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Algebra II – Midterm Review Packet
• GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to
class every day. Gather up all of your old quiz and test reviews as you might find them helpful. Use
them to help you with each chapter.
• DO NOT FALL BEHIND. Do the problems that are assigned every night and come to class prepared
to ask about the things you could not do.
• GET SERIOUS. The grade you earn on this exam is worth 20% of your semester grade.
• MAKE NOTES AS YOU WORK. As you do these problems, you will come across formulas,
definitions, problems, and graphs that you will want to put on your notecard.
• NOTECARD: I will provide you with a 5” x 8” notecard. You are allowed to include any information
on this notecard (front and back) that you think will be helpful for the exam. This will be turned in with
your exam. No points are awarded for making a note card – it is a helpful study tool! Your notecard
must be in your own writing.
• GRADE FOR PACKET: This packet is worth a 1-weight quiz grade. This grade is based on:
✓ Completion. I will check each day to make sure that day’s work is done. YOU MUST
SHOW WORK.
✓ Correctness. I will check random problems to make sure they are correct, or that you made
corrections as needed.
• There is nothing on the exam that you have not studied this year.
• You will turn in your review packet on the day that you take your midterm.
Midterm Review Packet Assignments
4th Hour Exam: Wednesday, January 17th, 8:00 – 9:30 a.m.
Assignment Due Date
Chapters 1 & 2 Monday, January 8th
Chapter 3 Tuesday, January 9th
Chapter 5 (ODDS) Wednesday, January 10th
Chapter 5 (EVENS) Thursday, January 11th
Chapter 6 Friday, January 12th
Algebra II – Midterm Review Answers CHAPTER 1 1. 19 2. 81 3. 8 4. -25 5. 25 6. 2 7. 22 8. -5 9. 2
10. Coeff: -5, 3, 6; Constant: -2; Like: 3x & 6x 11. 𝑥2 − 4𝑥 + 6 12. 4𝑥 − 6 13. −3𝑥 + 7
14. 4 15. 6 16. 2 17. 𝑦 = 2𝑥 + 3 18. 𝑦 = −2𝑥 − 3 19. 𝑦 = −3𝑥 + 4 20. C 21. B
22. A 23. D 24. C
CHAPTER 2 1 – 2. See key for graph 3. -37 4. -2 5. -2 6. undefined 7. 0.93°𝐹 8. 𝑦 = −3𝑥 + 2
9. 𝑦 = 2𝑥 − 5 10-12. See key for graph 13. parallel 14. perpendicular
15a. 𝑦 = 5𝑥 + 50 15b. $315 16. B 17. C 18. C 19. B 20. A 21. C 22. A
CHAPTER 3 1. (1, −6) 2. no solution 3. (2, 3) 4. (−4, −1) 5. (−3, −6) 6. (10, −1) 7. (6, −9)
8. (−6, 0) 9. baseball ticket: $90, hotel: $155 10. 14 blue fish, 10 rockfish 11. B 12. D
CHAPTER 5 1. Axis: x = 4; Vertex: (4, 19); opens down; max 2. Axis: x = 1; Vertex: (1, 4); opens up; min
3. Axis: x = -5; Vertex: (−5, −1); opens up; min 4. Axis: x = 2; Vertex: (2, 6); opens down; max
5. up 2 6. left 2 7. reflect over x-axis, down 4 8. 3𝑥2 + 8𝑥 − 3 9. 𝑥2 + 8𝑥 + 16
10. 2𝑥2 + 4𝑥 − 30 11. (𝑥 + 7)(𝑥 − 1) 12. 2(𝑥 − 5)(𝑥 + 2) 13. (𝑥 + 5)(𝑥 − 5) 14. (𝑥 + 1)(4𝑥 − 3)
15. 3(𝑥 + 3)(𝑥 − 3) 16. 3(2𝑥 + 3)(𝑥 − 2) 17. 11 − 7𝑖 18. −5 + 5𝑖 19. −10 + 6𝑖 20. 14 − 27𝑖
21. 3√2 22. 6√5 23. 9
7 24.
3√7
7 25. 4𝑖 26. 6𝑖√2 27. 5, −3 28. 0, 5 29. ±3𝑖 30.
5±𝑖√83
6
31. 6 ± √5 32. −1 ± √3 33. A 34. C 35. B36. D 37. C 38. B 39. A 40. C
CHAPTER 6
1. 27𝑥3𝑦6 2. 14𝑥3𝑦2 3. 2𝑦14
3𝑥3 4. 4𝑦4
9𝑥2 5. 4𝑥2 + 17𝑥 − 1 6. 12𝑥3 − 8𝑥2 − 2𝑥 + 21
7. 2𝑥3 − 7𝑥2 − 𝑥 + 21 8. 𝑥3 + 3𝑥2 − 6𝑥 − 8 9. 𝑥2 − 3𝑥 + 10 +−30
𝑥+2 10. 𝑥2 + 3𝑥 + 14 +
39
𝑥−3
11. 𝑥(𝑥 + 5)(𝑥 − 3) 12. 3𝑥(𝑥 + 5)(𝑥 + 5) 13. 3𝑥3(𝑥 + 5)(𝑥 − 5) 14. (𝑥 + 7)(𝑥 + 3)(𝑥 − 3)
15. (𝑥 + 3)(𝑥2 + 4) 16. 𝑥(𝑥 − 4) 17. 0, 12, −6 18. 0, 5, 2 19. 3, −4, 4 20. −3, 3
21. −5, −1, 1 22. −5, ±√7 23. Deg: 4; LC: 1; zeros: -3, 0; 𝐴𝑠 𝑥 → −∞, 𝑓(𝑥) → ∞𝐴𝑠 𝑥 → ∞, 𝑓(𝑥) → ∞
24. Deg: 3; LC: 1; zeros: -2, 0, 5; 𝐴𝑠 𝑥 → −∞, 𝑓(𝑥) → −∞
𝐴𝑠 𝑥 → ∞, 𝑓(𝑥) → ∞ 25. zeros: -1, 3, 0; Deg: 4; LC: negative
26. B 27. B
Simplify the expression.
1. 42 + 3(4 − 2) ÷ 2 2. 27 ÷ 3(5 − 2)2 3. 2 − 3[5 − (4 + 3)]
4. −52 5. (−5)2 6. 2[6 − (4 + 3)]2
Evaluate the expression at the given value.
7. 6𝑥 − 2 when 𝑥 = 4 8. −2𝑥2 + 3 when 𝑥 = −2 9. 𝑥2 − (2𝑥 + 1) when 𝑥 = 3
10. Given −5𝑥2 + 3𝑥 − 2 + 6𝑥 list the following:
Coefficient(s):
Constant(s):
Like Term(s):
Simplify the expression.
11. 3𝑥2 − 2(𝑥2 + 2𝑥 − 3) 12. 𝑥 + 3(𝑥 − 2) 13. 10 − 3(𝑥 + 1)
Solve the equation.
14. 3𝑥 + 7 = 5𝑥 − 1 15. 𝑥
2+ 5 = 8 16. 2(5𝑥 − 6) = −4(𝑥 − 3) + 4
CHAPTER 1 – Tools of Algebra
Solve the equation for y.
17. 𝑦 − 3 = 2𝑥 18. 2𝑦 = −4𝑥 − 6 19. 9𝑥 + 3𝑦 = 12
MULTIPLE CHOICE PRACTICE FOR CHAPTER 1
20. What is the value of the expression (2)3?
A. −32
B. −10
C. 8
D. 6
21. What is the value of 2𝑥 − (3𝑥 + 1)2 when 𝑥 = 3?
A. −4
B. −94
C. −44
D. −14
22. Simplify the following expression: −8𝑥2 + 𝑥 − 2 − 3𝑥2 + 2𝑥
A. −11𝑥2 + 3𝑥 − 2
B. 5𝑥2 + 3𝑥 − 2
C. −8𝑥2 − 2
D. −8𝑥4 + 3𝑥2 − 2
23. Solve the following equation: −3𝑚 − 2 = 13?
A. −4
B. −8
3
C. 9
D. −5
24. Solve the following equation: 4(𝑥 + 5) = 36
A. 12
B. 23
4
C. 4
D. -13
Graph the equation using a table of values.
1. 𝑦 = −2𝑥 + 3 2. 𝑦 = 3𝑥 − 2
x
y
Evaluate the function at the given value.
3. 𝑓(𝑥) = −5𝑥2 + 8 when 𝑥 = −3 4. 𝑓(𝑥) = 𝑥2 + 2𝑥 − 10 when 𝑥 = 2
Determine the slope between the points. **SLOPE FORMULA:
5. (4 , 6) , (3 , 8) 6. (10 , −2) , (10 , 5)
7. A can of Coke sitting on the counter is initially 38°F. After 15 minutes, the can warmed up to 52°F.
Find the average rate of change of the temperature of the Coke.
Write an equation in slope intercept form for the line with the following characteristics.
**SLOPE-INTERCEPT FORM: **POINT-SLOPE FORM:
8. Passes through (2, −4) and 𝑚 = −3 9. Passes through (1, −3) and (6, 7)
x
y
CHAPTER 2 – Linear Equations and Functions
Graph the equation using slope-intercept form.
10. 𝑦 = −2𝑥 + 3 11. 𝑦 − 2 =1
2𝑥 12. 3𝑦 = −2𝑥 + 9
m = ________ m = ________ m = ________
b = ________ b = ________ b = ________
Determine if the lines are parallel, perpendicular, or neither.
**PARALLEL LINES: **PERPENDICULAR LINES:
13. 𝐿𝑖𝑛𝑒 1: 𝑦 = 2𝑥 + 4𝐿𝑖𝑛𝑒 2: 2𝑦 = 4𝑥 − 6
14. 𝐿𝑖𝑛𝑒 1: 𝑦 = 4𝑥 + 1
𝐿𝑖𝑛𝑒 2: 𝑦 = −1
4𝑥 + 3
15. You decide to rent a moving truck to move your stuff to college. The truck company charges a
one-time insurance fee of $50 plus an additional $5 per mile the truck is driven.
a) Write an equation that gives the total cost of renting the truck as a function of the number of
miles driven.
b) How much would it cost to rent the truck if your college is 53 miles away.
MULTIPLE CHOICE PRACTICE FOR CHAPTER 2
16. Which two ordered pairs determine a line with a slope of −2
3?
A. (5, 7), (7, 4) C. (3, 2), (1, −3)
B. (−3, 0), (0, −2) D. (8, 2), (5, 0)
17. What is the slope of a line that is perpendicular to a line with a slope of −4?
A. −4 C. 1
4
B. −1
4 D. 4
18. Which graph represents the line 𝑦 = −3?
A. B. C.
19. Which graph represents the equation 𝑦 = −𝑥 − 2?
A. B. C.
20. A pediatrician uses the model ℎ = 3𝑎 + 28.6 to estimate the height ℎ of a boy, in inches, in terms
of the boy’s age 𝑎, in years, between the ages of 2 and 5. Based on the model, what is the
estimated increase, in inches, of a boy’s height each year?
A. 3 C. 5.7
B. 28.6 D. 14.3
21. Which equation matches the graph below?
A. 𝑦 = 𝑥 + 1 C. 𝑦 =3
2𝑥 + 1
B. 𝑦 = −3
2𝑥 + 1 D. 𝑦 =
2
3𝑥 + 1
22.
The graph above shows the distance traveled 𝑑, in feet, by a product on a conveyor belt 𝑚
minutes after the product is placed on the belt. Which of the following equations correctly
relates 𝑑 and 𝑚?
A. 𝑑 = 2𝑚 C. 𝑑 =1
2𝑚
B. 𝑑 = 𝑚 + 2 D. 𝑑 = 2𝑚 + 2
Solve the system by graphing.
1. 𝑦 = −4𝑥 − 2
−3𝑦 = 6𝑥 + 12 2.
𝑦 =1
2𝑥 + 2
−2𝑥 + 4𝑦 = −4
Solve the system by using the SUBSTITUTION method.
3. 𝑦 = 5𝑥 − 7
−3𝑥 − 2𝑦 = −12 4.
−3𝑥 − 8𝑦 = 20−5𝑥 + 𝑦 = 19
5. −4𝑥 + 𝑦 = 6
−5𝑥 − 𝑦 = 21
Solve the system by using the ELIMINATION method.
6. 𝑥 − 𝑦 = 11
2𝑥 + 𝑦 = 19 7.
7𝑥 + 2𝑦 = 248𝑥 + 2𝑦 = 30
8. 5𝑥 + 4𝑦 = −303𝑥 − 9𝑦 = −18
CHAPTER 3 – Systems of Equations
9. A travel agency offers two Boston outings. Plan A costs $645 and includes hotel accommodations
for three nights and two baseball tickets. Plan B costs $1135 and includes hotel accommodations
for five nights and four baseball tickets. Find the cost of one baseball ticket and one night’s hotel
accommodation.
10. On a fishing trip, Mary caught twenty-four fish. She caught some rockfish averaging 2.5 lb. and
some bluefish averaging 8 lb. The total weight of the fish was 137 lb. How many of each kind did
she catch?
MULTIPLE CHOICE PRACTICE FOR CHAPTER 3
11. A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of
the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled
to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-
person tents?
A. 30 C. 20
B. 19 D. 18
12. Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench
during the concert cost $75 each, and tickets to sit on the lawn during the concert cost $40
each. Organizers of the concert announced that 350 tickets had been sold and that $19,250
had been raised through ticket sales alone. Which of the following systems of equations could
be used to find the number of tickets for bench seats B, and the number of tickets for lawn seats
L, that were sold for the concert?
A. (75𝐵)(40𝐿) = 1,950
𝐵 + 𝐿 = 350
B. 75𝐵 + 40𝐿 = 350
𝐵 + 𝐿 = 19,250
C. 40𝐵 + 75𝐿 = 19,250
𝐵 + 𝐿 = 350
D. 75𝐵 + 40𝐿 = 19,250
𝐵 + 𝐿 = 350
**STANDARD FORM: **AXIS OF SYMMETRY:
Find the axis of symmetry and the vertex of the quadratic function. Tell whether the graph opens up or
down and identify whether the vertex is a max or a min.
1. 𝑦 = −𝑥2 + 8𝑥 + 3 2. 𝑦 = 𝑥2 − 2𝑥 + 5
Axis of Symmetry: Axis of Symmetry:
Vertex: Vertex:
Opens up or down? Opens up or down?
Max or Min? (Circle one) Max or Min? (Circle one)
**VERTEX FORM: **VERTEX:
Find the axis of symmetry and the vertex of the quadratic function. Tell whether the graph opens up or
down and identify whether the vertex is a max or a min.
3. 𝑦 = (𝑥 + 5)2 − 1 4. 𝑦 = −(𝑥 − 2)2 + 6
Axis of Symmetry: Axis of Symmetry:
Vertex: Vertex:
Opens up or down? Opens up or down?
Max or Min? (Circle one) Max or Min? (Circle one)
Describe the transformations the following equations would apply to 𝒚 = 𝒙𝟐.
5. 𝑦 = 𝑥2 + 2 6. 𝑦 = (𝑥 + 2)2 7. 𝑦 = −𝑥2 − 4
Multiply the expression. Write your answer in standard form.
8. (𝑥 + 3)(3𝑥 − 1) 9. (𝑥 + 4)2 10. 2(𝑥 − 3)(𝑥 + 5)
CHAPTER 5 – Quadratic Functions and Factoring
Factor the expression.
11. 𝑥2 + 6𝑥 − 7 12. 2𝑥2 − 6𝑥 − 20 13. 𝑥2 − 25
14. 4𝑥2 + 𝑥 − 3 15. 3𝑥2 − 27 16. 6𝑥2 − 3𝑥 − 18
Simplify the complex expression. **𝒊𝟐 =
17. (7 − 8𝑖) + (4 + 𝑖) 18. (−2 + 4𝑖) − (3 − 𝑖)
19. 2𝑖(3 + 5𝑖) 20. (3 − 4𝑖)(6 − 𝑖)
Simplify the expression.
21. √18 22. √2 ∙ 3√10 23. √81
49
24. √9
7 25. √−16 26. √−72
Solve the equation.
27. 𝑥2 − 2𝑥 = 15 28. 4𝑥2 − 20𝑥 = 0 29. 𝑥2 + 3 = −6
30. 3𝑥2 − 5𝑥 + 9 = 0 31. (𝑥 − 6)2 = 5 32. −2𝑥2 − 4𝑥 + 4 = 0
MULTIPLE CHOICE PRACTICE FOR CHAPTER 5
33. If the graph of 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 opens up, then which of the following must be true?
A. 𝑎 > 0 C. 𝑐 > 0
B. 𝑎 < 0 D. 𝑐 < 0
34. Which is a solution to the equation 𝑥2 = 9𝑥?
A. −9 C. 0
B. 3 D. 8
35. Solve the equation: 𝑥2 + 2𝑥 − 3 = 0
A. 0, 3 C. 2 ± √2
B. 1, −3 D. 3±𝑖√3
2
36. Which equation matches the graph below?
A. 𝑦 = (𝑥 + 1)2 + 3 C. 𝑦 = −(𝑥 + 1)2 + 3
B. 𝑦 = (𝑥 − 1)2 − 3 D. 𝑦 = −(𝑥 − 1)2 + 3
37. Which of the following is equivalent to the expression 𝑥2 + 6𝑥 + 4?
A. (𝑥 + 3)2 + 5 C. (𝑥 + 3)2 − 5
B. (𝑥 − 3)2 + 5 D. (𝑥 − 3)2 − 5
38. In the equation (𝑎𝑥 + 3)2 = 36, 𝑎 is a constant. If 𝑥 = −3 is a solution to the equation, what is a
possible value of 𝑎?
A. −11 C. −5
B. −1 D. 0
39. The function ℎ(𝑡) = −16𝑡2 + 110𝑡 + 72 models the height ℎ, in feet, of an object above ground 𝑡
seconds after being launched straight up in the air. What does the number 72 represent in the
function?
A. The initial height, in feet, of the object
B. The maximum height, in feet, of the object
C. The initial speed, in feet per second, of the object
D. The maximum speed, in feet per second, of the object
40. The graph of the equation 𝑦 = 3𝑥2 + 𝑏𝑥 + 5, where 𝑏 is a constant, is shown in the xy-plane below.
Which of the following could be a value of 𝑏?
A. 9 C. −6
B. 0 D. 15
Simplify the expression.
1. (3𝑥𝑦2)3 2. (2𝑥𝑦)(7𝑥2𝑦) 3. 8𝑥−2𝑦6
12𝑥𝑦−8 4. (2𝑥𝑦
3𝑥2𝑦−1)2
Simplify the polynomial expression.
5. (−𝑥2 + 3𝑥 + 8) + (5𝑥2 + 14𝑥 − 9) 6. 2(8𝑥3 − 4𝑥2 + 𝑥 + 6) − (4𝑥3 + 4𝑥 − 9)
7. (2𝑥 + 3)(𝑥2 − 5𝑥 + 7) 8. (𝑥 + 1)(𝑥 − 2)(𝑥 + 4)
Divide the polynomials using LONG or SYNTHETIC division.
9. (𝑥3 − 𝑥2 + 4𝑥 − 10) ÷ (𝑥 + 2) 10. (𝑥3 + 5𝑥 − 3) ÷ (𝑥 − 3)
CHAPTER 6 – Polynomials and Polynomial Equations
Factor the following polynomial functions.
11. 𝑥3 + 2𝑥2 − 15𝑥 12. 3𝑥3 + 30𝑥2 + 75𝑥
13. 3𝑥5 − 75𝑥3 14. 𝑥3 + 7𝑥2 − 9𝑥 − 63
15. 𝑥3 + 3𝑥2 + 4𝑥 + 12 16. 𝑥2 − 4𝑥
Factor and SOLVE the following polynomial functions.
17. 𝑥3 − 6𝑥2 − 72𝑥 = 0 18. 2𝑥3 − 14𝑥2 + 20𝑥 = 0
19. 𝑥3 − 3𝑥2 − 16𝑥 + 48 = 0 20. 4𝑥2 − 36 = 0
21. 𝑥3 + 5𝑥2 − 𝑥 − 5 = 0 22. 𝑥3 + 5𝑥2 − 7𝑥 − 35 = 0
A polynomial and its graph is given. Identify the degree, leading coefficient, y-intercept, and zeros of
the polynomial. Then state the end behavior.
23. 𝑓(𝑥) = 𝑥4 + 6𝑥3 + 9𝑥2 24. 𝑓(𝑥) = 𝑥3 − 3𝑥2 − 10𝑥
Degree: Degree:
L.C.: L.C.:
Zeros: Zeros:
End Behavior: End Behavior:
𝐴𝑠 𝑥 → −∞, 𝑓(𝑥) → _______𝐴𝑠 𝑥 → ∞, 𝑓(𝑥) → _______
𝐴𝑠 𝑥 → −∞, 𝑓(𝑥) → _______𝐴𝑠 𝑥 → ∞, 𝑓(𝑥) → _______
The graph of a polynomial is given. Identify the zeros, the degree, and the SIGN of the leading
coefficient of the polynomial.
25.
Zeros:
Degree:
LC:
MULTIPLE CHOICE PRACTICE FOR CHAPTER 6
26. What is the degree of the polynomial ℎ(𝑥) = −8𝑥2 − 3𝑥 + 5?
A. 1 C. 3
B. 2 D. −8
27. Which of the following could be the equation of the graph below?
A. 𝑦 = 𝑥(𝑥 − 2)(𝑥 + 3)
B. 𝑦 = 𝑥2(𝑥 − 2)(𝑥 + 3)
C. 𝑦 = 𝑥(𝑥 + 2)(𝑥 − 3)
D. 𝑦 = 𝑥2(𝑥 + 2)(𝑥 − 3)
