Algebra II Midterm Exam Review Packet...Algebra II Midterm Exam Review Packet Name:_____ Hour:_____...
Transcript of Algebra II Midterm Exam Review Packet...Algebra II Midterm Exam Review Packet Name:_____ Hour:_____...
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Algebra II
Midterm Exam Review Packet
Name:______________________
Hour:______________
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CHAPTER 1 Midterm Review
Evaluate the power.
1. 43 2. 55 3. 36 4. 47
Find the value of each expression given the value of each variable.
5. 5210 xwhenx
6. 6210
2 xwhenxx
7. 2452 xwhenxx 8. 7442
yandxwhenyx
Simplify the expression.
9. yxyx 2357
10. x 238
11. 10533 xx 12. 5423 xx
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Solve the equation. Check your solution.
13. 2437 s
14. 3665 c
15. 19)26(2
1w
16. 5236 xx
17. 74123 xx
18. 9235 yy
Solve each equation for y.
19. 1552 yx 20. 2436 yx
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CHAPTER 2 Midterm Review
Identify the domain and range. Then tell whether the relation is a function.
1.
2.
3. {(–4, 2), (–2, 0), (0, –2), (2, 0), (4, 2)}
Evaluate the function when 4x .
4. xxh 6
5. 53 2 xxf
6. 143 2 xxxv
Find the slope of the line passing through the given points.
7. 7,18,3
m = __________
8. 0,51,5
m = __________
9. 4,84,0
m = __________
Find the slope and y-intercept of the line. Then graph the equation.
10. 12 xy
m = ______ b = _____ ( , )
11. 53
2 xy
m = ______ b = _____ ( , )
12. 43
4 xy
m = ______ b = _____ ( , )
Domain: _______________ Range: ________________ Function: YES NO
Domain: ____________________ Range: _____________________ Function: YES NO
Domain: ___________________ Range: ____________________ Function: YES NO
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Write each form of a line. SLOPE−INTERCEPT FORM:_________________________ POINT−SLOPE FORM: _____________________________
Write an equation of the line in slope intercept form given the slope and a point.
13. slope = −3 and goes through the point (1, −4) _____________________________ Equation
14. slope = ½ and goes through the point (4, 2) _____________________________ Equation
PARALLEL LINES HAVE THE ________________ SLOPE.
PERPENDICULAR LINES HAVE _________________ SLOPES.
Given the equation of a line, write the slope of a parallel line and the slope of a perpendicular line.
15. 13
2 xy m = _______
Slope of a parallel line: __________ Slope of a perpendicular line: __________
16. 43 xy m = _______
Slope of a parallel line: __________ Slope of a perpendicular line: __________
Write an equation of a parallel line.
17. passes through (7, −4), parallel to the line 13 xy
_____________________________ Equation
18. passes through (2, 5), parallel to the line 12 xy
_____________________________ Equation
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Write an equation of a perpendicular line.
19.passes through (4, −16), perpendicular to the line
83
2 xy
_____________________________ Equation
20. passes through (1, 1), perpendicular to the line 52 xy
_____________________________ Equation
Draw a scatter plot of the data. Determine whether the data has positive, negative, or no correlation. 21.
Match each inequality on the left with its graph on the right.
22. 3 yx
23. 3 yx
24. 3 yx
A.
B. C.
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Graph the inequality in a coordinate plane.
25. 4 xy 26. 15 xy
27. 722 yx
CHAPTER 5 Midterm Review
STANDARD FORM: VERTEX FORM:
Write each quadratic equation in standard form.
1. 75 xxy
2. 23 xy
3. 262 xy
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For #4-5, Given the quadratic in STANDARD FORM, cbxaxy 2 : find all the information and then graph it.
Use the formulaa
bx
2
to help.
4. 562 xxy
Y-intercept __________
Vertex ( _____, ______)
Axis of Symmetry x = _________
Opens Up or Opens Down
Maximum or Minimum Max/Min Value __________
5. 862 xxy
Y-intercept __________
Vertex ( _____, ______)
Axis of Symmetry x = _________
Opens Up or Opens Down
Maximum or Minimum Max/Min Value __________
For #6-7, Given the quadratic equation in VERTEX FORM, khxay 2)( , find all the information and then graph.
6. 432 xy
Vertex ( _____, ______)
Axis of Symmetry x = _________
Opens Up or Opens Down
Maximum or Minimum
Max/Min Value __________ Y-intercept: _________
a = ____ b = ____ c = ____ a = ____ b = ____ c = ____
a = ____ b = ____ c = ____
a = ____ h = ____ k = ____
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7. 3422 xy
Vertex ( _____, ______)
Axis of Symmetry x = _________
Opens Up or Opens Down
Maximum or Minimum
Max/Min Value __________ Y-intercept: ____________ (a little big sorry!)
Identify which graph matches each equation. Use what you know about a, h, and k to help you match the graphs!
8. 21 xy
9. 912 xy
10. 3122 xy
A.
B.
C.
Factor the following expressions completely.
11. xx 122 12. xx 93 2
13. 4822 xx
14. 5292 xx
a = ____ h = ____ k = ____
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15. 299 2 xx 16. 3108 2 xx
17. 49142 xx 18. 9124 2 xx
19. 252 x 20. 1449 2 x
Solve the quadratic equation by factoring. Don’t forget to set the equation equal to 0 first!
21. 01452 xx 22. xx 15562
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23. 03114 2 xx 24. 05163 2 xx
25. 0116 2 xx 26. xx 102 2
Simplify the following radical expressions.
27. 24 28. 75 29. 36
30. 99 31. 5012 32. 30105
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Rationalize the denominators.
33. 3
2 34.
5
7
35. i2
2 36.
i3
5
37. ii 423 38. ii 3264
39. ii 5223 40. ii 164
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Find the solutions of each equation using square roots.
41. 492 x 42. 812 x
43. 2052x 44. 182
2x
Solve the quadratic equations using the Quadratic Formula. )(2
))()(4()()( 2
a
cabbx
45. 01083 2 xx 46. 0932 xx
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Find the discriminant and describe the nature of the roots for each quadratic equation.
47. 036122 xx
Discriminant: ___________ Nature of the roots: _______________________________
48. 0172 2 xx
Discriminant: ___________ Nature of the roots: _______________________________
CHAPTER 6 Midterm Review
EXPONENT PROPERTIES
Simplify the expressions.
1. 24 22
2. 242
3.
3
4
3
4. 07
5. 4
4 5
xx 6.
3
2
x
x
7. 7232 yx
8.
2
4
35
yx
yx
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9. yxyxyx 35232 82 10.
2
5
4
1
xy 11.
3
2
5
12.
64
32
zy
zy
13. 62
4
15
10
ba
ab
14. 2223 25 yxxy 15. 32
4x
16. 02xy
17. 238
x 18. 22 19. 25 x 20.
413
262
18
36
cba
cba
Tell whether the function is a polynomial function, if it is write it in standard form, find the degree, determine the leading coefficient, determine the constant and determine the type.
21. 753)( 3 xxxf
Polynomial? Yes or No Standard form:______________________ Degree=______________ Leading coefficient=_____ Constant=_____________ Type of function:___________________
22. 12472)( 25 xxxxf
Polynomial? Yes or No Standard form:______________________ Degree=______________ Leading coefficient=_____ Constant=_____________ Type of function:___________________
23. xxxf 72)( 4
Polynomial? Yes or No Standard form:______________________ Degree=______________ Leading coefficient=_____ Constant=_____________ Type of function:___________________
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24. 33 423 xx
25. 522123 2324 xxxx
26. 9322 34535 xxxxx 27. 27524 233 xxxxx
Multiply.
28. 11327 2 xxx 29. 18312 2 xxx
30. 33x 31. 417 xxx
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Divide using synthetic division.
32. 3683 2 xxx
33. 3922 23 xxxx
34. 53522 xxx
35. 315388 23 xxxx
Factor the polynomial in quadratic form.
36. 1214 x
37. 54 24 xx
38. 1811 24 xx
39. 145 24 xx
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Find ALL of the solutions for each polynomial. Don’t forget to use the degree to help determine how many TOTAL solutions/roots there should be!
40. 01012 2 xxx **This is factored already! 41. 09 24 xx
42. 283 24 xx
43. 0814 x
Match the following equation with its graph. Use the solutions/roots to help match! Think about where the solutions/roots are on the graph.
44. 32 xxy
45. 12 xxxy
46. 212 xxy
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Use the following graph to answer each question.
47.
How many turning points does the polynomial graphed have? __________ How many real zeros does the polynomial have? ___________ Describe the end behavior of the graph: ________y x
________y x
48.
How many turning points does the polynomial graphed have? __________ How many real zeros does the polynomial have? ___________ Describe the end behavior of the graph: ________y x
________y x
49.
How many turning points does the polynomial graphed have? __________ How many real zeros does the polynomial have? ___________ Describe the end behavior of the graph: ________y x
________y x
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CHAPTER 9 Midterm Review
Determine the asymptotes of each function.
1. 41
xy
x = _________ y = _________
2. 23
1
xy
x = _________ y = _________
3. 62
5
xy
x = _________ y = _________
Determine the domain and the range of each function.
4. 2
1
xy
Domain: ______________________ Range: _______________________
5. 64
9
xy
Domain: ______________________ Range: _______________________
6. 25
8
xy
Domain: ______________________ Range: _______________________
Match each graph to its equation. Use the asymptotes to help!
7. 2
3
xy
8. 21
4
xy
9. 2
3
xy
A.
B.
C.
Simplify.
10. 4
2
50
14
x
x
11. 65
4
2
2
aa
a
12. 427
427
x
x
Find the product.
13. 3
1
12
92
2
x
x
xx
x
14. 82
242
3612
42
2
2
2
xx
xx
xx
x
15. 76
214
189
28112
2
2
2
xx
xx
xx
xx
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Find the quotient.
16. 123
4
4
2 2
x
x
x
x
17. 53
2 105147
x
x
x
xx
18. xx
x
x
xx
123
535222
2
Simplify each expression.
19.
1
36
3
x
xx
x
20.
34
6333
6
2
2
xx
xx
xx
Simplify the following expressions.
21. 5
3
2
1
x 22.
2
3
3
2
x
23. 2
7
2
xx
x
24. 25
2
5
42
xx
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Solve the equations.
25. xx 2
8
32
4
26. 2
2
4
xx
27. 1
8
1
23
1
2
xx
x
x
x 28.
4
52
4
3
xx
Make sure everything is on your note card for the exam! Just a little more studying and you
are going to ROCK this exam.