Name: A2.MidtermRev2015

Algebra 2 Midterm Exam Review

Part 1: Multiple Choice (75pts)

UNIT 1

Patterns & Expressions

1. Which of the following is the seventh term in the pattern below?

𝟏𝟒, 𝟓, −𝟒, −𝟏𝟑, …

A. −22 B. −40 C. −49 D. −63

2. Which of the following is the eighth term in the pattern below?

−𝟏,𝟏

𝟐, −

𝟏

𝟒,𝟏

𝟖, …

3. Which of the following algebraic

expressions represents the pattern in the group of figures below? (𝟏𝒑𝒕)

A. 𝑛 − 2 B. 𝑛 − 11 C. 9 − 2𝑛 D. 11 − 2𝑛

4. Which of the following expressions represents the number of circles in the 𝑛th figure?

A. 3𝑛 B. 𝑛 + 3 C. 𝑛 − 3

D. 𝑛

3

Solving Absolute Value Equations & Inequalities

5. Which of the following is the solution the absolute value equation below?

|5ℎ − 10| = 15

A. ℎ = −15; ℎ = 15 B. ℎ = −5; ℎ = 5 C. ℎ = −5; ℎ = 1 D. ℎ = −1; ℎ = 5

6. Solve the absolute value equation below. Graph your answer on the number line provided.

|2𝑥 + 6| < 12

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UNIT 2

Section 1: Evaluating Functions

7. If 𝑓(𝑥) = 2𝑥2 − 𝑥 − 10, then find 𝑓(−2).

A. −20 B. 0 C. −16 D. −4

8. If 𝑓(𝑥) = 𝑥2 + 𝑥 − 3, then find 𝑓(−4).

A. 9 B. 15 C. −23 D. −17

Section 2: Characteristics of Functions

9. Which of the following relations does not represent a function?

A.

B. {(−2, −9), (0, −8), (2, −7)(4, −6)}

C. Domain Range

D.

10. Which of the following relations does not represent a function?

A.

B. {(−2, −9), (0, −8), (−2, −7)(4, −6)}

C. Domain Range

D.

Section 3: Slope of a Line

11. Find the slope of the line passing through the points (−1, 3) and (−4, 6).

12. Find the slope of the line passing through the points (2, −5) and (8, 1).

A. 1 B. −1 C. −2 D. 2

1

4 9

-1 1 2 3

𝒙 −2 −1 0 1

𝒚 3 5 4 1

-1 1 2 3

1

4 9

𝒙 −2 −1 0 1

𝒚 7 7 7 7

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Section 4: Writing Linear Equations

13. Write the equation for the line that goes through the point (5, 2) and has a slope

of −2

5.

A. 𝑦 = −2

5𝑥

B. 𝑦 = −2

5𝑥 + 4

C. 𝑦 = −2

5𝑥 +

29

5

D. 𝑦 = −2

5𝑥 + 2

14. Write the equation for the line that goes through the point (5, 2) and has a slope

of 2

5.

15. Write the equation for the line that goes through the point (−1, 2) and (3, −2).

16. Write the equation for the line that goes through the point (1, 4) and (−1, 2).

A. 𝑦 = 𝑥 + 5 B. 𝑦 = 𝑥 + 4 C. 𝑦 = 𝑥 + 3 D. 𝑦 = 𝑥 + 2

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Section 5: Graphing Inequalities

17. Which of the following is the solution to

the inequality below?

2𝑥 − 3𝑦 ≤ 6

A.

B.

C.

D.

18. Which of the following is the solution to the

inequality below?

3𝑥 − 2𝑦 > 4

A.

B.

C.

D.

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Section 6: Graphing Absolute Value Equations

19. Which of the following is the graph of the

absolute value equation below?

𝒚 = |𝒙 − 𝟑| + 𝟏

A.

B.

C.

D.

20. Graph the absolute value equation on the

coordinate grid below.

𝒚 = 𝟐|𝒙 + 𝟑| − 𝟒

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UNIT 3

Section 1: Solving Systems of Equations by Graphing

21. Solve the system of equations by graphing.

2𝑥 + 𝑦 = 1 3𝑥 − 𝑦 = 4

A.

(1, −1)

B.

(3, −5)

C.

(3, 5)

D.

(1, 1)

22. Solve the system of equations by graphing.

2𝑥 − 3𝑦 = −9

𝑥 + 𝑦 = −2

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Section 2: Solving Systems of Equations by Substitution

23. What is the value of 𝒙 in the system of equations below?

𝑦 + 3𝑥 = 10 2𝑥 − 5𝑦 = 1

A. −1 B. 1 C. −3 D. 3

24. Use substitution to solve the system of equations below.

7𝑤 − 4𝑧 = −16

𝑧 = 3𝑤 − 1

Section 3: Solving Systems of Equations by Elimination

25. Use elimination to find the solution of the system of equations below.

5𝑎 + 4𝑏 = −3

𝑎 + 3𝑏 = 6

26. What is the value of 𝒎 in the system of equations below?

2𝑚 + 3𝑛 = 1 4𝑚 − 𝑛 = 9

A. −1 B. 1 C. −2 D. 2

UNIT 4

Section 1: Factoring Quadratic Equations

27. The expression below represents the area, in square meters, of a rectangle.

𝑥2 − 8𝑥 + 12

Which of the following pairs of expressions

could represent the length and width, in meters, of the rectangle?

A. (𝑥 − 3)(𝑥 − 4) B. (𝑥 + 2)(𝑥 + 6)

C. (𝑥 − 2)(𝑥 − 6) D. (𝑥 + 3)(𝑥 + 4)

28. The expression below represents the area, in square meters, of a rectangle.

𝑥2 − 9𝑥 + 20

Which of the following pairs of expressions

could represent the length and width, in meters, of the rectangle?

A. (𝑥 + 5)(𝑥 + 4) B. (𝑥 + 2)(𝑥 + 10)

C. (𝑥 − 2)(𝑥 − 10) D. (𝑥 − 5)(𝑥 − 4)

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29. When factored the quadratic 𝑥2 + 𝑏𝑥 + 𝑐 equals (𝑥 − 3)(𝑥 + 3). What is the value of 𝑐?

A. 9 B. −9 C. 0 D. −3

30. When factored the quadratic 𝑥2 + 𝑏𝑥 +𝑐 equals (𝑥 − 6)(𝑥 + 6). What is the value of 𝑐?

A. −6 B. 0 C. −36 D. 36

UNIT 5

Section 1: Solving by Factoring

31. Which of the following are the solutions of the quadratic equation below?

𝑥2 − 𝑥 − 20 = 0

A. 𝑥 = −4; 𝑥 = 5 B. 𝑥 = −2; 𝑥 = 10

C. 𝑥 = 2; 𝑥 = −10 D. 𝑥 = 4; 𝑥 = −5

32. What are the solutions of the quadratic equation below?

𝑥2 − 𝑥 − 6 = 0

Section 2: Writing Equations from Graphs

33. A parabola is graphed on the coordinate

grid below.

Which of the following is the equation of the parabola?

A. 𝑦 = −1

3(𝑥 − 1)2 + 3 B. 𝑦 = 3(𝑥 − 1)2 + 3

C. 𝑦 = −3(𝑥 − 1)2 + 3 D. 𝑦 =1

3(𝑥 − 1)2 + 3

34. A parabola is graphed on the coordinate

grid below.

Write the equation of the parabola above in vertex form.

-1 0 1 2 3

3

2

1

-1

-5 -4 -3 -2 -1 0

1

-1

-2

-3

-4

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Section 3: Graphing in Vertex Form

35. Which of the following is the graph of the equation: 𝑦 = −(𝑥 − 2)2 − 1?

A.

B.

C.

D.

36. Which of the following is the equation of the equation: 𝑦 = (𝑥 + 2)2 + 1?

A.

B.

C.

D.

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Section 4: Converting Between Standard & Vertex Form

37. Rewrite the quadratic equation below in standard form.

𝑦 = 2(𝑥 − 3)2 − 8

38. Which of the following is the quadratic function below written in standard form?

𝑦 = 3(𝑥 + 2)2 − 6

A. 3𝑥2 − 2 B. 3𝑥2 + 12𝑥 − 6

C. 3𝑥2 + 12𝑥 + 6 D. 3𝑥2 + 12𝑥 + 12

39. Which of the following is the quadratic function below written in vertex form?

𝑦 = 𝑥2 − 2𝑥 − 5

A. 𝑦 = (𝑥 + 1)2 + 2 B. 𝑦 = (𝑥 − 1)2 + 6

C. 𝑦 = (𝑥 + 1)2 − 2 D. 𝑦 = (𝑥 − 1)2 − 6

40. Rewrite the quadratic equation below in vertex form?

𝑦 = 2𝑥2 − 4𝑥 − 5

Section 5: Quadratic Formula

41. Find the solutions of the quadratic equation below. Write your answer in simplest radical form.

𝑦 = 8𝑥2 − 12𝑥 + 3

42. Which of the following are the solutions of the quadratic equation below?

𝑦 = 9𝑥2 + 3𝑥 − 1

A. −1+√5

6,

−1−√5

6 B.

1+3√5

6,

1−3√5

6

C. 1+√5

6,

1−√5

6 D.

−1+3√5

6,

−1−3√5

6

Section 6: Simplifying Negative Square Roots

43. Which of the following is the expression below in simplest radical form?

√−12

A. −2√3 B. −4√3

C. 2𝒊√3 D. 4𝒊√3

44. Write the radical expression below in simplest terms.

√−8

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Section 7: Operations with Complex Numbers

45. Which of the following is equivalent to the expression below?

(2 + 3𝑖) − (5 − 7𝑖)

46. Which of the following is equivalent to the expression below?

(2 + 𝑖) − (7 − 4𝑖)

A. −5 + 5𝒊 B. 5 + 5𝒊

C. 5 − 3𝒊 D. −5 − 3𝒊

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Part 2: Open Response (25pts)

ON YOUR ANSWER SHEET, be sure to answer and label all parts of each question. Do not leave any questions blank.

1. Line 𝑞 is represented by the equation below.

𝑦 = −4

3𝑥 − 4

a. What is the slope of line 𝑞? Show or explain how you got your answer.

b. What is the 𝑦-intercept of line 𝑞? Show or explain how you got your answer.

c. What is the 𝑥-intercept of line 𝑞? Show or explain how you got your answer.

A coordinate plane is shown below. Copy the axes and the labels of the cordinate plane exactly as shown onto the grid in your Student Anser Booklet.

d. On the coordinate grid, graph line 𝑞.

e. Write an equation of the line that has the same the 𝑥-intercept as line 𝑞 and a slope of−2. Show or explain how you got your answer.

2. Line 𝑞 is represented by the equation below.

𝑦 = −5

2𝑥 + 10

a. What is the slope of line 𝑞? Show or explain how you got your answer.

b. What is the 𝑦-intercept of line 𝑞? Show or explain how you got your answer.

c. What is the 𝑥-intercept of line 𝑞? Show or explain how you got your answer.

A coordinate plane is shown below. Copy the axes and the labels of the cordinate plane exactly as shown onto the grid in your Student Anser Booklet.

d. On the coordinate grid, graph line 𝑞.

e. Write an equation of the line that has the same the 𝑥-intercept as line 𝑞 and a slope of−2. Show or explain how you got your answer.

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Unit 3: Systems of Linear Equations

For the situation below, you will find the value of the unknowns by writing and solving a system of equations. 3. A club of 18 students and 5 adults are going

on a canoe trip. There will be one adult in each canoe. Big canoes hold five people each, and small canoes hold four people each.

a. Write an equation that represents the total

number of canoes, where 𝒙 represents the number of big canoes and 𝒚 represents the number of small canoes.

b. Write an equation to represent the total

number of people all of the canoes can carry.

c. Use the two equations you wrote above to

find how many of each canoe that the group needs to rent.

For the situation below, you will find the value of the unknowns by writing and solving a system of equations. 4. A youth group with 26 members is going skiing.

Each of the five chaperones will drive a van or sedan. The vans can seat seven people, and the sedans can seat five people.

a. Write an equation that represents the total number of vehicles, where 𝑥 represents the number of vans and 𝑦 represents the number of sedans.

b. Write an equation to represent the total

number of people all of the vehicles can transport.

c. Use the two equations you wrote above to

find how many of each vehicle the youth group must drive.

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5. Solve the quadratic equation below using

any method.

3𝑥2 + 8𝑥 = −4

6. Solve the quadratic equation below using any method.

2𝑥2 − 5𝑥 = −3

7. Solve the quadratic equation below using any method.

4𝑥2 − 12𝑥 = 40

8. Solve the quadratic equation below using any method.

5𝑥2 + 20𝑥 = 60