Algebra 2 Honors Semester 1 (#2227) - Ms....

ALGEBRA 2 HONORS SEM 1 INSTRUCTIONAL MATERIALS Course: Algebra 2 Honors Semester 1 (#2227) 2016-2017

Released 8/22/16

Instructional Materials for WCSD Math Common Finals

The Instructional Materials are for student and teacher use and are aligned

to the 2016-2017 Course Guides for the following course:

Algebra 2 Honors Semester 1 (#2227)

When used as test practice, success on the Instructional Materials does not

guarantee success on the district math common final.

Students can use these Instructional Materials to become familiar with the

format and language used on the district common finals. Familiarity with

standards and vocabulary as well as interaction with the types of problems

included in the Instructional Materials can result in less anxiety on the part

of the students. The length of the actual final exam may differ in length

from the Instructional Materials.

Teachers can use the Instructional Materials in conjunction with the course

guides to ensure that instruction and content is aligned with what will be

assessed. The Instructional Materials are not representative of the depth

or full range of learning that should occur in the classroom.

*Students will be allowed to use a

Scientific or graphing calculator on

Algebra 2 Honors Semester 1 and

Algebra 2 Honors Semester 2 final

exams.


Released 8/22/16

Algebra 2 Honors Semester 1 Test Reference Sheet

Sum of Two Cubes 𝑎3 + 𝑏3 = (𝑎 + 𝑏)(𝑎2 − 𝑎𝑏 + 𝑏2)

Difference of Two Cubes 𝑎3 − 𝑏3 = (𝑎 − 𝑏)(𝑎2 + 𝑎𝑏 + 𝑏2)


Released 8/22/16

Multiple Choice: Identify the choice that best completes the statement or answers the question.

1. Write the piecewise function for the graph below:

A. 𝑓(𝑥) =

{

1

2𝑥 − 5, 𝑥 ≤ 0

−1

3𝑥 + 1, 0 < 𝑥 < 3

2𝑥 + 1, 𝑥 ≥ 3

B. 𝑓(𝑥) =

{

1

2𝑥 − 5, 𝑥 ≤ 0

2𝑥 + 1, 0 < 𝑥 < 3

−1

3𝑥 + 1, 𝑥 ≥ 3

C. 𝑓(𝑥) =

{

−

1

3𝑥 + 1, 𝑥 ≤ 0

2𝑥 + 1, 0 < 𝑥 < 3

1

2𝑥 − 5, 𝑥 ≥ 3

D. 𝑓(𝑥) =

{

1

2𝑥 − 5, 𝑥 ≤ 0

2𝑥 + 1, 0 ≤ 𝑥 ≤ 3

−1

3𝑥 + 1, 𝑥 ≥ 3

2. Graph the function 𝑓(𝑥) = {

−𝑥 + 3, 𝑥 ≤ −3

−𝑥2 + 6, 𝑥 > −3

A.

C.

B.

D.


Released 8/22/16

3. Three students were chosen to show their solutions for solving the equation

𝑦 = 𝑎(𝑥 − ℎ) + 𝑘 for x. Their work is shown below. Determine which students were

correct.

Student #1 Student #2 Student #3

𝑦 = 𝑎(𝑥 − ℎ) + 𝑘 𝑦 = 𝑎(𝑥 − ℎ) + 𝑘 𝑦 = 𝑎(𝑥 − ℎ) + 𝑘

𝑦 − 𝑘 = 𝑎(𝑥 − ℎ) 𝑦

𝑎= (𝑥 − ℎ) + 𝑘

𝑦

𝑎= (𝑥 − ℎ) +

𝑘

𝑎

(𝑦 − 𝑘)

𝑎= 𝑥 − ℎ

𝑦

𝑎− 𝑘 = 𝑥 − ℎ

𝑦

𝑎−𝑘

𝑎= 𝑥 − ℎ

(𝑦 − 𝑘)

𝑎+ ℎ = 𝑥

𝑦

𝑎− 𝑘 + ℎ = 𝑥

𝑦

𝑎−𝑘

𝑎+ ℎ = 𝑥

A. Student #1 and Student #2 C. Student #1 and Student #3

B. Student #2 and Student #3 D. All students were correct

4. Create a table to represent the graph:

A. Weight (lbs) Shipping Cost ($)

0 < 𝑥 ≤ 1.0 4.00 1.0 < 𝑥 ≤ 2.0 4.50 2.0 < 𝑥 ≤ 3.0 5.00 3.0 < 𝑥 ≤ 4.0 5.50 4.0 < 𝑥 ≤ 5.0 6.00

C. Weight (lbs) Shipping Cost ($)

0 < 𝑥 ≤ 0.9 4.00 1.0 < 𝑥 ≤ 1.9 4.50 2.0 < 𝑥 ≤ 2.9 5.00 3.0 < 𝑥 ≤ 3.9 5.50 4.0 < 𝑥 ≤ 4.9 6.00

B. Weight (lbs) Shipping Cost ($)

0 ≤ 𝑥 ≤ 1.0 4.00 1.0 ≤ 𝑥 ≤ 2.0 4.50 2.0 ≤ 𝑥 ≤ 3.0 5.00 3.0 ≤ 𝑥 ≤ 4.0 5.50 4.0 ≤ 𝑥 ≤ 5.0 6.00

D. Weight (lbs) Shipping Cost ($)

0 < 𝑥 < 0.9 4.00 1.0 < 𝑥 < 1.9 4.50 2.0 < 𝑥 < 2.9 5.00 3.0 < 𝑥 < 3.9 5.50 4.0 < 𝑥 < 4.9 6.00


Released 8/22/16

5. Which of the following graphs shows a function over the domain [−3, −1) ∪ (0, 5]

A.

C.

B.

D.

6. Given 𝑓(𝑥) = 4 (𝑥 −2

7)2

+1

9, identify the domain and range of the function.

A. Domain: (−∞, +∞)

Range: (−∞, −2

7)

C. Domain: (−∞, +∞) Range: (∞, 4)

B. Domain: [−∞, +∞]

Range: [∞, −2

7]

D. Domain: (−∞,+∞)

Range: [1

9, ∞)

7. Solve the following system for z:

{

𝑥 + 2𝑦 − 𝑧 = 5−3𝑥 − 2𝑦 − 3𝑧 = 114𝑥 + 4𝑦 + 5𝑧 = −18

A. 𝑧 = 0 C. 𝑧 = −4

B. 𝑧 = −2 D. 𝑧 = 8


Released 8/22/16

8. Compare the two functions represented below. Determine which of the following

statements is true.

Function 𝑓(𝑥) Function 𝑔(𝑥)

𝑔(𝑥) = (𝑥 − 6)2 − 4

A. The functions have the same vertex.

B. The minimum value of 𝑓(𝑥) is the same as the minimum value of 𝑔(𝑥).

C. The functions have the same axis of symmetry.

D. The minimum value of 𝑓(𝑥) is less than the minimum value of 𝑔(𝑥).

9. If the function 𝑓(𝑥) = 𝑥3 is translated left eight units and up ten units, how will the

domain and range of the function change?

A. The domain will become 𝐷: {𝑥|𝑥 ≥ −8} and

the range will become 𝑅: {𝑦|𝑦 ≥ 10}.

B. The domain will become 𝐷: {𝑥|𝑥 ≥ 8} and

the range will become 𝑅: {𝑦|𝑦 ≥ 10}.

C. The domain will become 𝐷: {𝑥|𝑥 ≥ −8} and

the range will remain 𝑅: {𝑦|𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}.

D. The domain will remain 𝐷: {𝑥|𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠} and

the range will remain 𝑅: {𝑦|𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}.

10. Which equation is obtained after the graph below is translated 4 units to the left and

5 units up?

A. 𝑓(𝑥) = −

1

3(𝑥 + 7)3 + 3

B. 𝑓(𝑥) = −1

3(𝑥 − 1)3 + 3

C. 𝑓(𝑥) = −3(𝑥 + 8)3 − 6

D. 𝑓(𝑥) = −3(𝑥 + 2)3 − 6


Released 8/22/16

11. State where the function is increasing and

decreasing.

A. Never Increasing

Decreasing: (−∞,+∞)

B. Increasing: (−8, 0) ∪ (0,+ ∞) Decreasing: (−∞,−8)

C. Increasing: (−∞,−8) ∪ (0, 8) Decreasing: (−8, 0)

D. Increasing: (−8,−4) ∪ (0,+∞) Decreasing: (−∞,−8) ∪ (−4, 0)

12. The function 𝑓(𝑥) =1

2𝑥3 +

1

4𝑥2 −

15

4𝑥 is graphed to

the right. Over which intervals of x is the graph

positive?

A.

B.

C.

D.

13. What are the values of the relative maxima and/or minima of the function graphed?

A. relative maxima: 0

relative minima: −4, 4

B. relative maxima: 10

relative minima: −1, 2

C. relative maxima: 3.3, 4.7

relative minima: 0

D. relative maxima: 2, 10

relative minima: −1


Released 8/22/16

14. Simplify: 4𝑖(10 + 𝑖) − 6(2 − 3𝑖)

A. 28 + 22𝑖 C. −8 + 58𝑖

B. −16 + 58𝑖 D. 8 + 22𝑖

15. Simplify: (𝑖√5 + 2)2

A. −1 + 4𝑖√5 C. 3𝑖√5

B. −1 + 𝑖√10 D. −1

16. Simplify: (𝑖√7 + 8)(𝑖√7 − 8)

A. 7𝑖 − 64 C. −57

B. 𝑖√7 − 64 D. −71

17. Simplify:

2𝑖(6−4𝑖)

3+3𝑖

A. 4𝑖 C. 60 +

2

3𝑖

B. 8

3+ 4𝑖 D.

10

3+2

3𝑖


Released 8/22/16

18. Write

7𝑖(1+2𝑖)+5

3𝑖 as a complex number in standard form.

A.

16𝑖

3 C.

7

3+ 3𝑖

B. −9 + 7𝑖

3𝑖 D. 7 +

5

3𝑖

19. What are the solutions to the quadratic equation, 3𝑥2 + 21𝑥 = 5𝑥 − 60?

A. 𝑥 =−8 ± 4𝑖√29

3 C. 𝑥 =

−8 ± 2𝑖√61

3

B. 𝑥 =−8 ± 2𝑖√29

3 D. 𝑥 =

−8 ± 𝑖√61

2

20. Solve: 5(𝑥 + 1)2 = 120

A. 𝑥 = ±√23 C. 𝑥 = −1 ± 2√6

B. 𝑥 =−5 ± 2√30

5 D. 𝑥 = −3√6 𝑜𝑟 √6

21. Given 𝑓(𝑥) = 2𝑥2 + 16𝑥 + 18, find the value of 𝑘 if the function is written in vertex

form, 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘.

A. 𝑘 = −9 C. 𝑘 = −14

B. 𝑘 = 4 D. 𝑘 = 7


Released 8/22/16

22. Which function is represented by the graph?

A. 𝑓(𝑥) =

1

3(𝑥 − 3)(𝑥 − 6)

B. 𝑓(𝑥) = (𝑥 + 3)(𝑥 + 6)

C. 𝑓(𝑥) = (𝑥 − 3)(𝑥 − 6)

D. 𝑓(𝑥) = 3(𝑥 − 3)(𝑥 − 6)

23. Which of following functions does not represent the parabola with a vertex at (1, 4) and

x-intercepts (−1, 0) and (3, 0).

A. 𝑓(𝑥) = −𝑥2 + 𝑥 + 4 C. 𝑓(𝑥) = −𝑥2 + 2𝑥 + 3

B. 𝑓(𝑥) = −(𝑥 − 1)2 + 4 D. 𝑓(𝑥) = −(𝑥 + 1)(𝑥 − 3)

24.

Which of the following functions represent the parabola opening upwards with a

compression factor of 1

4 and x-intercepts (−4, 0) and (6, 0).

I. 𝑦 =1

4(𝑥 + 4)(𝑥 − 6)

II. 𝑦 =1

4𝑥2 +

5

2𝑥 − 6

III. 𝑦 = 4(𝑥 − 4)2 + 6

IV. 𝑦 =1

4𝑥2 −

1

2𝑥 − 6

V. 𝑦 =1

4(𝑥 − 1)2 −

25

4

A. Options I, IV, and V C. Options I, III, and IV

B. Options I, III, and V D. Options II, IV, and V


Released 8/22/16

25. Compare the axis of symmetry and the minimum values for the two functions below.

ℎ(𝑥) = 2(𝑥 + 3)(𝑥 − 7)

𝑗(𝑥) = 𝑥2 − 4𝑥 − 21

Determine which of the following statements is correct.

A. The functions ℎ(𝑥) and 𝑗(𝑥) have the same axis of symmetry, but the minimum value

of ℎ(𝑥) is less than the minimum value of 𝑗(𝑥).

B. The functions ℎ(𝑥) and 𝑗(𝑥) have the same axis of symmetry, but the minimum value

of ℎ(𝑥) is greater than the minimum value of 𝑗(𝑥).

C. The functions ℎ(𝑥) and 𝑗(𝑥) do not have the same axis of symmetry, and the minimum

value of ℎ(𝑥) is less than the minimum value of 𝑗(𝑥).

D. The functions ℎ(𝑥) and 𝑗(𝑥) do not have the same axis of symmetry, and the minimum

value of ℎ(𝑥) is greater than the minimum value of 𝑗(𝑥).

26. Given the diagram below, approximate to the nearest foot how many feet of walking

distance a person saves by cutting across the lawn instead of walking on the sidewalk.

A. 60 𝑓𝑒𝑒𝑡 C. 36 𝑓𝑒𝑒𝑡

B. 48 𝑓𝑒𝑒𝑡 D. 24 𝑓𝑒𝑒𝑡

27. Which of the following is the quadratic equation for a parabola with a vertex of (−8, 2) going through the point (−13, 12) ?

A. 𝑦 = −

10

441(𝑥 + 8)2 + 2 C. 𝑦 =

2

5(𝑥 + 8)2 + 2

B. 𝑦 = −2

5(𝑥 − 8)2 + 2 D. 𝑦 =

10

441(𝑥 − 8)2 + 2


Released 8/22/16

28. A parabola has x-intercepts at −3 and 7and goes through the point (−5, 6). What other

point is on the parabola?

A. (−8, 42) C. (8, 44)

B. (−1, 22) D. (11, 14)

29. A water balloon is launched upward from an initial height (ℎ0) of 15 feet with an initial

velocity (𝑣0) of 50 feet per second. The height of the water balloon can be modeled by the

equation ℎ = −16𝑡2 + 𝑣0𝑡 + ℎ0 where t is time in seconds and h is the height above the

ground. Find the time it takes the water balloon to hit the ground level. Round your

answers to the nearest hundredth.

A. Time at ground level: 𝑡 = 3.50 𝑠𝑒𝑐 C. Time at ground level: 𝑡 = 3.13 𝑠𝑒𝑐

B. Time at ground level: 𝑡 = 3.40 𝑠𝑒𝑐 D. Time at ground level: 𝑡 = 3.27 𝑠𝑒𝑐

30. Which of the following systems of equations could a student use to write a quadratic

function in standard form for the parabola passing through the points (1, 4), (3, −2), and

(−2, 17)?

A. {

𝑎 + 4𝑏 + 𝑐 = 𝑦9𝑎 − 2𝑏 + 𝑐 = 𝑦−4𝑎 + 17𝑏 + 𝑐 = 𝑦

C. {2𝑎 + 𝑏 + 𝑐 = 46𝑎 + 3𝑏 + 𝑐 = −2−4𝑎 − 2𝑏 + 𝑐 = 17

B. {𝑎 + 𝑏 + 𝑐 = 4

9𝑎 + 3𝑏 + 𝑐 = −24𝑎 − 2𝑏 + 𝑐 = 17

D. {

𝑥2 + 4𝑥 + 𝑐 = 𝑦

3𝑥2 − 2𝑥 + 𝑐 = 𝑦

−2𝑥2 + 17𝑥 + 𝑐 = 𝑦


Released 8/22/16

31. Solve the following system to find the y-coordinates of the solution:

{𝑦 = 2𝑥2 − 6𝑥 + 7𝑦 = 5𝑥 − 5

A. 𝑦 =

5

2 𝑎𝑛𝑑 𝑦 = 15 C. 𝑦 = −20 𝑎𝑛𝑑 𝑦 = −45

B. 𝑦 =3

2 𝑎𝑛𝑑 𝑦 = 4 D. 𝑦 = −3 𝑎𝑛𝑑 𝑦 = −8

32. What are the 𝑥-coordinates of the points of intersection given the system below?

{ 𝑥2 + 6𝑥 + 5𝑦 + 16 = 0

2𝑥 + 𝑦 = −3

A. 𝑥 = 2 + √3, 𝑥 = 2 − √3 C. 𝑥 = 4 + 2√3, 𝑥 = 4 − 2√3

B. 𝑥 = 2 + 𝑖√15, 𝑥 = 2 − 𝑖√15 D. 𝑥 = −8 + √33, 𝑥 = −8 − √33

33. In the figure below, the perimeter is 4𝑥2 + 8𝑥 − 2𝑦 units and the length is 2𝑥2 + 𝑥 + 𝑦.

What is the width?

A. 𝑤 = 2𝑥2 − 7𝑥 − 3𝑦 C. 𝑤 = 6𝑥 − 4𝑦

B. 𝑤 = 2𝑥2 + 8𝑥 − 2 D. 𝑤 = 3𝑥 − 2𝑦

34. Multiply: (2𝑥2 + 4𝑥 − 5)(−𝑥2 + 3𝑥 + 6)

A. −2𝑥4 + 2𝑥3 + 29𝑥2 + 9𝑥 − 30 C. −2𝑥4 + 9𝑥2 + 21𝑥 − 30

B. 2𝑥4 + 10𝑥3 + 19𝑥2 + 9𝑥 − 30 D. −2𝑥4 + 24𝑥2 − 30


Released 8/22/16

35. Factor: 4𝑥4 − 13𝑥2 + 9

A. (2𝑥2 − 9)(2𝑥2 − 4) C. (4𝑥2 − 9)2(𝑥2 − 1)2

B. (2𝑥 − 3)(2𝑥 + 3)(𝑥 + 1)(𝑥 − 1) D. (4𝑥 − 3)(𝑥 + 3)(𝑥 + 1)(𝑥 − 1)

36. Factor: 125𝑥3 − 343

A. (5𝑥 − 7)(5𝑥2 + 35𝑥 + 9) C. (5𝑥 − 7)(25𝑥2 + 35𝑥 + 49)

B. (5𝑥 − 7)(5𝑥2 + 35𝑥 − 9) D. (5𝑥 − 7)(25𝑥2 − 35𝑥 − 49)

37. Factor the following using imaginary numbers: 9𝑥2 + 49

A. (3𝑥 − 7)2 C. (3𝑥 + 7𝑖)(3𝑥 − 7𝑖)

B. (√3𝑥 + 7)(√3𝑥 − 7) D. (3𝑥 + 7𝑖)2

38 Solve: 10𝑦3 − 4𝑦2 − 2𝑦 = −5𝑦3 + 3𝑦2

A. 𝑦 = −3, 𝑦 = 0, 𝑦 = 10 C. 𝑦 = 0, 𝑦 =

1 ± √41

10

B. 𝑦 = −1

5, 𝑦 = 0, 𝑦 =

2

3 D. 𝑦 = 0


Released 8/22/16

39. Solve: 𝑥4 − 64 = 0

A. 𝑥 = ±√8, 𝑥 = ±8𝑖 C. 𝑥 = ±8, 𝑥 = ±8𝑖

B. 𝑥 = ±2√2, 𝑥 = ±2𝑖√2 D. 𝑥 = ±4, 𝑥 = ±4𝑖

40. What is the remainder in the division (6𝑥3 − 𝑥2 + 4𝑥 − 9) ÷ (2𝑥 − 3)?

A. 15 C. 3

B. −3 D. −15

41. Find the quotient of (3𝑥3 − 44𝑥 + 8) ÷ (𝑥 − 4)?

A. 3𝑥2 − 12𝑥 + 4 C. 3𝑥2 − 32 +

−120

𝑥 − 4

B. 3𝑥2 − 12𝑥 + 4 +−8

𝑥 − 4 D. 3𝑥2 + 12𝑥 + 4 +

24

𝑥 − 4

42. What is the end behavior for the function, 𝑓(𝑥) = (𝑥4 − 5𝑥 − 3)(−9𝑥5 + 6𝑥3)?

A. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → +∞

B. as 𝑥 → −∞, 𝑓(𝑥) → +∞ and as 𝑥 → +∞, 𝑓(𝑥) → +∞

C. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → −∞

D. as 𝑥 → −∞, 𝑓(𝑥) → +∞ and as 𝑥 → +∞, 𝑓(𝑥) → −∞


Released 8/22/16

43. The equation 𝑥3 − 3𝑥2 + 4𝑥 − 12 = 0 is graphed below. Use the graph to help solve

the equation and find all the roots of the function.

A. 𝑥 = 3,−2, 2

B. 𝑥 = −12, 1, 3

C. 𝑥 = 3,−2𝑖, 2𝑖

D. 𝑥 = 12,3 − 𝑖√7

2,3 + 𝑖√7

2

44. Which polynomial is graphed below?

A. 𝑓(𝑥) = (𝑥 + 1)(𝑥 − 3)

B. 𝑓(𝑥) = (𝑥 − 1)(𝑥 + 1)(𝑥 + 3)

C. 𝑓(𝑥) = 𝑥(𝑥 − 3)(𝑥 + 1)

D. 𝑓(𝑥) = 𝑥(𝑥 + 3)(𝑥 − 1)

45. Find all of the zeros of 𝑓(𝑥) = 𝑥3 − 3𝑥2 + 4𝑥 − 2.

A. 𝑥 = 1 + 𝑖, 1 − 𝑖, 1 C. 𝑥 = −2 , −1, 1, 2

B. 𝑥 = 1 D. 𝑥 = −1,−2𝑖, 2𝑖


Released 8/22/16

46. Write a polynomial function of least degree that has rational coefficients, a leading

coefficient of 1, and the zeros 3𝑖, √2 , −4.

A. 𝑓(𝑥) = 𝑥5 − 4𝑥4 + 7𝑥3 + 28𝑥2 − 18𝑥 − 76

B. 𝑓(𝑥) = 𝑥5 − 4𝑥4 − 13𝑥3 − 52𝑥2 + 36𝑥 + 144

C. 𝑓(𝑥) = 𝑥5 + 4𝑥4 + 7𝑥3 + 28𝑥2 − 18𝑥 − 72

D. 𝑓(𝑥) = 𝑥6 − 9𝑥4 − 130𝑥2 + 288

47. A manufacturer is going to package their product in an open rectangular box made from a

single flat piece of cardboard. The box will be created by cutting a square out from each

corner of the rectangle and folding the flaps up to create a box. The original rectangular

piece of cardboard is 20 𝑖𝑛𝑐ℎ𝑒𝑠 long and 15 𝑖𝑛𝑐ℎ𝑒𝑠 wide. Write a function that

represents the volume of the box.

A. 𝑉(𝑥) = 𝑥3 − 35𝑥2 + 300𝑥 C. 𝑉(𝑥) = 𝑥2 − 35𝑥 + 300

B. 𝑉(𝑥) = 4𝑥3 − 70𝑥2 + 300𝑥 D. 𝑉(𝑥) = 4𝑥2 − 70𝑥 + 300


Released 8/22/16

48. Sketch the graphs of 𝑓(𝑥) and 𝑔(𝑥) on the same coordinate plane given the following

information:

𝑓(𝑥) has zeros at −1, 4, 8

As 𝑥 → −∞, 𝑓(𝑥) → +∞ and as 𝑥 → +∞, 𝑓(𝑥) → −∞

𝑓(𝑥) has a local minima at approximately (6, 3) and a local maxima at

approximately (1, −4) 𝑔(𝑥) = 2𝑥 + 1

How many real solutions exist when 𝑓(𝑥) = 𝑔(𝑥)?

A. 𝑛𝑜 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

B. 1 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

C. 2 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

D. 3 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

49. Identify any holes, asymptotes, and intercepts of 𝑓(𝑥) =𝑥2−𝑥−6

𝑥2+7𝑥+10

A. Horizontal Asymptote: 𝑦 = −2, 3

Vertical Asymptote: 𝑥 = −5,−2

Hole: 𝑛𝑜𝑛𝑒

x-intercept: (10, 0) y-intercept: (0, −6)

C. Horizontal Asymptote: 𝑦 = 1

Vertical Asymptote: 𝑥 = −5

Hole at 𝑥 = −2

x-intercept: (3, 0)

y-intercept: (0,−3

5)

B. Horizontal Asymptote: 𝑛𝑜𝑛𝑒

Vertical Asymptote: 𝑥 = −5

Hole at 𝑥 = −2

x-intercept: (3, 0) y-intercept: (0, −5)

D. Horizontal Asymptote: 𝑦 = −5

Vertical Asymptote: 𝑥 = 1

Hole: 𝑛𝑜𝑛𝑒

x-intercept: (−2, 0), (−5, 0) y-intercept: (0, −2), (0, 3)


Released 8/22/16

50. State the Domain and Range of the function: 𝑦 = 𝑥+7

3𝑥−15

A. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≠ −5} 𝑅𝑎𝑛𝑔𝑒: {𝑦|𝑦 ≠ −7}

C. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≠ 5}

𝑅𝑎𝑛𝑔𝑒: {𝑦|𝑦 ≠13}

B. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≠ −5}

𝑅𝑎𝑛𝑔𝑒: {𝑦|𝑦 ≠ −715}

D. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≠ 5}

𝑅𝑎𝑛𝑔𝑒: {𝑦|𝑦 ≠ −73}

52. Which statement describes the end behavior of the function 𝑓(𝑥) = −5𝑥+4

2𝑥−3 ?

A. as 𝑥 → −∞, 𝑓(𝑥) → +3

2 and as 𝑥 → +∞, 𝑓(𝑥) → −

5

2

B. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → +3

2

C. as 𝑥 → −∞, 𝑓(𝑥) → −5

2 and as 𝑥 → +∞, 𝑓(𝑥) → −

5

2

D. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → −5

2

51. Which of the following is the graphing form of 𝑓(𝑥) = 4𝑥−14

𝑥−6 ?

A. 𝑓(𝑥) =6

𝑥 − 3+ 10 C. 𝑓(𝑥) =

4

𝑥 − 6+ 4

B. 𝑓(𝑥) =4

𝑥 − 3+ 10 D. 𝑓(𝑥) =

10

𝑥 − 6+ 4


Released 8/22/16

53. Which is a graph of 𝑓(𝑥) = 4𝑥+4

𝑥+2 with any asymptotes indicated by dashed lines?

A.

C.

B.

D.

54. Translate the graph of 𝑓(𝑥) = 6𝑥+7

𝑥+1 one unit down and four units left. Which of the

following is the function after the translations?

A. 𝑔(𝑥) =1

𝑥 − 4− 1 C. 𝑔(𝑥) =

1

𝑥 − 3+ 5

B. 𝑔(𝑥) =6

𝑥 − 4− 1 D. 𝑔(𝑥) =

1

𝑥 + 5+ 5


Released 8/22/16

55. Which of the following functions is modeled by the graph below?

A. 𝑓(𝑥) = −

2

𝑥 + 3+ 4

B. 𝑓(𝑥) =2

𝑥 + 3+ 4

C. 𝑓(𝑥) =

2

𝑥 − 3+ 4

D. 𝑓(𝑥) = −2

𝑥 − 3+ 4

56. Simplify: 𝑥2−9𝑥+14

𝑥2−6𝑥+5

𝑥2−8𝑥+7

𝑥2−7𝑥+10

A. (𝑥 − 7)2

(𝑥 − 5)2 C.

(𝑥 − 5)(𝑥 − 7)

2(𝑥 − 1)

B. (𝑥 − 2)2

(𝑥 − 1)2 D.

(𝑥 − 7)

2(𝑥 − 1)

57. Perform the indicated operation: 𝑥+2

𝑥+5∙ 𝑥2

𝑥+2

𝑥+1

𝑥+5

A. 𝑥2(𝑥 + 1)

(𝑥 + 5)2 C.

(𝑥 + 5)2

𝑥2(𝑥 + 1)

B. (𝑥 + 2)2

𝑥2(𝑥 + 1) D.

𝑥2

𝑥 + 1


Released 8/22/16

58. Perform the indicated operation: 𝑥+4

𝑥+8+𝑥−1

𝑥−3−

5𝑥−6

𝑥2+5𝑥−24

A. 2𝑥2 + 3𝑥 + 41

(𝑥 + 8)2(𝑥 − 3)2 C.

2𝑥2 + 3𝑥 − 14

(𝑥 + 8)(𝑥 − 3)

B. 10𝑥2 − 2𝑥 − 12

(𝑥 + 8)(𝑥 − 3) D.

−3𝑥 + 9

(𝑥 + 8)(𝑥 − 3)

59. Simplify: 1

1−𝑥+

𝑥

𝑥−1

A. 1 C. 𝑥 + 1

1 − 𝑥

B. 𝑥 + 1

𝑥 − 1 D.

𝑥 + 1

(𝑥 − 1)2

60. If each of the following expressions is defined, which is equivalent to 𝑥 − 1 ?

A. (𝑥 + 1)(𝑥 − 1)

(𝑥 − 1) C.

(𝑥 + 1)(𝑥 + 2)

𝑥 − 2÷𝑥 + 2

𝑥 − 2

B. (𝑥 − 1)(𝑥 + 2)

𝑥 + 1∙𝑥 + 1

𝑥 + 2 D.

𝑥 + 1

𝑥 + 2+𝑥 − 1

𝑥 + 2


Released 8/22/16

61. Perform the indicated operation:

𝑥−3

2−4

𝑥+1+𝑥

3

A. 3𝑥 + 3

2(𝑥 + 4) C.

3𝑥2 − 6𝑥 − 9

−8𝑥

B. 𝑥3 − 𝑥2 − 15𝑥 + 36

6(𝑥 + 1) D.

3𝑥2 − 6𝑥 − 9

2(−4 + 𝑥)

62. Solve: 2

𝑥2−4=

1

2𝑥−4

A. 𝑥 = −2 C. 𝑥 = 2

B. 𝑥 = 0 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

63. Solve: 𝑥−1

𝑥+1+𝑥+7

𝑥−1=

4

𝑥2−1

A. 𝑥 = −1,− 2 C. 𝑥 = −2

B. 𝑥 = −1, 1 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛


Released 8/22/16

64. Let 𝑓(𝑥) = 2𝑥+3

𝑥+3 and 𝑔(𝑥) = −3𝑥 − 7. Use the graph of 𝑓(𝑥) below to help determine

the values of x for which 𝑓(𝑥) = 𝑔(𝑥).

A. 𝑥 = −1, 5

B. 𝑥 = −2,−4

C. 𝑥 = −3, 2

D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛


Released 8/22/16

Algebra 2 Honors Semester 1 Instructional Materials 2016-2017

Answers

1. B 14. B 27. C 40. A 53. B

2. A 15. A 28. D 41. D 54. D

3. C 16. D 29. B 42. D 55. A

4. A 17. D 30. B 43. C 56. B

5. D 18. C 31. A 44. C 57. D

6. D 19. B 32. A 45. A 58. C

7. C 20. C 33. D 46. C 59. A

8. B 21. C 34. A 47. B 60. B

9. D 22. D 35. B 48. B 61. A

10. A 23. A 36. C 49. C 62. D

11. D 24. A 37. C 50. C 63. C

12. A 25. A 38. B 51. D 64. B

13. B 26. D 39. B 52. C

Date post:	23-Sep-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Algebra 2 Honors Semester 1 (#2227) - Ms....

Documents