Free Printable Algebra 2 Semester Review S2

1.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

2.

What do you call this mathematical expression?

a)

fraction

b)

radical

c)

exponent

d)

binomial

3.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

4.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

5.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

6.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

7.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

8.

Solve by the Extraction of Roots method: -5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

9.

Solve by the Extraction of Roots method: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

10.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

11.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

12.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

13.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

14.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

15.

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

16.

Solve by ANY method you have learned: x²−2x+11=0

a)

1±i√10

b)

1±√10

c)

-1±i√10

d)

-1±√10

17.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

18.

Factor x²-11x+24

a)

(x-3)(x-8)

b)

(x-2)(x-12)

c)

(x+3)(x+8)

d)

(x+2)(x+12)

19.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

20.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

21.

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

a)

x = −2, 3

b)

x = 2, 3

c)

x = 2, −3

d)

x = −2, −3

22.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

23.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

24.

Which is in the proper factored form to use the Zero Product Property ?

a)

$x^2-x=12$

b)

$x\left(x-1\right)=12$

c)

$\left(x-4\right)\left(x+3\right)=1$

d)

$\left(x-4\right)\left(x+3\right)=0$

25.

Given this graph is the function of

y=x^2-2x-8

, what is the solution to

x^2=2x+8

?

a)

(1, 9)

b)

x = {-2, 4}

c)

(0, 8)

d)

x = {5, 2}

26.

What is the color of the graph that has exactly one real zero?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs has exactly one zero.

27.

What is the color of the graph that has no real zeros?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs have no real zeros

28.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

29.

What is/are the solution(s) to

3x^2-1=74

?

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

30.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

31.

a)

√3

b)

±√3

c)

-3

d)

No real solution

32.

a)

±√9

b)

±3

c)

±1

d)

No real solution

33.

If the discriminant equals 0, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

34.

What is the discriminant?

a)

b²-4ac

b)

b²/2a

c)

4ac

d)

b²±4ac

35.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solutions

36.

If the discriminant is positive, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

37.

If the graph of a quadratic does not intercept the x axis at any point, then it has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

38.

Convert x²+6x+9 to factored form and identify the solution.

a)

(x+3)(x+3); x=-3

b)

(x+4)(x+5); x=-4, -5

c)

(x-3)(x-3); x=3

d)

Not factorable

39.

Convert x²-6x+9 to factored form and identify the solution.

a)

(x-3)(x-3); x=3

b)

(x+3)(x+3); x=-3

c)

(x+4)(x+2); x=-4, -2

d)

Not factorable

40.

Select the solutions to the equation

2x² - 3x - 2 = 0

a)

x = 2

b)

x = -0.5

c)

x = - 3

d)

x = - 2

41.

Select the solutions to the equation

2x² - 13x + 15 = 0

a)

x = 1.5

b)

x = 5

c)

x = - 6

d)

x = 2

42.

Select the solutions to the equation

x² + 2x - 1 = 2

a)

x = 0.5

b)

x = -2.5

c)

x = -3

d)

x = 1

43.

Select the solutions to the equation

x² - x + 1 = 7

a)

x = 0

b)

x = 1

c)

x = -2

d)

x = 3

44.

If the decay rate is 20%, which of the following represent the decay factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

45.

If the growth rate is 80%, what is the growth factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

46.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

47.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

48.

Jack invest $600 earning 5% interest rate. How much will he have after 5 years?

a)

$630

b)

$729.30

c)

$765.77

d)

$4556.25

49.

Which equation represents the given table?

a)

$y=15\left(1.8\right)^x$

b)

$y=15\left(0.8\right)^x$

c)

$y=15\left(1.2\right)^x$

d)

$y=15\left(0.2\right)^x$

e)

$y=-3x+15$

50.

Which of these functions is a growth function? Check all that apply.

a)

$f\left(x\right)=7\left(1.2\right)^x$

b)

$f\left(x\right)=5\left(0.8\right)^x$

c)

$f\left(x\right)=0.5\left(3\right)^x$

d)

$f\left(x\right)=3\left(\frac{4}{3}\right)^x$

51.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

52.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

53.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

54.

Moody's Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

55.

Now you try:

What is the solution:

\sqrt{\frac{25}{100}}

Make sure your answer is in simplest form :)

(a)

56.

What is the solution for

\sqrt{-16}

please type in the answer

(a)

57.

Now you try:

Find the solution:

\sqrt{-49}

(a)

58.

a)

A

b)

B

c)

C

d)

D

59.

a)

A

b)

B

c)

C

d)

D

60.

a)

A

b)

B

c)

C

d)

D

61.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

62.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

63.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

64.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

65.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

66.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

67.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

68.

What kind of function is shown?

a)

Quadratic

b)

Linear

c)

Exponential

d)

Square Root

e)

Absolute Value

69.

Identify which functions are exponential.

a)

f(x) = 2x - 5

b)

g(x) = 3^x

c)

k(x) = 3x⁴ - 6x + 9

d)

k\left(x\right)=3\cdot\left(\frac{1}{2}\right)^x

70.

Does the graph represent growth, decay, linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

71.

Which function is exponential?

a)

f(x)

b)

h(x)

c)

g(x)

72.

What is the definition of an asymptote?

a)

a curved line

b)

a curve at the origin

c)

a line that continually approaches a given curve but does not meet it at any finite distance

73.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

74.

What is the equation of this table?

a)

y=512(1/4)^x

b)

y=32(4)^x

c)

y=32(1/4)^x

d)

y=512(4)^x

75.

Which type of regression model does the scatter plot appear to show?

a)

linear

b)

exponential

c)

quadratic

76.

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data: Find the exponential model of the function.

a)

y = 100(8.7)^x

b)

y = 100(1.87)^x

c)

y = 100(.87)^x

d)

y = 100(.13)^x

77.

Which scatter plot shows no relationship?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

78.

What topic do you feel like you need more focused practice before the final?

4 lines

79.

If h(a) = 3 - 2x², find h(-3).

a)

33

b)

21

c)

39

d)

-15

80.

Evaluate f(-2) if f(x) = x²+ 3.

a)

-1

b)

1

c)

7

d)

-7

81.

For which function would f(3) = 17

a)

f(x) = 5x

b)

f(x) = 2(x + 4) + 3

c)

f(x) = x - 10

d)

f(x) = 3x + 6

82.

My face when my teacher says to do work

83.

Mrs. Murchie's FAVORITE food is (a)

84.

Mrs. Murchie says, "If you are copying down the answers, then copy with an (a) to understand/learn.

85.

In order to "study" math and "learn" math you must ______ it!

a)

DO

b)

HATE

c)

LOVE

d)

GO

86.

Finish the sentence: Math is NOT _________________

4 lines

87.

Advice I would give to next years Algebra II students:

4 lines

88.

How do you think you will do on your final exam this semester?

a)

A - all the way

b)

B - for sure

c)

C - I think I can do okay

d)

D's and F's

I will do my best to pass, but It's questionable at best.

89.

Tell me your most memorable moment from class this year.

4 lines

90.

Name something you can't live without.

(a)

Algebra 2 Semester Review S2

Total questions: 90

Worksheet time: 3hrs 2mins

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