Exercícios de Física Geral 2010

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Physics 2010 Sid Rudolph
General Physics
MATH EXERCISES
The following small collection of practice mathematical exercises is intended to focus your
attention on some of the mathematical skills you were expected to bring with you to this course. 
Please take the time, no more than an hour, to go over these exercises before you meet your first
Physics 2010 discussion section. Your TA’s have been given a copy of these exercises as well
as a brief review document. They will hand that document out to all of you tomorrow. The
items included in these exercises are regarded as minimal skills you need for this course. 
Obviously there are many more.
EXERCISES:
A. Complete the following and/or express in scientific notation:
2. 86,400 =
3. 9,816,762.5 =
4. 0.0000000398 =
4. (4 x 108)(9 x 109) =
5. (3 x 107)(6 x 10-12) =
6. 75 x 10-11/5 x 10-3 =
7. (3 x 106)(8 x 10-2)/(2 x 1017)(6 x 105) =
Note: the two numbers to the right of the “divide” (“/”) symbol are in the denominator.
B. In the following exercises, solve for x:
8. a = 1/(1+x)
9. 3x - 5 = 13
10. ax - 5 = bx + 2
11. 5/(2x + 6) = 3/(4x + 8)
C. Complete the following:
12. 3
2
 x 3
3 =
13. x5x-8 = 
14. x
10
/x-5 =
15. 51/3 = (Use your calculator.)
16. 601/4 = (Use your calculator.)
17. (x
4
)
3 = 
D. Solve the following quadratic equations:
18. x2 + 2x -3 =0
19. 2x2 - 5x +2 = 0
20. 2x2 - 4x -9 = 0
E. Exercise in graphing and linear equations:
21. Draw graphs of the following straight lines:
(a) y = 5x + 3 (b) y = -2x + 4 (c) y = -3x - 6
22. Find the slopes of the straight lines given in exercise E.21.
23. Find the slopes of the straight lines that pass through the following sets of points.
(a) (0, -4) and (4, 2) (b) (0, 0) and (2,-5), and 
(c) (-5, 2) and (4, -2)
F. Simultaneous Equations:
Solve the following pairs of simultaneous equations involving two unknowns:
24. x + y = 8 
x - y = 2
25. 98 - T = l0a
T - 49 = 5a
26. 6r + 2y = 6
8r - 4y = 28
G. Trigonometry:
27. Evaluate the following trigonometric expressions:
(a) sin30o (b) cos150o (c) tan313o
(d) If 0.375 = sin(�) determine values of � between 0o and 360o.
(e) If -0.750 = cos(�) determine values of � between 0o and 360o.
(f) In exercise E.21b what is the angle, measured counterclockwise from the positive
x-axis, to the straight line as given?