Name: ______Date: ______

ALGEBRA 2 - FINAL EXAM REVIEW #2

Chapter 1 – Sequences

1) In a geometric sequence, the first term is 7 and the common ratio is 4. What is the sum of the first 6 terms?

  1. 28,672
  2. 7,168
  3. 9,555
  4. 38,220

2)Given the sequence -0.05, -0.10, -0.20, -0.40… Find the 8th term of the sequence.

Chapter 3 – Linear Equations

3)Melanie has m packs of gum, with 15 pieces in each pack. If she brings all but 3 packs on a class trip, which expression shows the maximum number of pieces of gum she could share with her classmates?

  1. 5 + m
  2. 15m – 3
  3. 15 – 3m
  4. 15m – 45

4)Bruce owns a t-shirt printing company. He buys plain t-shirts in bulk for $3 each and then charges customers $7 for the shirt and $0.50 per letter printed on the shirt. Last month he sold 310 shirts with n amount of letters on them. Write an equation for the total profit Bruce made during that month.

  1. 7(310) + 0.50n – 3(310)
  2. 310(10.50n)
  3. 7(310)(0.50n – 3)
  4. 3(310) – 7.50n(310)

5)What is the y-coordinate of the y-intercept for the graph of 4x – y = 8?

  1. 8
  2. -8
  3. -2
  4. 0

6)What is the solution to the system of equations?

  1. (24, 11)
  2. (5, 11)
  3. (5, 5/3)
  4. (11, 7/3)

7)What is the solution to the system of equations?

  1. (2, 3, 24/5)
  2. (1, 2, 11/5)
  3. (2, -1, -2)
  4. (0, -5, -10)

8)A tennis shoe company modeled their expenses vs their income on the graph below. The company wants to keep their income and expenses within $20,000 of each other.

How many pairs of shoes must be sold for the income and expenses to be less than $20,000 within each other?

  1. Between 0 and 250 pairs of shoes.
  2. Between 0 and 1,600 pairs of shoes.
  3. Less than 400 and over 1,200 pairs of shoes.
  4. Between 400 and 1,200 pairs of shoes

9)Ace Truck Rental charges a daily fee plus a mileage fee. Samantha was charged $125 for 2 days and 100 miles when she rented a truck and Lucas was charged $275 for 3 days and 400 miles when he rented a truck. What is Ace Truck Rental’s daily fee?

  1. $35.00
  2. $45.00
  3. $50.00
  4. $56.25

10)Which point represents the solution to the following system of equations:

4x + 7y + 5 = 0

x – y + 4 = 0

a. ( -1/3 , 11/3)

b. (-3, 1)

c. (-45/11 , -1/11)

d. (-11, -7)

Chapter 4 – Functions, Relations & Transformations

11)For which of the following equations is x = 5 not a solution?

a. │x│ = 5

b. x2 = 25

c. (x – 1)(x + 4) = 36

d. (2x + 2)(x – 4) = 14

12)Which ordered pair best approximates a point of intersection for the graphs of the two functions below.

y = 2x2 – 7x + 3

y = x2 + x – 5

  1. (1.6, -4.5)
  2. (1.17, -2.45)
  3. (3.22, 5.12)
  4. (-.67, 6.45)

13)The graphs off(x) = x - 5 and f(x) = x2 - 7 are shown below.

Which statement best explains the reason (-1.2, -6.25) is a solution.

a)At (-1.2, -6.25) the functions both have x and y values

b)The functions intersect in the 3rd quadrant

c)x2 – 7 = x – 5 when x = -1.2

d)The domain and range of the functions are the same.

14)The graphs of y = 7 and y = are shown below.

Which statement explains why 4 is an x-coordinate of a solution to the system of functions?

  1. A solution to a system is where the functions have the same height. Since both functions reach a height of 4, a solution must be x = 4.
  2. A solution to a system is an x-coordinate where the graphs intersect. Since both graphs have the same height at x = 4, a solution must be x = 4.
  3. There are always two solutions to absolute value functions. Since x = -4 is one solution, it follows that its opposite, x = 4, is the other solution.
  4. There are always two solutions when a horizontal line intersects an absolute value function. Since the horizontal line has a height of 4, the x-coordinate of the solutions must be x = 4 and x = -4.

15)When graphed, which equation will yield the same maximum value as the graph of y = -2x2 + 12x – 10?

A)y = -2(x – 3)2 + 8

B)y = -2(x + 3)2 – 8

C)y = 2(x – 3)2 + 8

D)y = 2(x + 3)2 – 8

16)Which of the following represents the function f(x) = 1/x4?

A.B.

C.D.

17)Which equation below has a graph that is symmetric with respect to the y-axis?

  1. ½ x + y = 7
  2. x = 2y
  3. y = x4 + x8
  4. y = x5 + x

18)The following represents y = .

What is the solution 0 = .

  1. -5
  2. -4
  3. -1
  4. 0.5

19)Which system of equations is represented by the graph shown below?

  1. y = ½ (x – 2)2 – 3

¾ x + y = 3

  1. y = ½ (x + 2)2 – 3

- ¾ x + y = 3

  1. y = ¼ (x – 2)2 – 3

- ¾ x + y = 3

d. y = ¼ (x + 2)2 – 3

¾ x + y = 3

20)Abby is going to launch a rocket from the ground. Ezra is going to hold a laser light 4 meters above the ground and point it in the path of the rocket. The height, y, in meters, of the rocket can be represented by the equation y = -4.9x2 + 20x, where x is time in seconds. The graph below represents this situation.

Model Rocket

The equation that represents the path of the laser light is y = 3.1x + 4

Which two times most closely approximate when the laser light will strike the rocket after its launch?

a. 0 seconds and 4 seconds

b. 0.25 seconds and 3.2 seconds

c. 0.02 seconds and 3.2 seconds

d. 0.10 seconds and 3 seconds

Time (seconds)

Chapter 4 – Solving Radical Equations

21)Larry solved this equation to determine x.

  1. 16
  2. 8
  3. 4
  4. 2

22)Morris wrote the following steps as the solution to

Step 1: 5x = (2x – 3)2

Step 2: 5x = 4x2 -12x + 9

Step 3: 0 = 4x2 – 7x + 9

Step 4: x =

Which step is not equivalent to the preceding step?

  1. Step 1
  2. Step 2
  3. Step 3
  4. Step 4

23)If , what is the value of x?

  1. 11
  2. 31
  3. 41
  4. 116

Chapter 5 – Exponential, Power & Logarithmic Functions

24)What is equivalent to (2x2)3?

  1. 8x8
  2. 8x6
  3. 6x6
  4. 6x5

25)What is equivalent to (-3x3y2z)2?

  1. -9x5y4z2
  2. 6xyz
  3. 9x6y4z2
  4. -6x5y4z

26)Which equation is equivalent to 6(10)4x = 48

  1. x = log8 – log4
  2. x = log4(8)
  3. x = log(4√48)
  4. x = log(4√8)

27)Simplify

  1. 2xy5
  2. ½ xy4
  3. ½ xy5
  4. 6xy4

28)Simplify.

  1. 72x8
  2. 12x8
  3. 12x32
  4. 72x32

29)Mandy bought a car for $15,000. The value of the car depreciates by about 11% each year. What will be the value of the car after 5 years and 6 months? Round to the nearest whole dollar amount.

Chapter 7 – Quadratic & Higher-Degree Functions

30)Which of the following functions has the same zeros as:f(x) = x2 – 2x – 15.

  1. g(x) = x2 + 8x - 14
  2. g(x) = x3 – 3x – 15
  3. g(x) = x2 – 16
  4. g(x) = 2x2 – 4x – 30

31)Which set of ordered pairs represents the x-intercepts of the function y = (x – 1)(2x + 5).

  1. (-1, 0) and (0, -5/2)
  2. (1, 0) and (-5/2, 0)
  3. (1, 0) and (5/2), 0)
  4. (0, 1) and (0, -5/2)

32)What is the factored form of 6x2 – xy2 – 35y4?

  1. (-3x + 7y)(5x + y)
  2. (6x + y)(x – 3y)
  3. (3x + 2y2)(2x – 8y2)
  4. (3x + 7y2)(2x – 5y2)

33)Which expression is equivalent to 6x2 – 30x + 36 in factored form?

  1. 6(x + 6)(x – 6)
  2. 6(x – 5)(x + 6)
  3. 6(x – 6 )(x – 1)
  4. 6(x – 2)(x – 3)

34)Write an equation in factored form for a polynomial function with real coefficients, x-intercepts -1, 1, -5, and a y-intercept at 2.5.

35)Find the Quotient: 6 – 3i

-4 – 4i

36)Given the graph at the right, write the equation in factored form.

37) Roscoe hit a ball straight up at a speed of 96 ft/s. His bat hit the ball at a height of 3 ft above the ground.

a) After how many seconds did the ball hit the ground?

b) When does the ball pass the point from which it was hit?

c) What is the maximum height reached by the ball? When does it reach this height?

38)Consider the polynomial function: P(x) = 2x5+ 3x4– 30x3– 57x2– 2x+ 24

a) Use the Rational Root Theorem to find all possible rational zeros of the function.

b) Use synthetic division to find all rational zeros.

c) Find the other zeros

d) Write the equation in factored form.