Part I Number Sense

1) Simplify and write all exponents as positive integers

  1. 5x5 (10x -6)b) (2x5y3/12x7y2)3c) 6x-8y2z-12/x5y-6z10

2) Explain the relationship among the following number types and give an example of each:

real, whole, natural, rational, irrational, complex, integer and imaginary

3) Classify each using the most specific type of number (see list above)

  1. ______
  2. -6- ______
  3. 66 ______
  4. ______
  5. 1/6 ______
  6. 6 + 6i ______
  7. 0 ______

4) Which property is shown for each example?

  1. 5x + 3y = 3y + 5x

b. 2 * ½ = 1

c. rational + rational = rational

d. 3 + 0 = 3

e. 3(x + 2) = 3x + 6

f. (x + 2)(x - 3) = 0

so either x + 2 = 0 or x - 3 = 0

5) Write each of the following in simplified radical form - at most only one radical!

  1. (2000y)¼b. a 4/5c. b -1/2

d. x 2/3 y 1/4e.

6) Write each with a fractional exponent in simplest form

  1. b. c.

d. 2

7) Simplify - answers should be in terms of i

  1. b. c.

8. Rewrite in a +bi form

  1. (3 + 2i) + (5 + 8i)

b. (3 + 2i) - (5 + 8i)

c. (3 + 2i)(5 + 8i)

Part II Functions

  1. The accompanying graph shows the temperature, in degrees Celsius, of a cup of coffee during a 10-minute interval.

  1. Is the graph above a function? Why or why not?
  1. What is the domain?
  1. What is the range?
  1. What is the value of f(2)? What does this mean about the coffee?
  1. What is the value for f(x) = 40? What does this mean about the jogger?
  1. What is the average rate of change between x = 1 and x = 2? What does this tell us?

2. On January 1, I deposited $200 into an account for my son. I will continue to deposit $200 each month until he graduates high school. If x represents the time, in months, and y represents the balance of the account, in dollars,

  1. what kind of function would best represent this situation?Why?

b. sketch a graph of how this situation would look

c. write an equation to model the graph

3. An object is launched directly upward at 48 feet per second (ft/s) from a platform 20 feet high.

  1. write an equation to model the path of the object.
  1. What will be the object's maximum height? When will it attain this height?

c. When will the object hit the ground?

4. Given f(x) = x2 + 8x + 15

Determine if if the function is increasing or decreasing along the following intervals:

  1. x<-5 ______
  2. -5<x<-4 ______
  3. -4<x<-3 ______
  4. x>-3 ______

Part III. Quadratic Functions

  1. Write in intercept form (factor)

write the answers using the correct notation

  1. what are the x intercepts
  2. what’s the y intercept
  3. vertex
  4. AOS
  5. sketch a graph to the right
  6. domain
  7. range

2. Write in vertex form (complete the square)

write the answers using the correct notation

  1. what are the x intercepts
  2. what’s the y intercept
  3. vertex
  4. AOS
  5. sketch a graph to the right
  6. domain
  7. range

3. Solve the equation below using the quadratic formula

write the answers using the correct notation

  1. what are the x intercepts
  2. what’s the y intercept
  3. vertex
  4. AOS
  5. sketch a graph to the right
  6. domain
  7. range