Final Exam - Formated
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Algebra 2 Semester 1 Final Name:__________________________ PART 1: NO CALCULATORS.
Do the following problems. Make sure your answers are fully reduced. You may write answers
either in mixed form or as improper (top-heavy) fractions. SHOW YOUR WORK. (5 pts each)
1.
272
183 +
Answer:________
2.
5
15
3
14
7
2
10
3
Answer:________
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Give an example of each of the following types of numbers. (2 pts each)
3. A number that is rational but not an integer
Answer:______________
4. A number that is irrational
Answer:______________
5. A negative integer Answer:______________
6. A complex number that is not imaginaryAnswer:______________
7. A number that is neither even nor oddAnswer:______________
TRUE OR FALSE circle one (1 pt each)
8. is imaginary
TRUE FALSE
9. 0 is imaginary
TRUE FALSE
10. 0 is evenTRUE FALSE
11. 3.7 is odd
TRUE FALSE
12. i5 is irrational
TRUE FALSE
13. 0 is positive
TRUE FALSE
Draw a reasonable graph of the function. (3 pts)
14. The length of time an oven has been turned on and the ovens temperature are related.
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State the domain and range of the following function. (4 pts)
15.
D:_______________
R:_______________
Are the following relations functions? (2 pts each)
16. ( ) ( ) ( ){ }15,7,24,3,17,24
Answer:________
17.
1
45
52
73
yx
Answer:________
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18. Draw a graph that is not a function. (2 pts)
19. Draw a graph that is a function (2 pts)
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Draw the graph of a function with the stated domain and range. (5 pts)
20. D: 52
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22. xy =
23.12362 =+ zyx
(be sure to label your axes)
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24. (5, 2, -1)
25. Sketch the graph of a parabola with x-intercepts of 2 and 8 and y intercept of -3.
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28. 2
3
23
10
22
x
y
y
x
Answer:_________________
29. )23)(5( ii +
Answer:_________________
30. 36
Answer:_________________
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31. 23i
Answer:_________________
32. Give three examples of mathematical expressions that are not polynomials (3 pts)
maximum credit for different types of examples
33. Give two examples of mathematical expressions that are polynomials (2 pts)
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Give the special names for the following polynomials, based on degree and number of terms.
(2 pts each)
34. 3415 xx
Answer:___________________________________35. 13 2 ++xx
Answer:___________________________________
36. x271
Answer:___________________________________
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Scratch Paper (please write see scratch paper by original problem.)
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PART 2: CALC OK Name:________________________
Do the indicated operation. Be sure answer is simplified (no parentheses). (5 pts each)
37. )12()3( 2 xx
Answer:_________________________
38. 2)53( +x
Answer:_________________________
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Factor the following expressions completely. (5 pts each)
39. 105718 2 + xx
Answer:________________________________
40. 23 714 xx
Answer:________________________________
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41. 481 2 x
Answer:________________________________
Solve the following equations and inequalities. (5 pts each)
42. 33129
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43. 1174 x
Answer:________________________________
44. 875 =+x
Answer:________________________________
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45. 51030123 2 +=++ xxx
Answer:________________________________
46. 100)17( 2 =+x
Answer:________________________________
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State the following equations (5 pts each)
47. Give the equation of the line with x-intercept of 72 and going through the point
(36,4). (Hint: start by writing the x-intercept as a point.)
Answer:________________________________
48.Give the equation of the line perpendicular to )7(
5
43 =+ xy with
y-intercept of -10.
Answer:________________________________
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49. Give the equation of the parabola with vertex of (2,5) and going through
the point (-1,8).
Answer:________________________________
Let 73)( += xxf and xxxg 2)(2+= Find the following values: (5 pts each)
50. )3(g
Answer:________________________________
51. )7( +xf
Answer:________________________________
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Let 73)( += xxf and xxxg 2)(2+= Find the following values: (5 pts each)
52. )2(fg
Answer:________________________________
53. Find x if 3)( =xf
Answer:________________________________
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State whether the system is inconsistent, independent or dependent. IF the equations is solvable,
then solve it and give the solution. (5 pts each)
54.3664
3935
=+
=
yx
yx
Type of system:_______________________________
Solution:________________________________
55.324518
366024
=
=
yx
yx
Type of system:_______________________________
Solution:________________________________
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Graph the following quadratic equation by finding the x- and y-intercepts and the vertex.
(5 pts)
56. 12)( 2 ++= xxxf
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EXTRA CREDIT: No Hints Given
A. Easier. Find the x- and y-intercepts for the graph of the following equation. (3 pts)xxyxy +=+ 2
2
x-int:_____________
y-int:_____________
B. Harder. Give an equation for a quadratic function that has solutions of ix = 5 (5 pts)
Answer:________________________________
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Scratch Paper (please write see scratch paper by original problem.)