Algebra 2 Final

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Find the determinant of image1.png.

a.

–152

c.

152

b.

676

d.

–50

____ 2. Write a quadratic function in standard form with zeros 7 and –3.

a.

image2.png

c.

image3.png

b.

image4.png

d.

image5.png

____ 3. Use Pascal’s Triangle to expand the expression image6.png.

a.

image7.png

b.

image8.png

c.

image9.png

d.

image10.png

____ 4. Find the intercepts of image11.png, and graph the line.

a.

x-intercept: –4, y-intercept: 4

image12.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

x-intercept: image13.emf

3

, y-intercept: image14.emf

3

image15.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

x-intercept: image16.emf

3

, y-intercept: 4

image17.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

x-intercept: –4, y-intercept: image18.emf

3

image19.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 5. Write the set in set-builder notation.

image20.emf

024680–2–4–6–8x

a.

[–2, 4)

c.

image21.png

b.

image22.png

d.

[–2, 4]

____ 6. Graph image23.png.

a.

image24.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

image25.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

image26.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

image27.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 7. Graph the line with slope image28.emf

1

that passes through (–6, 0).

a.

image29.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

c.

image30.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

b.

image31.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

d.

image32.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

____ 8. Determine whether the binomial (image33.png) is a factor of the polynomial image34.png.

a.

(image35.png) is not a factor of the polynomial image36.png.

b.

Cannot determine.

c.

(image37.png) is a factor of the polynomial image38.png.

____ 9. Use Cramer’s rule to solve the system of equations.

image39.png

a.

(–22, 37)

c.

(–37, 22)

b.

(40, 34)

d.

(–74, 44)

____ 10. Solve image40.png.

a.

image41.png

c.

image42.png

b.

image43.png

d.

image44.png

____ 11. In slope-intercept form, write the equation of the line that is parallel to y = –5x + 23 and passes through (4, 5).

a.

y = image45.emf

1

5

x image46.emf

4

1

5

c.

y = –5x + 25

b.

y = –5x + 22

d.

y = image47.emf

1

5

x image48.emf

5

4

5

____ 12. Find the absolute value image49.png.

a.

9

c.

image50.emf

3

b.

image51.emf

53

d.

image52.emf

35

____ 13. Translate image53.png so that the vertex is at (3, –6). Then graph.

a.

image54.png

image55.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

image56.png

image57.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

image58.png

image59.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

image60.png

image61.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 14. Write the augmented matrix for image62.png, and solve. Round your answer to the nearest tenth.

a.

image63.png; image64.png, image65.png

c.

image66.png; image67.png, image68.png

b.

image69.png; image70.png, image71.png

d.

image72.png; image73.png, image74.png

____ 15. Solve the equation image75.png by completing the square.

a.

x = 10 or x = –18

c.

x = 7 or x = –7

b.

x = –5 or x = 9

d.

x = 5 or x = –9

____ 16. Identify the zeros and asymptotes of image76.png. Then graph.

a.

Zeros: image77.png and 3

Vertical asymptotes: image78.png, image79.png

Horizontal asymptote: image80.png

image81.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

c.

Zeros: image82.png and 3

Vertical asymptotes: image83.png, image84.png

Horizontal asymptote: image85.png

image86.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

b.

Zeros: image87.png and 2

Vertical asymptotes: image88.png, image89.png

Horizontal asymptote: image90.png

image91.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

d.

Zeros: image92.png and 2

Vertical asymptotes: image93.png, image94.png

Horizontal asymptote: image95.png

image96.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

____ 17. Identify the degree of the monomial image97.png.

a.

4

c.

6

b.

2

d.

–2

____ 18. Graph the function image98.png.

a.

image99.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

c.

image100.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

b.

image101.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

d.

image102.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

____ 19. Simplify the expression image103.png. Assume that all variables are positive.

a.

image104.png

c.

image105.png

b.

image106.png

d.

image107.png

____ 20. Find the zeros of the function image108.png by factoring.

a.

image109.png or image110.png

c.

image111.png or image112.png

b.

image113.png or image114.png

d.

image115.png or image116.png

____ 21. The parent function image117.png is reflected across the x-axis, vertically stretched by a factor of 4, and translated right 9 units to create g. Use the description to write the quadratic function in vertex form.

a.

image118.png

c.

image119.png

b.

image120.png

d.

image121.png

____ 22. Solve the equation image122.png.

a.

image123.png

c.

image124.png

b.

image125.png

d.

image126.png

____ 23. Solve the compound inequality. Then graph the solution set.

image127.png and image128.png

a.

{s | –8  s  2}

image129.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

b.

{s | s  –8 or s  2}

image130.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

c.

{s | –8  s  2}

image131.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

d.

{s | s  –8 or s  2}

image132.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

____ 24. Simplify image133.png. Identify any x-values for which the expression is undefined.

a.

image134.png

The expression is undefined at image135.png.

b.

image136.png

The expression is undefined at image137.png and image138.png.

c.

image139.png

The expression is undefined at image140.png and image141.png.

d.

image142.png

The expression is undefined at image143.png.

____ 25. Determine whether the data in the table are linear. Explain.

Session Length (min)

1

8

15

22

30

Cost ($)

1.60

4.05

6.50

8.95

12.80

a.

No, the rate of change is not constant. For example, to the nearest hundredth, image144.png and image145.png.

b.

Yes, the difference between successive session lengths is constant. For example, image146.png, image147.png, and so on.

c.

Yes, the rate of change is constant. For example, image148.png, image149.png, and so on.

d.

No, the ratio of the cost to the session length is not constant. For example, to the nearest hundredth, image150.png and image151.png.

____ 26. Solve the equation image152.png.

a.

There is no solution.

c.

image153.png

b.

image154.png image155.emf

3

2

d.

image156.png

____ 27. Identify the property demonstrated by the equation 4 + (5 + 8) = (4 + 5) + 8.

a.

Distributive Property

c.

Commutative Property

b.

Closure Property

d.

Associative Property

____ 28. Solve image157.png. Check your answer.

a.

image158.png

b.

image159.png

c.

image160.png

d.

There is no solution because the original equation is undefined at image161.png.

____ 29. Simplify the expression image162.png.

a.

image163.png

c.

image164.emf

16

25

b.

image165.png

d.

image166.emf

4

5

____ 30. Use elimination to solve the system image167.png.

a.

(6, –2)

c.

(–2, 6)

b.

(–8, –15)

d.

(–6, –8)

____ 31. Solve the equation image168.png.

a.

x = 23

c.

x = 13

b.

x = 23 or x = –7

d.

x = 13 or x = 3

____ 32. Express image169.png as a single logarithm. Simplify, if possible.

a.

image170.png

c.

6

b.

729

d.

image171.png

____ 33. A sawyer (person who cuts down trees) wants to know the height of a tree. The sawyer measures the shadow of his friend, who is 5 feet tall and standing beside the tree, and measures the shadow of the tree. If his friend’s shadow is 12 feet long and the tree’s shadow is 60 feet long, how tall is the tree?

a.

144 feet

c.

25 feet

b.

1 foot

d.

53 feet

____ 34. Which function is vertically stretched by a factor of 5 and translated 6 units right from the parent function?

a.

image172.png

c.

image173.png

b.

image174.png

d.

image175.png

____ 35. Order the numbers 4, image176.emf

1

8

, image177.png, 0.6632, image178.png from least to greatest.

a.

image179.emf

1

8

, 0.6632, image180.png, image181.png, 4

c.

image182.png, 4, image183.png, 0.6632, image184.emf

1

8

b.

4, image185.emf

1

8

, image186.png, 0.6632, image187.png

d.

image188.emf

1

8

, 0.6632, image189.png, 4, image190.png

Algebra 2 Final

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Find the determinant of image1.png.

a.

–152

c.

152

b.

676

d.

–50

____ 2. Write a quadratic function in standard form with zeros 7 and –3.

a.

image2.png

c.

image3.png

b.

image4.png

d.

image5.png

____ 3. Use Pascal’s Triangle to expand the expression image6.png.

a.

image7.png

b.

image8.png

c.

image9.png

d.

image10.png

____ 4. Find the intercepts of image11.png, and graph the line.

a.

x-intercept: –4, y-intercept: 4

image12.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

x-intercept: image13.emf

3

, y-intercept: image14.emf

3

image15.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

x-intercept: image16.emf

3

, y-intercept: 4

image17.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

x-intercept: –4, y-intercept: image18.emf

3

image19.emf

246810–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 5. Write the set in set-builder notation.

image20.emf

024680–2–4–6–8x

a.

[–2, 4)

c.

image21.png

b.

image22.png

d.

[–2, 4]

____ 6. Graph image23.png.

a.

image24.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

image25.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

image26.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

image27.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 7. Graph the line with slope image28.emf

1

that passes through (–6, 0).

a.

image29.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

c.

image30.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

b.

image31.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

d.

image32.emf

3691215–3–6–9–12–15x

3

6

9

12

15

–3

–6

–9

–12

–15

y

____ 8. Determine whether the binomial (image33.png) is a factor of the polynomial image34.png.

a.

(image35.png) is not a factor of the polynomial image36.png.

b.

Cannot determine.

c.

(image37.png) is a factor of the polynomial image38.png.

____ 9. Use Cramer’s rule to solve the system of equations.

image39.png

a.

(–22, 37)

c.

(–37, 22)

b.

(40, 34)

d.

(–74, 44)

____ 10. Solve image40.png.

a.

image41.png

c.

image42.png

b.

image43.png

d.

image44.png

____ 11. In slope-intercept form, write the equation of the line that is parallel to y = –5x + 23 and passes through (4, 5).

a.

y = image45.emf

1

5

x image46.emf

4

1

5

c.

y = –5x + 25

b.

y = –5x + 22

d.

y = image47.emf

1

5

x image48.emf

5

4

5

____ 12. Find the absolute value image49.png.

a.

9

c.

image50.emf

3

b.

image51.emf

53

d.

image52.emf

35

____ 13. Translate image53.png so that the vertex is at (3, –6). Then graph.

a.

image54.png

image55.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

c.

image56.png

image57.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

b.

image58.png

image59.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

d.

image60.png

image61.emf

2468–2–4–6–8–10x

2

4

6

8

10

–2

–4

–6

–8

–10

y

____ 14. Write the augmented matrix for image62.png, and solve. Round your answer to the nearest tenth.

a.

image63.png; image64.png, image65.png

c.

image66.png; image67.png, image68.png

b.

image69.png; image70.png, image71.png

d.

image72.png; image73.png, image74.png

____ 15. Solve the equation image75.png by completing the square.

a.

x = 10 or x = –18

c.

x = 7 or x = –7

b.

x = –5 or x = 9

d.

x = 5 or x = –9

____ 16. Identify the zeros and asymptotes of image76.png. Then graph.

a.

Zeros: image77.png and 3

Vertical asymptotes: image78.png, image79.png

Horizontal asymptote: image80.png

image81.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

c.

Zeros: image82.png and 3

Vertical asymptotes: image83.png, image84.png

Horizontal asymptote: image85.png

image86.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

b.

Zeros: image87.png and 2

Vertical asymptotes: image88.png, image89.png

Horizontal asymptote: image90.png

image91.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

d.

Zeros: image92.png and 2

Vertical asymptotes: image93.png, image94.png

Horizontal asymptote: image95.png

image96.emf

24681012–2–4–6–8–10–12x

2

4

6

8

10

12

–2

–4

–6

–8

–10

–12

y

____ 17. Identify the degree of the monomial image97.png.

a.

4

c.

6

b.

2

d.

–2

____ 18. Graph the function image98.png.

a.

image99.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

c.

image100.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

b.

image101.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

d.

image102.emf

123456–1–2–3–4–5–6x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

____ 19. Simplify the expression image103.png. Assume that all variables are positive.

a.

image104.png

c.

image105.png

b.

image106.png

d.

image107.png

____ 20. Find the zeros of the function image108.png by factoring.

a.

image109.png or image110.png

c.

image111.png or image112.png

b.

image113.png or image114.png

d.

image115.png or image116.png

____ 21. The parent function image117.png is reflected across the x-axis, vertically stretched by a factor of 4, and translated right 9 units to create g. Use the description to write the quadratic function in vertex form.

a.

image118.png

c.

image119.png

b.

image120.png

d.

image121.png

____ 22. Solve the equation image122.png.

a.

image123.png

c.

image124.png

b.

image125.png

d.

image126.png

____ 23. Solve the compound inequality. Then graph the solution set.

image127.png and image128.png

a.

{s | –8  s  2}

image129.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

b.

{s | s  –8 or s  2}

image130.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

c.

{s | –8  s  2}

image131.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

d.

{s | s  –8 or s  2}

image132.emf

0123456789100–1–2–3–4–5–6–7–8–9–10s

____ 24. Simplify image133.png. Identify any x-values for which the expression is undefined.

a.

image134.png

The expression is undefined at image135.png.

b.

image136.png

The expression is undefined at image137.png and image138.png.

c.

image139.png

The expression is undefined at image140.png and image141.png.

d.

image142.png

The expression is undefined at image143.png.

____ 25. Determine whether the data in the table are linear. Explain.

Session Length (min)

1

8

15

22

30

Cost ($)

1.60

4.05

6.50

8.95

12.80

a.

No, the rate of change is not constant. For example, to the nearest hundredth, image144.png and image145.png.

b.

Yes, the difference between successive session lengths is constant. For example, image146.png, image147.png, and so on.

c.

Yes, the rate of change is constant. For example, image148.png, image149.png, and so on.

d.

No, the ratio of the cost to the session length is not constant. For example, to the nearest hundredth, image150.png and image151.png.

____ 26. Solve the equation image152.png.

a.

There is no solution.

c.

image153.png

b.

image154.png image155.emf

3

2

d.

image156.png

____ 27. Identify the property demonstrated by the equation 4 + (5 + 8) = (4 + 5) + 8.

a.

Distributive Property

c.

Commutative Property

b.

Closure Property

d.

Associative Property

____ 28. Solve image157.png. Check your answer.

a.

image158.png

b.

image159.png

c.

image160.png

d.

There is no solution because the original equation is undefined at image161.png.

____ 29. Simplify the expression image162.png.

a.

image163.png

c.

image164.emf

16

25

b.

image165.png

d.

image166.emf

4

5

____ 30. Use elimination to solve the system image167.png.

a.

(6, –2)

c.

(–2, 6)

b.

(–8, –15)

d.

(–6, –8)

____ 31. Solve the equation image168.png.

a.

x = 23

c.

x = 13

b.

x = 23 or x = –7

d.

x = 13 or x = 3

____ 32. Express image169.png as a single logarithm. Simplify, if possible.

a.

image170.png

c.

6

b.

729

d.

image171.png

____ 33. A sawyer (person who cuts down trees) wants to know the height of a tree. The sawyer measures the shadow of his friend, who is 5 feet tall and standing beside the tree, and measures the shadow of the tree. If his friend’s shadow is 12 feet long and the tree’s shadow is 60 feet long, how tall is the tree?

a.

144 feet

c.

25 feet

b.

1 foot

d.

53 feet

____ 34. Which function is vertically stretched by a factor of 5 and translated 6 units right from the parent function?

a.

image172.png

c.

image173.png

b.

image174.png

d.

image175.png

____ 35. Order the numbers 4, image176.emf

1

8

, image177.png, 0.6632, image178.png from least to greatest.

a.

image179.emf

1

8

, 0.6632, image180.png, image181.png, 4

c.

image182.png, 4, image183.png, 0.6632, image184.emf

1

8

b.

4, image185.emf

1

8

, image186.png, 0.6632, image187.png

d.

image188.emf

1

8

, 0.6632, image189.png, 4, image190.png

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