2) and (-1,3).
(d) Line passing through the points (1,2) and (0,2).
13. Write down an equation of a line passing through the points (-1,2) and (2,4).
14. Write down an equation of a line passing through the points (-1,3) and (-1,4).
15. Write down an equation of a line passing through the points (-1,3) and (3,3).
16. Find the slope and the -intercept of the line with the equation .
17. Write down an equation of a line with -intercept equal to 5 and slope equal to 3.
18. A nurse is mixing two solutions. The first solution contains 0.7 mg of substance A per ounce of solution. The second solution contains 1.0 mg of substance A per ounce. In what proportions should the two solutions be mixed to obtain a solution containing 0.8 mg of substance A per ounce ?
19. Graph .
20. Graph on the coordinate plane.
21. Graph on the coordinate plane.
22. Graph the following system.


23. A lab assistant is preparing a meal for a lab rat. The meal will consist of two types of food. The first type of food has 100 calories and 20 mg of vitamin A per ounce. The second type of food has 50 calories and 5 mg of vitamin per ounce. The rat has to get at least 200 mg of vitamin but no more than 500 calories. Describe all the food combinations which can be fed to the rat.
24. Find the intercepts of the parabola .
25. Write down the equation of the circle centered at (2,3) and with the radius equal to 3.
26. What is the center and the radius of the circle ?
27. Let , let . What is the formula and the domain for ?
28. Let let . What is the formula and the domain for ?
29. Let let . What is the formula and the domain for ?
30. Graph .
31. Graph .