The following is meant to jump start your math skills. Except for the question 5 which is Calculus, you are assumed to be comfortable with this material. Ask if you have any questions.  Note that Appendix E in our book has a brief math review. 

1. Find the following without the use of a calculator:
a. z³ z³ for z = 2
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)²

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. 1006
f. 0.000000000019

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 diagonal BC 20 m long and angle BCD 35^o. Find the lengths of each of the sides of the rectangle.
(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
(c) v_f² = vo² + (1/2)at² : find a if v_f = 0, v_o = 20, and t = 4
(d) F = mv²/r : find r if F = 455, m = 94, and v = 22

5. Determine the derivative with respect to the indicated variable.
a. 3x² -3x + 3 (d/dx)
b. 9z⁵ + 4z² (d/dz)
c. 2 Cos (5 t) (d/dt)

6.
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 volume of a cube with an edge length of 2 cm?
d. What is the surface area of the above cube?
e. What is the volume of a sphere with diameter of 1.5 m