Free Printable Units 5 and 6 Review 12/13

1.

A complex number can be expressed as a + bi. What does a represent?

a)

the real part of the complex number

b)

the imaginary part of the complex number

c)

depends on the sign of the number

d)

the square root of the complex number

2.

Leon is asked to simplify √-120. A good first step would be to...

a)

divide 120 by 2

b)

replace the negative with an i on the outside of the radical

c)

take the square root of -120

d)

graph y = √-120

3.

The complex conjugate can be found by...

a)

Changing the sign of both a and b

b)

Changing the sign of a

c)

Changing the sign of b

d)

Switching the a and b values

4.

If you are adding two complex numbers you should

a)

add all the numbers together then divide by 2

b)

add only the real numbers and subtract the complex numbers

c)

add only the complex numbers and subtract the real numbers

d)

add only the real numbers together and then add only the complex numbers together then stop

5.

(3 + 2i) + (4 - 5i)

a)

7 + 7i

b)

1 - 3i

c)

1 - 7i

d)

7 - 3i

6.

(4 - 2i) - (3 + 6i)

a)

7 - 4i

b)

1 + 4i

c)

1 - 8i

d)

7 - 8i

7.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

8.

a)

$\frac{27x^{15}z^3}{y^6}$

b)

$\frac{9x^{15}z^3}{y^6}$

c)

$27x^8yz^4$

d)

$\frac{27x^8z^4}{y}$

9.

a)

$\frac{16x^{16}z^{32}}{y^{28}}$

b)

$\frac{-16x^{16}z^{32}}{y^{28}}$

c)

$\frac{x^{16}z^{32}}{16y^{28}}$

d)

$-8x^{-8}y^3z^{-12}$

10.

How do you solve:
(2x⁵)(6x⁴)

a)

MULTIPLY coefficients
MULTIPLY exponents

b)

DIVIDE coefficients
SUBTRACT exponents

c)

Combine like terms

d)

MULTIPLY coefficients
ADD exponents

11.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

12.

According to exponent rules, when we multiply two powers with the same base we _______ the exponents.

Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

13.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

14.

Anything (other than zero) raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

15.

Simplify the following expression:

(xyz)⁰ =

a)

0

b)

1

c)

xyz

d)

-1

16.

Simplify so there are no negative exponents in the answer.

\left(3n^3\right)^{-3}

a)

$\frac{1}{27n^9}$

b)

$\frac{-27}{n^9}$

c)

$\frac{-27}{n^6}$

d)

$\frac{-9}{n^6}$

17.

Simplify so there are no negative exponents in the answer.

\frac{3x^3\cdot4x^4}{x^2}

a)

$12x^5$

b)

$12x^9$

c)

$7x^5$

d)

$7x^4$

18.

Simplify so there are no negative exponents in the answer.

$\frac{3x^0y^{-3}\cdot2x^4y^2}{2x^4}$

a)

$\frac{3}{y}$

b)

$\frac{6}{x^4y^6}$

c)

$\frac{5xy^2}{2}$

d)

$\frac{3x}{y}$

19.

√24 =

a)

4√6

b)

2√6

c)

6√2

d)

2√12

20.

√45 =

a)

3√5

b)

5√3

c)

9√5

d)

5√9

21.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

22.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

23.

a)

A

b)

B

c)

C

d)

D

24.

Simplify the expression

a)

6a⁵b³√6b

b)

2a⁵b³√54b

c)

3a⁵b³

d)

6√2a¹⁰b⁷

25.

The expression $\sqrt{x^{33}}$ is equivalent to

a)

$x^{16}\sqrt{x}$

b)

$x^4\sqrt{x}$

c)

$x^8\sqrt{x}$

d)

$x^2\sqrt{x}$

26.

Which statement best explains why there is no real solution to the following quadratic equation.

x²- 3x + 4 = 0

a)

The value of 9 - 4 (4) is not a perfect square.

b)

The value of 9 - 4 (4) is negative.

c)

The value of 9 - 5 - 4 is equal to zero.

d)

The value of 9 + 4 (4) is positive.

27.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

28.

How many solutions does the equation 4x² + 4x + 1 = 0 have?

a)

0

b)

1

c)

2

d)

More than 2

29.

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

30.

Does the equation open or or down?
Y = -3x² +7x - 2

a)

up

b)

down

31.

Use the quadratic formula to determine the solutions.

2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

32.

Use the quadratic formula to determine the solutions.

2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

33.

The formula to determine how many solutions a quadratic equation is called the discriminant which is...

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

34.

What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

35.

If the discriminant is negative, you will have....

a)

two real solutions

b)

two irrational solutions

c)

no solution

d)

one solution

36.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

37.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

38.

7r³-8r²+42r-48

a)

(r²+6)(7r+8)

b)

(r²+6)(7r-8)

c)

(r²+6)(r²+8)

d)

(r²+6)(7r+6)

39.

20x³-25x²+4x-5

a)

(5x²-5)(4x+1)

b)

5(x²-1)(4x+5)

c)

(5x²+1)(4x-5)

d)

(5x²+1)(4x-1)

40.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

41.

Factor by grouping
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

42.

Factor 30-24x²

a)

6(5-4x²)

b)

x(5-4x)

c)

6(5x-4x²)

d)

6(15-12x²)

43.

Write in factored form.

3x + 12

a)

3(x+12)

b)

3x(1+4)

c)

3(x+4)

d)

3(x-4)

44.

Write in factored form.

12x + 20

a)

2(6x + 10)

b)

3(4x + 5)

c)

4(3x + 20)

d)

4(3x + 5)

45.

To calculate the TIME that a maximum height occurs, you should use:

a)

-b/(2a)

b)

Quadratic formula

c)

the c value

d)

0

46.

To calculate the maximum height, you should:

a)

Use the time you got from -b/(2a) and plug it in for each "t"

b)

-b/(2a)

c)

use the c value

d)

use the b value

47.

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t²+ 90t gives the height h of the ball after t seconds.
What is the maximum height of the ball?

a)

126.56 ft

b)

5.625 sec

c)

2.81 sec

d)

90 ft

48.

A toy rocket is launched and its height is modeled by the equation h = -16t² + 32t + 48. What is the initial heigh of the object?

a)

48 ft.

b)

16 ft.

c)

32 ft.

d)

2 ft.

49.

What is the vertex?

a)

(-1,-2)

b)

(-2,-1)

c)

(-3,-1)

d)

(2,1)

50.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

51.

If path of a projectile is modeled by:
h(t) = -16t² + 20t +6, what is the height after 1 second?

a)

6 feet

b)

20 feet

c)

10 feet

d)

4 feet

52.

If the graph shows price vs profit, what is the maximum profit?

a)

35

b)

12,000

c)

12,500

d)

60

53.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

54.

If I want to find out when an object hits the ground, I should _________.

a)

Use x = (-b/2a) as my answer.

b)

Set my equation = 0 and solve.

c)

Replace x with 0 and evaluate.

d)

Find the y-coordinate of the vertex.

55.

What is the vertex for
f(x)=4(x-2)² + 3

a)

(-2, 3)

b)

(2,-3)

c)

(4,3)

d)

(2,3)

Units 5 and 6 Review 12/13

Total questions: 55

Worksheet time: 3hrs 57mins

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