Free Printable Advanced Algebra

1.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

2.

Simplify
√-25

a)

-5i

b)

5

c)

5i

d)

-5

3.

Simplify
3i - (4 + 7i)

a)

-4 + 10i

b)

21 - 12i

c)

4 - 10i

d)

-4 - 4i

4.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

5.

Multiply:
(4 – 3i)(7 + 2i)

a)

A. 22 - 13i

b)

B. 28 - 19i

c)

C. 34 - 13i

d)

D. -34 - 29i

6.

i⁷

a)

i

b)

-i

c)

1

d)

-1

7.

i⁶⁶

a)

1

b)

i

c)

-1

d)

-i

8.

What is the simplified form of (-6i)(3i)

a)

-18

b)

-18i

c)

18

d)

-18i²

9.

$-\ \sqrt[]{-72}$

a)

$-14i\ \sqrt[]{7}$

b)

$-4i\ \sqrt[]{13}$

c)

$6i\ \sqrt[]{2}$

d)

$-6i\ \sqrt[]{2}$

10.

$\sqrt[]{-75}\times3\sqrt[]{-49}$

a)

$35i\ \sqrt[]{3}$

b)

$-3i\ \sqrt[]{25}$

c)

$-105\sqrt[]{3}$

d)

$105i\sqrt[]{3}$

11.

a)

A

b)

B

c)

C

d)

D

12.

What is the conjugate of $-2+5i$ ?

a)

$-5+2i$

b)

$-2-5i$

c)

$2+5i$

d)

$5-2i$

13.

a)

A

b)

B

c)

C

d)

D

14.

Solve $x^2+49=0$

a)

$-7$

b)

$7$

c)

$7i$

d)

$\pm7i$

15.

Solve $3\left(x+4\right)^2=81$

Hint: No need to expand

a)

$x=-4\pm3\sqrt{3}$

b)

$x=-4\pm9i$

c)

$x=-4\pm9\sqrt{3}$

d)

$x=-4\pm3i$

16.

Solve the equation

$x^2-2x+2=0$

a)

$x=1\pm i$

b)

$x=3,-6$

c)

$x=-1\pm i$

d)

Maths Error

Undefined

17.

Solve the quadratic equation

$x^2-3x+10=0$

a)

$\frac{-3\pm\sqrt{31}}{2}$

b)

$\frac{3\pm i\sqrt{31}}{2}$

c)

$3\pm i\sqrt{31}$

d)

$i\sqrt{31}$

18.

Determine ALL solutions for the equation:

$x^3-5x^2+5x-25=0$

a)

$x=5$

b)

$x=5$

$x=\ -5i$

$x=\ 5i$

c)

$\left(x^2+5\right)\left(x-5\right)=0$

d)

$x=5$

$x=i\sqrt{5}$

$x=-i\sqrt{5}$

19.

Solve the exponential equation:

a)

-11/4

b)

6

c)

9/4

d)

8

20.

Solve for x:

(1/8)^x = 2³

a)

x=−3

b)

x=3

c)

x=−1

d)

x=1

21.

(1/8)^{-2x - 6} > (1/32)^-x+11

a)

x > -73

b)

x < -73

c)

x > -37

d)

x < -37

22.

$\frac{x+3}{4}=\frac{x+6}{6}$

a)

Rational Expression

b)

Rational Equation

c)

Rational Inequality

d)

Non Polynomial

23.

$\frac{3-2x}{x-1}\le2$

a)

Rational Expression

b)

Rational Equation

c)

Rational Inequality

d)

Non Polynomial

24.

$\frac{x^2+5}{x+2}$

a)

Rational Expression

b)

Rational Equation

c)

Rational Inequality

d)

Non Polynomial

25.

What is the rule for inequalities?

a)

If you add or subtract by a negative - flip the sign.

b)

If you multiply or subtract by a negative - flip the sign.

c)

Never flip the sign, ever.

d)

If you multiply or divide by a negative - flip the sign.

26.

Solve for x:
(3x + 3)/6 = 10

a)

19

b)

-19

c)

21

d)

-21

27.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

28.

Do I need to flip my sign?
3x ≥ 12

a)

Yes

b)

No

29.

An elevator has a maximum capacity of 500 pounds. If the luggage weighs 200 pounds, what is the maximum weight allowable for passengers (p).

a)

p ≤ 300

b)

p ≤ 500

c)

p ≥ 200

d)

p ≥ 500

30.

You have $137.26 in a bank account. The bank requires you to have at least $50 in your account or else you are charged a fee. Write and solve an inequality that shows the amount you can write your next check for without being charged.

a)

x < $87.26

b)

x ≥ $76.51

c)

x ≤ $87.26

d)

x ≤ $187.26

31.

James bought a video game for $42.00. He found the same video game at a different store for z dollars less. Which open sentence will be the most helpful for finding the price of the video game at the other store?

a)

42 • z = ?

b)

z – 42 = ?

c)

z + 42 = ?

d)

42 – z = ?

32.

Which is a solution to the inequality
14 + n ≤ 21

a)

n ≤ 6

b)

n ≤ 8

c)

n ≤ 5

d)

n ≤ 7

33.

A salesperson at an electronics store a monthly target of 30 tablets to sell and a fixed salary of $ 2,800 per month. She gets $60 more for every tablet above her target that she sells. If she wants to earn $240 apart from the fixed salary, which number line shows the minimum number of extra tablets she must sell?

a)

A

b)

B

c)

C

d)

D

34.

When you graph an inequality, use a closed circle with which symbols?

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

35.

When graphing an inequality, use an open circle with which symbols?

a)

<, >

b)

≤, ≥

c)

≤, <

d)

≥, >

36.

What is the inverse operation of division?

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

37.

When solving an equation, our goal is to:

a)

add all the numbers together.

b)

use a calculator.

c)

eat lunch.

d)

isolate the variable to solve.

38.

Find the solution set for the equation 5x + 2 = 3x - 4.

a)

x = -3

b)

x = -7

c)

x = 0

d)

x = 5

39.

Solve the inequality 2x + 3 > 7.

a)

x > 2

b)

x > 5

c)

x = 2

d)

x < 2

40.

Find the solution set for the inequality 4 - 3x < 10 + 2x.

a)

x < 6/5

b)

x > 6/5

c)

x > -6/5

d)

x < -6/5

41.

Solve the inequality 2(x - 5) ≥ 3x - 4.

a)

x ≥ -4

b)

x ≤ -5

c)

x ≥ -6

d)

x ≤ -6

42.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

a)

x + y = 1430
20x + 50y = 49

b)

x + y = 49
10x + 5y = 1430

c)

x + y = 49
20x + 50y = 1430

d)

x + y = 49
x + y = 1430

43.

What are the coordinates of the y-intercept of

y=2x^{2\ }-8x+3

a)

(0,3)

b)

(3,0)

c)

(0,2)

d)

(0,-8)

44.

Are the points on the line part of the solution set or not?

a)

Yes, they are part of the solution set

b)

No, they are NOT part of the solution set

45.

Which ordered pair is a solution of the inequality?

y ≥ 4x – 5

a)

(3, 4)

b)

(3, 0)

c)

(2, 1)

d)

(1, 1)

46.

It expresses a relationship between two variables (such as x and y), and can be represented by a table of values or a graph.

a)

Rational Function

b)

Rational Equation

c)

Rational Inequalities

47.

An equation involving rational expressions.

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

48.

Determine what type of expression is the given: $12x\ >\frac{1}{x+2}$

a)

Rational Function

b)

Rational Equation

c)

Rational Inequality

d)

None of these

49.

$\frac{1}{2}\left(2x+6\right)=3x+13$

a)

No Solution

b)

$x=-5$

c)

$x=8$

d)

$x=7$

50.

Which point makes the inequality true?

$-4x\ +9\le-23$

a)

$x=-4$

b)

$x=7$

c)

$x=-10$

d)

$x=9$

51.

Solve:

$4+\frac{x}{-4}\le2$

a)

$x\le6$

b)

$x\ge6$

c)

$x\ge3$

d)

$x\ge8$

52.

$\frac{a+3}{7}=3$

a)

$a=18$

b)

$a=21$

c)

$a=4$

d)

$a=11$

53.

Solve:
4(2a + 3) < 3(a - 1)

a)

a<-3

b)

a>-3

c)

a<3

d)

a>3

54.

Solve the equation:
3x - x + 2 = 4(2x - 1)

a)

infinite solutions

b)

x = 1

c)

x = -1

d)

no solution

55.

Solve the following exponential equation:

3^3=3^{4x+2}

a)

$x=\frac{1}{4}$

b)

$x=-\frac{1}{4}$

c)

$x=\frac{1}{2}$

d)

$x=-\frac{1}{2}$

56.

Solve the following exponential inequality:

$\left(\frac{1}{64}\right)^{\ x+3}\le8^x$

a)

$x\ge3$

b)

$x\le3$

c)

$x\ge-2$

d)

$x\le-2$

57.

10^4x+1 > 100^{x - 2}

a)

x > 10

b)

x > -2/5

c)

x < -5/2

d)

x > -5/2

58.

1/81 < 9^2x-4

a)

x < 1

b)

x > 9

c)

x > 1

d)

x < -1

59.

What inequality does the number line graph represent?

a)

x >= 3

b)

x > 3

c)

x < -3

d)

x <= 3

60.

What inequality does the number line graph represent?

a)

2x +1 < -3

b)

x + 2 < 4

c)

-x + 3 > 1

d)

x + 4 >= 2

61.

3x - 2 ≥ 34

a)

x ≥ -12

b)

x ≤ -12

c)

x ≤ 12

d)

x ≥ 12

62.

Solve

a)

n < 6

b)

n > 6

c)

n < 14

d)

n > 14

63.

Identify the zeros:

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

64.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

65.

What is the factored form of a function if it has zeros of 2, 3 and -1?

a)

(x-2)(x-3)(x+1)

b)

(x-1)(x-2)(x-3)

c)

(x-1)(x+2)(x+3)

d)

(x+1)(x+2)(x+3)

66.

What does the degree of a polynomial function tell you?

a)

how hot it is

b)

how many x-intercepts it can have

c)

how many y-intercepts it has

d)

how many terms it has

67.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

68.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

69.

What does this graph represent?

a)

Exponential Decay

b)

Exponential Growth

70.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

71.

What is the y-intercept?

a)

(0,0)

b)

(0,1)

c)

(-3,0)

d)

(0,-3)

72.

Which equation best describes the graph?

a)

y = 2^x + 4

b)

y = 2^x - 3

c)

y = 2^x - 4

d)

y = 2^x + 3

73.

Is this a function?

a)

Yes

b)

No

74.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

75.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

76.

Identify the domain:
f(x) = x² + 4x + 3

a)

[3, oo)

b)

(-oo, 3]

c)

x ≠ 3

d)

(-oo, oo)

77.

If f(x) = x²-x+3, what would the function look like once you substitute in a -3 to find f(-3)?

a)

f(-3) = -3²-3+3

b)

f(-3) = (-3)² -(-3)+3

c)

f(-3) = (-3)² -3+3

78.

What is the range of this function?

a)

$\left(0,\ \infty\right)$

b)

$\left(-\infty,\ 0\right)$

c)

$\left(1,\ \infty\right)$

d)

$\left(-\infty,\infty\right)$

79.

Identify the type of function.

a)

Linear

b)

Quadratic

c)

Exponential

80.

Identify the type of function.

a)

Linear

b)

Quadratic

c)

Exponential

81.

What type of a function is this?

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

82.

What kind of Function is f(x) = 5 + 3|x - 9|

a)

Linear

b)

Absolute Value

c)

Quadratic

d)

Exponential

e)

None of the above

83.

Determine which type of function the following is:

$y=5x^2-7x+9$

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

84.

Determine which type of function the following is:

$y=5\left(6.1\right)^x-12$

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

85.

Which type of function is shown?

a)

linear

b)

quadratic

c)

absolute value

d)

Square Root

86.

Is the following function an exponential function?

f\left(x\right)=5\cdot7^{\left(x\right)}+9

a)

Yes

b)

No

87.

Is the following function an exponential function?

y=2x^2+4x-9

a)

Yes

b)

No

88.

Is the following function an exponential function?

f\left(x\right)=x^3-2x^2+4x+6

a)

Yes

b)

No

89.

Is the following function an exponential function?

f\left(x\right)=5\cdot7^{\left(x\right)}+9

a)

Yes

b)

No

90.

Is this function graph an exponential function graph?

a)

Yes

b)

No

91.

Is this function graph an exponential function graph?

a)

Yes

b)

No

92.

Does the following graph have a maximum or minimum.

a)

Maximum

b)

Minimum

93.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

94.

Domain of

f\left(x\right)=\sqrt{x-2}

a)

real numbers

b)

$\left[2,\infty\right)$

c)

$\left(2,\infty\right)$

d)

$\left(\infty,2\right]$

95.

Graph of

f\left(x\right)=2^{3-x}

?

a)

b)

c)

96.

Choose an equation of the line that goes through the pair of points:

(-2, 5) and (-6, 1).

a)

$y=2x-5$

b)

$y=x+7$

c)

$y=-2x+5$

d)

$y=x+5$

97.

If\ f\left(x\right)\ =\ x^2-5x+6\ and\ g\left(x\right)=-6x+8,\ find:

f\left(x\right)+g\left(x\right)

.

a)

$x^2-11x+14$

b)

$x^2+x+14$

c)

$x^2-x+14$

d)

$-10x^2+14$

98.

If\ f\left(x\right)\ =\ x^2-5x+6\ and\ g\left(x\right)=-6x+8,\ find:

f\left(x\right)-g\left(x\right)

.

a)

$x^2+x-2$

b)

$x^2-11x+14$

c)

$x^2-x+14$

d)

$x^2+x+14$

99.

If\ f\left(x\right)\ =\ x^2-5x+6\ and\ g\left(x\right)=-6x+8,\ find:

f\left(-3\right)-g\left(-3\right)

.

a)

-4

b)

4

c)

10

d)

24

100.

If\ f\left(x\right)\ =\ x^2-5x+6\ and\ g\left(x\right)=-6x+8,\ find:

g\left(x\right)-5

.

a)

$6x+3$

b)

$6x-13$

c)

$-6x+3$

d)

$-6x-13$

Advanced Algebra - Online Final Exam

Total questions: 100

Worksheet time: 6hrs 56mins

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