algebra ii midterm exam review packet...algebra ii midterm exam review packet name:_ hour:_...

Algebra II

Midterm Exam Review Packet

Name:______________________

Hour:______________

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

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


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

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

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.

Graph the inequality in a coordinate plane.

25. 4 xy 26. 15 xy

27. 722 yx


STANDARD FORM: VERTEX FORM:

Write each quadratic equation in standard form.

1. 75 xxy

2. 23 xy

3. 262 xy

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 ( _____, ______)



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 ( _____, ______)



Maximum or Minimum

Max/Min Value __________ Y-intercept: _________

a = ____ b = ____ c = ____ a = ____ b = ____ c = ____

a = ____ b = ____ c = ____

a = ____ h = ____ k = ____

7. 3422 xy

Vertex ( _____, ______)



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 = ____

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

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

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

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

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: _______________________________


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

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


23. xxxf 72)( 4


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

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

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

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.


________y x

49.


________y x


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

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

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.

algebra ii midterm exam review packet...algebra ii midterm exam review packet name:_____ hour:_____...

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algebra ii midterm exam review packet...algebra ii midterm exam review packet name:_ hour:_...