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Standardized Test PrepMultiplying Powers With the Same Base

Multiple ChoiceFor Exercises 1–5, choose the correct letter.

1. What is the simpli!ed form of (-3x3y2)(5xy-1)?

-15x3

y2 -15x3y2 -15x4y 15x4y

2. What is the simpli!ed form of a-9m12n

45ba2m

13n

25b ?

-18m16n

825 -18m

56n

65 -18m5n6

m6n5 -18mn8

m6n25

3. A rectangular pasture has a fence around the perimeter. "e length of the fence is 16x7 and the width is 48x4. What is the area of the pasture?

3x3 128x11 768x11 768x28

4. What is the simpli!ed form of (3.25 * 103)(7.8 * 106) written in scienti!c notation?

2.535 * 1010 2.535 * 1018 2.535 * 1019 25.35 * 109

5. "e size of a certain cell is 2.5 * 10-9 m. Another cell is 1.5 * 103 times larger. How large is the larger cell in scienti!c notation?

4 * 10-27 m 4 * 10-12 m 3.75 * 106 m 3.75 * 10-6 m

Extended Response

6. "e distance between two astronomical bodies is 6.75 * 106 miles. "e distance from the !rst body to a third body is 3.56 * 104 times the distance between the !rst two bodies.

a. Write an expression that represents the distance between the !rst and third bodies.

b. Simplify the distance in part a. c. Write an expression that represents the distance light would travel from the

!rst body to the third body and back to the !rst. d. Simplify the distance the light travels in part c.

C

G

C

F

3.56 × 6.75 × 104 × 106 mi2.403 × 1011 mi

2 × 3.56 × 6.75 × 104 × 106 mi4.806 × 1011 mi

[4] Correct answers to each part of the question[3] Mostly correct answers to each part with a few computational errors[2] Correct answers to 2 or 3 parts with a significant error in understanding or

solving the other parts[1] Correct answer to 1 part of the problem with significant errors in solving the

remaining parts[0] No effort made or no parts solved correctly

D

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Multiple Choice

For Exercises 1–6, choose the correct letter.

1. Which of the following is equivalent to x5y2

xy 12

when x ≠ 0 and y ≠ 0?

x6y52 x5y x4y x4y

32

2. Which expression is not equal to 125?

5°53

25¢2

a53

54b-3 5-2

5-5 5 a55

53b 3. A fraction reduces to 36. If its numerator is (6x)5, what is its denominator?

63x 63x5 6x5 67x5

4. Which is the correct simpli!cation of 5.4 * 1012

1.2 * 103 written in scienti!c notation?

4.5 * 107 4.5 * 109 45 * 106 6.48 * 107

5. Which of the following statements is not true regarding operations with exponents?

To divide powers with the same base, subtract the exponents.

To subtract powers with the same base, divide the exponents.

To multiply powers with the same base, add the exponents.

To raise a power to a power, multiply the exponents.

6. Which of the following expressions is written in simplest form?

35x2 (5y)3 a0b x2y3z

Short Response

7. A rectangle has an area of 12x3 y4 cm2. It has a width of 3xy cm. What ratio would you set up to determine the length? What is the length of the rectangle?

Standardized Test PrepDivision Properties of Exponents

D

F

B

G

B

12x3y4

3xy ; 4x2y3

[2] Student uses the correct ratio and finds the correct length.[1] Student either finds the correct ratio or shows the ability to

find the correct length.[0] Student’s response shows no effort or does not correctly

find the ratio or the length.

I

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Multiple Choice

For Exercises 1–4, choose the correct letter.

1. Which of the following expressions is equivalent to (32b)23?

A. 2(32b)3 B. 823 2b2 C. 3223 b2 D. 23 (8b)2

2. Which of the following expressions is equivalent to 223 x5?

F. 2x53 G. (2x)

53 H. 2x

35 I. (2x)

35

3. Which of the following expressions is equivalent to a2144a3b - a23 27b2b ?

A. 9(ab)32 B. 12a

32 - 3b

23

C. 12a3 - 3b2 D. (144a)32 - (27b)

23

4. A rectangle has an area equivalent to 426 x7 square units. Which of the following expressions could be used to !nd the area of the rectangle?

F. a8x23bax

12b G. (8x)

12 (x)

23 H. (8x)

23 ax

12b I. a8x

12bax

23b

Short Response

5. Simplify ax14b (20x)

12 using the properties of exponents, and then write the

expression in radical form.

Standardized Test PrepRational Exponents and Radicals

B

F

B

H

ax14b (20x)

12 = x

14(2)(15)x

12 = (215)ax

34b = 215 42x3

[2] Student correctly applies the properties of exponents and correctly simplifies to find the radical form.

[1] Student incorrectly applies the properties of exponents OR simplifies incorrectly.

[0] Student’s response shows no effort OR does not correctly use the properties of exponents and does not simplify correctly.

Name  Class  Date 

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Standardized Test PrepAdding and Subtracting Polynomials

Multiple ChoiceFor Exercises 1–6, choose the correct letter.

1. What is the degree of the monomial 3x2y3?

A. 2 B. 3 C. 5 D. 6

2. What is the simpli!ed form of 8b3c2 + 4b3c2?

F. 12bc G. 12b3c2 H. 12b6c4 I. 12b9c4

3. How is 6d - 8 + 4d2 written in standard form?

A. 4d2 + 6d - 8 B. 4d2 + 6d + 8 C. 4d2 - 6d - 8 D. 4d2 - 6d + 8

4. What is the simpli!ed form of (4j2 + 6) + (2j2 - 3)?

F. 6j2 - 3 G. 6j2 + 3 H. 6j2 + 9 I. 4j 4 + 3

5. What is the di"erence of the following polynomials?

6x3 - 2x2 + 4

- (2x3 + 4x2 - 5)

A. 4x3 - 2x2 - 1 B. 8x3 + 6x2 - 1 C. 4x3 - 2x2 + 1 D. 4x3 - 6x2 + 9

6. What is the simpli!ed form of (3x2 - 4x + 6x) + (5x3 + 2x2 - 3x) in standard form?

F. 5x3 + 10x2 - x G. 8x3 - 2x2 + 3x H. 5x3 + 10x2 - 5x I. 5x3 + 5x2 - x

Short Response

7. Suppose you have been given this polynomial. 5b + 4b2 - 3b4 + 3

a. How can you write this polynomial in standard form?

b. What is the degree of this polynomial? Explain.

C

G

G

D

I

A

−3b4 + 4b2 + 5b + 3

4; b4 is the term with the greatest degree

[2] Both parts answered correctly with full explanations[1] One part answered correctly or both parts answered correctly with incomplete

explanations[0] Neither part answered correctly

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Multiple ChoiceFor Exercises 1–5, choose the correct letter.

1. What is the simpli!ed form of (x - 2)(2x + 3)? Use the Distributive Property. A. 2x2 - x - 6 B. 2x2 - 6 C. 2x2 - 7x - 6 D. 2x2 + x - 6

2. What is the simpli!ed form of (3x + 2)(4x - 3)? Use a table. F. 12x2 + 18x + 6 G. 12x2 + x - 6 H. 12x2 + 18x - 6 I. 12x2 - x - 6

3. What is the simpli!ed form of (4p - 2)(p - 4)? A. 4p2 + 6p - 16 B. 4p2 - 18p + 8 C. 4p2 - 14p - 6 D. 4p2 - 6p + 16

4. "e radius of a cylinder is 3x - 2 cm. "e height of the cylinder is x + 3 cm. What is the surface area of the cylinder?

F. 2p(3x2 + 10x - 8) G. 2p(12x2 + 7x - 2) H. 2p(12x2 - 2x + 13) I. 2p(12x2 - 5x - 2)

5. What is the simpli!ed form of (2x2 + 4x - 3)(3x + 1)? A. 6x3 + 10x2 - 5x + 3 B. 6x3 + 14x2 + 5x - 3 C. 6x3 + 14x2 - 5x - 3 D. 6x3 - 10x2 - 5x - 3

Short Response 6. A soup can that is a cylinder has a radius of 2x - 1 and a height of 3x. What is

the surface area of the soup can? Show your work.

Standardized Test PrepMultiplying Binomials

A

I

B

I

C

[2] Correct polynomial written with all work shown[1] Polynomial written with minor calculation error or inadequate work shown[0] No correct work shown

20Px2 − 14Px + 2P

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Standardized Test PrepComplex Numbers

Multiple ChoiceFor Exercises 1!8, choose the correct letter.

1. What is the simpli!ed form of (-8 + 5i) + (3 - 2i)?

-14 + 31i -5 + 3i -11 + 7i 5 - 3i

2. What is the simpli!ed form of (11 - 6i) - (-4 + 12i)?

7 + 6i 7 - 18i 15 + 6i 15 - 18i

3. What is the simpli!ed form of (5 + 1-36) - (-4 - 1-49)?

9 - 13i 9 + 85i 1 - i 9 + 13i

4. What is the simpli!ed form of (-5i)(-3i)?

-15i -15 15 15i

5. What is the simpli!ed form of (-3 + 2i)(1 - 4i)?

-2 - 2i -11 - 10i 5 + 14i -3 - 8i

6. What is the simpli!ed form of (8 - 3i)2?

73 16 - 6i 55 - 48i 55 + 48i

7. What is 5 + 3i4 - 2i written as a complex number?

710 + 11

10i 1310 + 1

10i 54 - 3

2i 710 - 11

10i

8. What is the factored form of the expression4x2 + 36?

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

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

Short Response 9. What are the solutions of 2x2 + 3x + 6 = 0? Show your work.

B

I

D

G

C

H

A

G

[2] −34 t 139

4 i;[1] quadratic formula properly used, but some computational

errors OR correct solutions without work shown[0] incorrect answers and no work shown OR no answers given