Physics 201 Math Review

(stuff you should already know)

Here are some exercises which include many mathematical skills you should be proficient with. This is not an exhaustive sample of the necessary math skills, but it gets you on the right track.

1. Find the following without the use of a calculator:

a. z3 z5

b. 107 x 10-3

c. (4 x 104)/(2 x 10-6)

d. (2.5 x 10-6)(4x106)

e. (1.6 x 10-19)2

f. (6 x 106)(4 x10-5)4

g. (0.004 x 32,000 x 0.6)/6400 x 3000 x 0.08

2. Express the following as powers of 10 (i.e., scientific notation)

a. 32,600

b. 0.831

c. 0.0002

d. 186,000

e. (0.000081)1/2

f. 1006

g. 0.000000000019

h. 300,000,000

3. (a) You are given a right triangle with one acute angle of 30o and the hypotenuse of length 10 cm. Find the other acute angle and the lengths of the other two sides.

(b) ABCD is a rectangle with the diagonal, AC, 20 m long and angle DAC 35o. Find the lengths of sides AB and AD.

(c) In right triangle ABC, AB is 4 cm long, BC is 3 cm long, and angle ABC is 90o. Find the length of side AC and the size of angle CAB.

4. Given the following equations, solve for the indicated unknown.

(a) 3t2 = 5t + 2: find t

(b) 50 = 10 + 5a : find a

(c) vf2 = vo2 + (1/2)at2 : find a if vf = 0, vo = 20, and t = 4

(d) F = mv2/r : find r if F = 455, m = 94, and v = 22

5. You are driving to Columbia, SC and due to a traffic jam can only go 30 mph for the first 20 miles. After that you drive the remaining 90 miles at 60 mph. Sketch a graph of distance versus time, and one of speed versus time.

6. Determine the derivative with respect to the indicated variable.

a. 3x2 -3x + 3       (d/dx)

b. 3 Sin2(4 x+ p)       (d/dx)

c. A Cos (k x - w t)       (d/dt)

7.

a. What is the area of a circle with a diameter of 8 cm?

b. What is the circumference of the circle above?

c. What is the area of a sphere with a radius of 5 cm - express the answer in square meters.

d. What is the volume of a cube with an edge length of 2 cm?

e. What is the surface area of the above cube?

f. What is the volume of a sphere with diameter of 1.5 m

8. What is the area under the graph represented by the function y= 2x3-2x between x=0 and x=3?

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