Algebra II / Mr. Hansen

Name: _____________________________

Test on Chapter 9 (3/6/2000)

 

Ground Rules for Re-Do:
If you are happy with how you think you did in class, you can stay with your current grade (2 omissions OK). However, if you complete the re-do, you must work all problems that you omitted or did poorly on because of lack of time. That means, at a minimum, that you must work the 2 problems that you omitted on Monday.

You may compare answers with friends (document their names here: ___________________________ ), but the work you do must be your own. You are on your honor.

Using the sample test is permitted, but again, please (on your honor) work all problems as well as you can on your own first.

Initial here ____________ to indicate that you understand and have complied with the ground rules.

Show all work
For full credit, show all work. You may use your calculator in any way that you wish, including study aids stored into your calculator’s memory, but you must show sufficient work on your paper to demonstrate clearly that you understand the concepts. For example, if you assert that the semimajor axis of an ellipse is 7, you should show the algebraic transformations needed to put the equation into "x – h, y – k" form showing the number 7 in the appropriate position. Also, if you are asked to find x- or y-intercepts, show your work; do not simply use your calculator to find the answer. It is always a good idea to use your calculator to check your work. In fact, if your answer is wrong, you will receive more partial credit if you explain why you can tell that it’s wrong.

Formula bin
The following formulas are furnished without explanation. Please use them if they help you.
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
B2 – 4AC
(x – h)2 + (y – k)2 = r2
, c2 = a2 – b2
, c2 = a2 + b2, asymptote slopes ± b/a
x – h = a(y – k)2 or y – k = a(x – h)2

1.

Use the discriminant to identify each of the following conic sections. Show your work.

 

(a)
–xy + 15x + 4y = 17

 

(b)
7,148,553,818x2 + 7,148,553,818y2 + 51,998x – 7999y = 714,898

 

(c)
66x2 – 72y2 + 8y = 21

 

(d)
x2/4 + y2/9 = 0

 

(e)
2y2 = 3x – 7y

 

(f)
2y2 = 3x2 – 7y

 
2.
Sketch (c) and (e) from the previous question. Rough sketches are perfectly acceptable. For (c), label the coordinates of the center, foci, and y-intercepts, and sketch the asymptotes as dotted lines. For (e), label the coordinates of the vertex (or vertices), x-intercept(s), and y-intercept(s).

 

3.
Fill in the blanks below with the name of the proper conic section. No term is used more than once.

 

(a)
The set of points in a plane that are equidistant from a point F and a line (directrix) is called a(n) __________ .

 

(b)
The set of points in a plane that are equidistant from a single fixed point is called a(n) __________ .

 

(c)
The set of points P in a plane such that PF1 + PF2 (for foci F1 and F2) is a constant is called a(n) __________ .

 

(d)
The set of points P in a plane such that |PF1 – PF2| (for foci F1 and F2) is a constant is called a(n) __________ .

 

4.
Write the equation for each of the following relations. For part (a) only, write the equation in Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 form; for the other parts, any form is acceptable.

 

(a)

High and low points marked are at (–3, –4) and (–3, 8). Major axis is vertical, and focal radius is 4.

 

(b)

The axis of symmetry is the line y = 2, the x-intercept is at 11, and the point (–1, –8) is on the curve.

 

(c)

Center is (4, –6); x-radius and y-radius are both 16.

 
5.
Use your calculator to plot problem 4(c) accurately. Raise your hand when you are ready to show it to your instructor. Do not worry if the last pixel at the left and right edge are skipped.

 
6.
Solve the following system graphically (show your graphs clearly):
5x2 + 9y2 = 161
x2 – 4y = 4

 
7.
Solve the system in #6 algebraically.