MS 100 Midterm Examination 24 June 2005 • Name:

1. Find the center (h, k) and radius of the circle (x − 1)² + y² =9

2. On Tuesday evening I was running and juggling back northbound into Piyuul from the Malem river bridge. I took 10.8 minutes to run the 1.826 kilometers.

a. Given that pace = time/distance, what was my pace on Tuesday?

b. I usually run and juggle (joggle) at a 6.5 minute per kilometer pace. Was I slower or faster on Tuesday evening than my usual pace?

3. For y = − x² + 5x − 4

a. Find the y-intercept.

b. Find the x-intercepts.

4. Solve for x: 3x² − 6x − 6 =0 by completing the square.

5. Multiply the following complex conjugates: (2.5 + 1.5i)(2.5 − 1.5i)

6. For y = x² − 5x + 8.5

a. Find the y-intercept.

b. Find the x-intercepts, whether real or complex.

7. Solve for x:

8. Solve the inequality and sketch the solution on a number line:

9a. Find the equation of the line through (− 2, 0) and (2.5, 2.25)

b.
Is y = − 2x − 5 parallel, perpendicular, or neither to
the line in 9a?

c. Is y = 2x − 5 parallel, perpendicular, or
neither to the line in 9a?

d. Is y = 0.5x − 5 parallel,
perpendicular, or neither to the line in 9a?

e. Is y = −
0.5x − 5 parallel, perpendicular, or neither to the line in 9a?

10. A yard of fabric is marked down from $2.50 per yard to $2.25 per yard. What is the percentage difference?

11. For y = x³ − 3x² − 6x + 8

a. Calculate the integer values of y for this equation over the domain − 3 ≤ x ≤ 5

b. Sketch a graph of the equation.

c. Determine the y-intercept.

d. Find the x-intercepts.

e. Does the graph have x-axis symmetry, y-axis symmetry, origin symmetry, or no symmetry?

f. Is the graph symmetric about any line? If so, what line?

g. Is the equation a function?

h. Does the graph pass the vertical line test?

i. Mark the increasing and decreasing intervals on the graph.

j. Mark the sections of positive and negative curvature on the graph.

k. Mark the local minimum and maximums on the graph.

l. Mark the inflection point.

m. Use the x-intercepts to determine the factorization of the equation.