1. Find the equation of the line seen on the graph below. Note that the line of the equation passes through the intersections of the grid lines.
2. On the same graph above, sketch the equation:
3. Solve the following equation for x:
4. In a period of one week the price of gas went from $5.66 to $5.84 What is the percentage increase in the price of gas? Answer: 3% or 3.2% or 0.03 or 0.032. NOT 0.03%! That means 0.0003!
5. The following graph (may be on the next page) has the form y = x² + bx + c. Determine b and c. That is, use the graph to find the equation of the curve, the lead coefficient on the squared term being equal to one.
x = −16, x = 18 ∴ x + 16 = 0, x − 18 = 0 ∴ (x+16)(x−18)=0 ∴ y = x² − 2x − 288
6. Yes. Does the graph in number five pass the vertical line test?
7. Yes. Is the graph in number five a function?
8. On the graph in number five label the zeros of the function, the y-intercept, the vertex, and the axis of symmetry.
9. No. Does the graph for number five have an inflection point?
10. Use the following equation for 10a to 10e:
10a. y = 16 Find the y-intercept (where x = 0).
10b. x = 8 + 8i, x = 8 − 8i Find the x-intercepts whether real or imaginary (roots, where y = 0).
10c. axis of symmetry x = 8 Find the x-value for the axis symmetry.
10d. (8, 8) Find the coordinates of the vertex.
10e. m = 0.25x − 2 Toughie: Find the equation of the slope.
11. Add: (x − 4 + 8i) + (x − 4 − 8i). Solution: 2x - 8
12. Multiply: (x − 4 + 8i)(x − 4 − 8i)
13. Yes Does the following data represent a function?
| x | y |
|---|---|
| −9 | 81 |
| −4 | 16 |
| −1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 4 | 16 |
| 9 | 84 |
14. No. Does the following data represent a function?
| x | y |
|---|---|
| 9 | −3 |
| 4 | −2 |
| 1 | −1 |
| 0 | 0 |
| 1 | 1 |
| 4 | 2 |
| 9 | 3 |
The test was based in large part on questions from test one and test two. As noted in class, I focused on those which students missed on those tests as based on the item analysis handout. There was little in the way of new material on the test.
There were theoretically 40 possible points including the slope of the quadratic, 38 if that "toughie" is disincluded. No one exceeded 35 points on the test, and the course average was far lower at 46%, a solid "F".
Algebra is difficult for most students. As with any field of mathematics, there is a requirement of long hours of practice, of pushing one's mind to think in the way mathematicians think. To understand the notation and why numbers are put where they are put. For me the process is like distance running. You put in lots of hours of practice that really no one else sees or understands. Then on race day, test day in math class, you go out and do what you did in practice. If you practiced well,you can finish the long run. If you did not put in the time and effort, then you will not even finish the race.
Think about it another way. You eat three times a day. You cannot simply eat once a week and thrive. If you study for a test only on the night before, then you are eating once a week. You have to study three times a day. Morning, noon, and night.
In the end I only mark an answer right or wrong. Students sometimes say, "Thank-you for my grade" but this puzzles me. It would be like the runner thanking the timer for giving the runner a fast time. The runner earns their time by running, the timer only reports the time. The effort is that of the runner. This class is the same. A right question is worth a point. A wrong question earns no point. I am only the timer, marking them right or wrong. You are the runner. You have to make the effort.