Physics 202 Math Review

(stuff you should already know)

Here are some exercises which include many mathematical skills you should be proficient with. You should be able to do these without having to look anything up in a book. Just sit down and do them. This is not an exhaustive sample of the necessary math skills, but it gets you on the right track. Note that many of these are the same ones handed out at the beginning of phys201. More calculus related problems have been added at the end.

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

3. (a) You are given a right triangle with one acute angle of 30^o 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 35^o. 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 90^o. 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

(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)

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. For velocity as a function of time, with velocity (v) in m/s and time (t) in seconds, what does the area under the graph v= 2t³-2t between t=0 and t=3 represent? What is the numerical value of this "area"?

9. Vector A has a magnitude of 4 units and a direction of 140 degrees clockwise from the positive x-axis. Vector B has a magnitude of 7 units and a direction of 300 degrees clockwise from the positive x-axis. Determine the vector C = 2A+ B in both component and magnitude/direction form.

10. Calculate the value of the integral of (x dx)/(x²+h²)^3/2 between the limits -L/2 to +L/2

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