Free Printable Algebra 2 Final Exam Practice

1.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

2.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

3.

Divide (x⁴ + x³ +2x² +x -1) by (x+1)

a)

x² + 2x -1

b)

x³ + 2x-1

c)

x² - 2x + 1

d)

x³ - 2x + 1

4.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

5.

∣ 2x + 9 ∣ = 15

a)

x = 3

b)

x = 3
x = -6

c)

x = 3
x = -12

d)

x = 6
x = -12

6.

(4a + 2)(6a² − a + 2)

a)

24a³ + 16a² + 6a + 4

b)

24a³ + 8a² + 10a + 4

c)

24a³ + 8a² + 6a + 4

d)

24a³ - 8a² - 6a + 4

7.

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

8.

Evaluate f(-2) if f(x) = x + 3

a)

-1

b)

1

c)

5

d)

-5

9.

Given
f(x)= 2x² + 5x - 17, find f(-1).

a)

f(-1) = -20

b)

f(-1) = -24

10.

What is the quadratic function in vertex form for a vertex of (-3,-5) and when a = -2? Remember: $y=a\left(x-h\right)^2+k$

a)

y = -2(x-3)²+5

b)

y = -2(x+3)²+5

c)

y = -2(x+3)²-5

d)

y = -2(x-3)²-5

11.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

12.

What is the vertex of y = x²+ 4x + 3? $Remember\ the\ x\ of\ vertex:\ \ \ x\ =\ -\frac{b}{a^2}$

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

13.

What are the x-intercepts of the function f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

14.

Solve:
2x² - 9x = 35

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

15.

What is the range?

a)

-7 ≤ y ≤ 5

b)

-9 ≤ y ≤ 3

c)

-5.5 ≤ y ≤ -0.5

d)

-∞ ≤ y ≤ 5

16.

The function f(t) = -2|t - 15| + 50 is graphed and represents weekly sales of shoes, f(t) in $1000s, where t is weeks. What is the maximum sales?

a)

$40,0000

b)

$20,0000

c)

$50,000

d)

$10,0000

17.

What is the vertex of the following function?
y= -4|x+2|+5

a)

(-4,2)

b)

(-2,5)

c)

(-4,-2)

d)

(2,5)

18.

Solve the equation:
|2x - 1| = 3

a)

x = 2

b)

x = 2 or x = -1

c)

x = 1 or x = 2

d)

x = -2 or x = -1

19.

Solve the inequality.
|x - 4| < 7

a)

all real numbers

b)

x < 11

c)

x < -3 or x > 11

d)

-3 < x < 11

20.

Solve the inequality.
|x + 3| > 9

a)

no solution

b)

x < -12 or x > 6

c)

x > 6

d)

-12 < x < 6

21.

At what approximate time did d=22 miles ?

a)

1.47 hours

b)

7.5 hours

c)

2 hours

d)

3 hours

22.

Evaluate f(3)

a)

-4

b)

8

c)

-2

d)

-1

23.

Evaluate f(-4)

a)

-4

b)

-8

c)

2

d)

1

24.

Evaluate f(-4)

a)

-2

b)

-3

c)

11

d)

-5

25.

What is the solution to this system of equations?

a)

(4, -1)

b)

(-1, 4)

c)

(-4, 1)

d)

(-4, -1)

26.

Solve the system of equations.
x + 2y = -3
x - y = -12

a)

(-9, 3)

b)

(-7 ,5)

c)

(3, 15)

d)

(9, 6)

27.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

28.

Solve for x and y:
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

29.

Solve:
x + y = 4
-5x - 6y = -18

a)

(6, -2)

b)

(-6, 10)

c)

(2, 2)

d)

(-2, 6)

30.

Solve:
-2x + 5y = -1
4x - 2y = -6

a)

(-2, -1)

b)

(2, 7)

c)

(3, 1)

d)

(-1, -2)

31.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

a)

y = 6.80 + .65x
y=7.30+.90x

b)

x + y = 6.80
x + y = 7.30

c)

y = 6.80+.90x
y = 7.30 + .65x

d)

y + .90x = 6.80
y + .65x = 7.30

32.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

33.

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

a)

yes

b)

no

34.

Solve the following system by graphing. What is the solution?

a)

(-4, 2)

b)

(4, 2)

c)

(2, -4)

d)

(2, 4)

35.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

a)

45 minutes

b)

90 minutes
2x + 4y = 315

c)

60 minutes
3x + 4y = 450

d)

30 minutes

36.

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104

a)

(10, 11)

b)

(12, 9)

c)

(11, 10)

d)

(9, 12)

37.

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. How many of each type of ticket were sold?

a)

10 adults, 11 children

b)

12 adults , 9 children

c)

11 adults, 10 children

d)

9 adults, 12 children

38.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings can you get at each Pizzeria so that the price of a large pizza is the same?

a)

3 toppings

b)

1 topping

c)

2 toppings

d)

4 toppings

39.

Identify the zeros/x-intercepts.

a)

x=-2, x=-1, x=0

b)

x=-2, x=0

c)

x=-1, x=0, x=2

d)

x=-2, x=0, x=1

40.

Identify the zeros/x-intercepts:

a)

x=-2, x=-1, x=0

b)

x=-2, x=0

c)

x=-1, x=0, x=2

d)

x=-2, x=0, x=1

41.

Factor:

3b² + 17b + 20

a)

(2b - 5)(b - 7)

b)

(5b - 7)(b - 2)

c)

(b + 5)(3b + 4)

d)

(3b + 5)(b + 4)

42.

Factor:

x² + x - 6

a)

(x - 6)(x - 9)

b)

(x + 3)(x + 2)

c)

(x + 3)(x - 2)

d)

(x + 2)(x + 4)

43.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

44.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

45.

What is y when x equals 8?

a)

-9

b)

-5

c)

2

d)

4

46.

If f(x) = 2x² + 5x - 3, evaluate f(-1).

a)

f(-1) = -6

b)

f(-1) = 1

c)

f(-1) = -10

d)

f(-1) = -1

47.

Solve!

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

48.

Solve :

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

49.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

50.

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

51.

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released (t = 0)?

a)

2 meters

b)

5 meters

c)

40 meters

d)

20 meters

52.

A ball is thrown into the air. Its height, h, after t seconds is given by the function h = -16t² + 64t + 960. How many seconds did it take for the ball to reach its maximum height (x of the vertex)?

a)

10 seconds

b)

64 seconds

c)

960 seconds

d)

2 seconds

53.

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation h = -2t²+ 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second (t = 1)?

a)

2

b)

4

c)

9

d)

10

e)

15

54.

a)

21

b)

-21

c)

-3

d)

3

55.

Use the exponential regression to find an equation that fits the data, where x is the years since 1990.

a)

y=8.92•1.23^x

b)

y=1.23•8.92^x

c)

y=8.92+1.23x

d)

y=8.92x+1.23

56.

Find the population for 1975.

HINT: Read the headers on the table!

a)

623 thousand people

b)

650 thousand people

c)

599 thousand people

d)

513 thousand people

57.

Which Quadratic equation best represents the table?

a)

$y=-2.7x+7.4$

b)

$y=0.95x^2-2.08x-0.75$

c)

$y=-.05x-3.26$

d)

$y=0.95x^2+2.08x+0.75$

58.

What is the Perimeter?

a)

3x - 3 inches

b)

6x - 6 inches

c)

3x - 6 inches

d)

6x - 3 inches

59.

What is the Area?

a)

$2x^2-3x-18$ sq, in.

b)

$2x^2+3x+18$ sq. in.

c)

$2x^2+9x-18$ sq. in.

d)

$2x^2-9x-18$ sq. in.

60.

Find the perimeter of the triangle

a)

$4x+64$

b)

$4x^2+64$

c)

$3x+50$

d)

$3x^2+50$

61.

Sonya has $40 in her lunch account and pays $2 each day to eat lunch. Which equation can be used to find the amount of money Sonya has left on her account after x days?

a)

y = 40 + 2x

b)

y = 40 - 2x

c)

y = 2 + 40x

d)

y = 2 - 40x

62.

For lunch, Amanda had a hamburger and some potato chips. The hamburger totaled 325 calories and each chip had 12 calories. Write a liner equation to represent the situation.

a)

y = 12 + 325

b)

y = 12x + 325

c)

y = 325 - 12x

d)

y = 325x + 12

63.

Which equation shows the number of bottles left after x days?
A family buys a case of water with 48 bottles and drinks 5 bottles per day.

a)

y = 48x + 5

b)

y = -5 + 48x

c)

y = -5x - 48

d)

y = 48 - 5x

64.

A plumber charges $50 to make a house call. He also charges $25 per hour for labor.

How much would it cost for 2.5 hours of labor?

a)

$100

b)

4.50

c)

$112.50

d)

$65.00

e)

$123.45

65.

Your new job is at the Custom T Shop, where T Shirts are printed to order. For each order, Custom T Shop charges $8 per shirt plus a one time set up fee of $15, represented by the equation y=8x+15

How much would 50 shirts cost?

a)

y= 40

b)

y= 400

c)

y= 415

d)

y= 65

e)

y= 390

66.

A 100-point test has x questions worth 2 points apiece and y questions worth 4 points apiece.

If you have 24 questions worth 4 points apiece, how many questions will be worth 2 points apiece?

a)

24

b)

2

c)

5

d)

0

67.

You are selling drinks at the carnival to raise money. You sell lemonade for $2 per cup and orange drinks for $3 per cup. Your sales totaled $240. Let x be the number of cups of lemonade and y be the number of orange drinks.

Write an equation to represent the situation

a)

2x - 3y = 240

b)

3y - 2x = 240

c)

2x + 3y = 240

d)

2 + 3 = 240

68.

You are selling drinks at the carnival to raise money. You sell lemonade for $2 per cup and orange drinks for $3 per cup. Your sales totaled $240. Let x be the number of cups of lemonade and y be the number of orange drinks.

If you sold 60 cups of lemonade, how many cups of orange drink did you sell?

a)

60

b)

40

c)

10

d)

120

69.

Determine the vertex for each absolute value function

a)

(-3, -1)

b)

(-3, 1)

c)

(3, -1)

d)

(3, 1)

70.

Determine the vertex of the function

a)

(-2, 5)

b)

(-2, -5)

c)

(2, 5)

d)

(2, -5)

71.

Determine the vertex of the function.

a)

(0, -5)

b)

(0, 5)

c)

(-2, 5)

d)

(-2, -5)

72.

Which function is graphed?

a)

f(x) = -|x - 3| + 5

b)

f(x) = -|x + 5| - 3

c)

f(x) = -|x + 3| + 5

d)

f(x) = -|x - 5| - 3

73.

Which function is graphed?

a)

f(x) = 2|x + 2| -4

b)

f(x) = 2|x - 4| + 2

c)

f(x) = 2|x - 2| - 4

d)

f(x) = 2|x - 4| - 2

74.

What is the equation of the absolute value function?

a)

f(x)= |x+4|

b)

f(x)= |x-4|

c)

f(x)= |x| + 4

d)

f(x)= |x| - 4

75.

What kind of function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

Algebra 2 Final Exam Practice

Total questions: 75

Worksheet time: 6hrs 39mins

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