EOC Integrated Math II Practice Test - Obion County Schools

Integrated Math IIPractice Test

Subpart 1, Subpart 2, & Subpart 3

Tennessee Comprehensive Assessment Program

TCAP

Student Name

Teacher Name

Published under contract with the Tennessee Department of Education by Questar Assessment Inc., 5550 Upper 147th Street West, Minneapolis, MN 55124. Copyright © 2016 by Tennessee Department of Education. All rights reserved. No part of this publication may be copied, reproduced, or distributed in any form or by any means, or stored in a database or retrieval system, without the prior express written consent of the Tennessee Department of Education and Questar Assessment Inc.

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Directions

Test Administrator Instructions:

This practice test has Subpart 1, Subpart 2, and Subpart 3. There is also an answer document and an answer key at the end of this document. It is recommended that you print one copy of this practice test and pull the answer key before copying and distributing the practice test and answer document to your students.

This practice test is representative of the operational test but is shorter than the actual operational test. To see the details about the operational test, please see the blueprints located on the Tennessee Department of Education website.

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Sample Questions

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Directions

Subpart 1 of this Practice Test booklet contains constructed-response items and selected-response items in Integrated Math II. Write all answers on your answer document.

You MAY NOT use a calculator in Subpart 1 of this test booklet.

Sample 1: Constructed-Response

1. The sum of two consecutive odd integers is 72.

1. Write an algebraic equation to determine the two integers.

2. What are the two integers?

Write your answers in the spaces provided on your answer document.

Sample 2: Selected-Response

2. Factor the polynomial:

s2 + 12s + 32

A. (s + 4)(s − 8)

B. (s − 2)(s + 16)

C. (s + 4)(s + 8)

D. (s + 16)(s + 2)

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Integrated Math II, Subpart 1 Practice Test

1. What is the best first step in solving the equation 3x2 + 8x = –5?

A. adding 5 to both sides

B. dividing both sides by 3

C. taking the square root of both sides

D. factoring an x out of the left side of the equation

2. Fannie is making a rectangular blanket. The length of the blanket is 10 inches greater than its width, w, in inches.

Write the function, f (w), that describes the area, in square inches, of Fannie’s blanket as a function of the width, w.

Write your answer in the space provided on your answer document.

3. Simplify the expression (2 – 3i)(4 + 2i).

A. 14

B. 6i

C. 2 – 8i

D. 14 – 8i

4. The length of a rectangle is 7 inches longer than its width. The area of the rectangle is 260 square inches.

What is the length, in inches, of the rectangle?


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5. Determine which statement is true in regard to ABC and LMN.

A. ABC ~ LMN by AA criterion.

B. ABC ~ LMN by SAS criterion.

C. ABC ~ LMN by SSS criterion.

D. ABC and LMN are not similar.

6. Which expression is the correct factorization of x6 – y6?

A. (x + y)3(x – y)3

B. (x2 – y2)(x4 + 2xy + y4)

C. (x – y)(x + y)(x2 + xy + y2)(x2 – xy + y2)

D. (x – y)(x2 + 2xy + y2)(x + y)(x2 – 2xy + y2)

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7. A function is graphed on the coordinate plane.

Select the function that is graphed on the coordinate plane.

A. f x x( ) = + −1 2

B. f x x( ) = − +1 2

C. f x x( ) = + −2 1

D. f x x( ) = − +2 1

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8. Let c represent any non-zero rational number.

Select all values that, when added to c, will produce an irrational number.

A. − 513

B. p2

C. 36

D. 8.73

E. 95

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STOP

This is the end of Subpart 1 of the Integrated Math II Practice Test. Proceed to Subpart 2.

9. The function f(x) = x2 – 3x – 4 is graphed on the coordinate plane.

Consider f(x – 3). Which option correctly describes the transformation to the graph?

A. up 3 units

B. down 3 units

C. left 3 units

D. right 3 units

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Directions


You MAY use a calculator in Subpart 2 of this test booklet.

10. Consider the equation x2 – 12x + 49 = 22.

Which equation has the same solution(s) as the given equation?

A. (x – 6)2 = 9

B. (x – 7)2 = 22

C. (x + 7)2 = 4.7

D. (x – 12)2 = –27

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11. A support wire is attached to the top of an antenna. The support wire connects to the ground 15 feet from the bottom of the antenna. The support wire and the ground meet at an angle with measure 70°, as shown.

To the nearest foot, what is the height of the antenna?


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12. A survey asked whether students would eat food served in the school cafeteria. The results are recorded in the table shown.

What is the probability that a tenth-grade student will not eat food served in the school cafeteria, rounded to the nearest hundredth?


13. Calvin purchases a piece of heavy machinery for $32,300. The value of the machine depreciates at an annual rate of 8.3%. Which function represents the value of the machine with an approximate equivalent monthly depreciation rate?

A. f t t( ) , ( . )= 32 300 0 917112

B. f t t( ) , ( . )= 32 300 1 083112

C. f t t( ) , ( . )= 32 300 0 917112 12

D. f t t( ) , ( . )= 32 300 1 083112 12

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14. The graph of a system of equations is shown.

What are the x-values for the solutions to this system?


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15. RSV ~ UST

Select all statements that are true.

A. STU is a right triangle.

B. RS is 43

x cm in length.

C. ∠ ≅ ∠VRS STU

D. The area of RSV is 98

x cm2.

E. m RSV m UST∠ + ∠ = °90

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16. A healthcare company surveys customers to determine whether each customer would be willing to pay an additional $35 monthly for extra coverage. The results of the survey are shown.

What is the probability a customer below the age of 50 would be willing to pay an extra $35 monthly?


17. The chart gives the number of people owning cell phones as a function of years.

The number of people owning cell phones, N(t), is modeled by the equation N(t)=A

0P

t, where t represents the number of years since 1977.

What is the value of A0?

A. 0.30

B. 2.0

C. 1.80

D. 2.1

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STOP

This is the end of Subpart 2 of the Integrated Math II Practice Test. Proceed to Subpart 3.

18. In the figure shown, cos(w˚) = 0.60.

What is sin(x˚)?

A. 0.36

B. 0.40

C. 0.60

D. 0.80

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Directions


You MAY use a calculator in Subpart 3 of this test booklet.

19. Simplify the expression (3x4 + 9x3 – 7x + 15) + (–6x4 – 8x2 + 5x – 3).


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20. Consider the function f (x) = x2 – 2x.

Graph the function f (x) on the coordinate plane provided on your answer document.

21. Consider the equation 3(x – 5)2 + 6 = 54.

What value(s) of x makes the equation true? Enter one solution in each space provided on your answer document. If there is only one solution, leave one space blank.

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22. A quadratic equation has the following coefficients: a = 2, b = –3, and c = 3. Write the solution(s) of the equation. Enter one solution in each space provided on your answer document. If there is only one solution, leave one space blank.

23. � ∼�RST UVW . The dilation that maps RST UVW to has a dilation factor of 23

.

The measure of angle R is 20° and the measure of angle S is 100°.

What is the measure, in degrees, of angle W?


24. The length of one side of a shoebox is 8 cm more than twice the width. The base of the shoebox has an area of 72 cm2. Write an equation to represent this situation with w representing the width.


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25. A right triangle has leg lengths 0.3 centimeters and 0.4 centimeters. What is cosθ where θ is the smallest angle of the triangle?


26. A quadratic function is given as f (x) = 4x2 + 8x + 10.

Write an equivalent function by inserting the numerals 1–9 and operational signs (+, –) into the vertex form given. Write the complete equation in the space provided on your answer document.

f(x) = ____(x____ ____)2____ ____

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27. Each day, an investor deposits twice as much into the bank as she did the day before. Her initial investment is $3.

Using the elements 1, 2, 3, 6, 9, and x, write an exponential equation to model her daily deposit, y, on day x. Write the complete equation in the space provided on your answer document.

y = ____(____)____

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28. The equation y = –2(x – 1)2 + 18 is used to determine the profit earned, y, from the sales of product, with x representing the price per unit sold.

Plot the points representing the x-intercept(s), y-intercept(s), and maximum or minimum point, whichever one is appropriate, on the coordinate grid provided on your answer document.

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STOP

This is the end of the test.

29. Chris is looking up at the top of a tree. He is standing 20 feet from the tree, and his line of sight is 35° from horizontal. His eyes are 5 feet above the ground.

To the nearest foot, how tall is the tree?


30. A quadratic function is given as f (x) = 3x2 + 24x + 25.

Write the vertex form of the given function.


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TNReady Math Reference Sheet—High School

1 inch = 2.54 centimeters1 meter = 39.37 inches

1 mile = 5,280 feet 1 mile = 1,760 yards 1 mile = 1.609 kilometers

1 kilometer = 0.62 mile

1 pound = 16 ounces 1 pound = 0.454 kilograms

1 kilogram = 2.2 pounds 1 ton = 2000 pounds

1 cup = 8 fluid ounces 1 pint = 2 cups

1 quart = 2 pints 1 gallon = 4 quarts 1 gallon = 3.785 liters

1 liter = 0.264 gallons 1 liter = 1000 cubic centimeters

Pythagorean Theorem: a b c2 2 2+ =

Quadratic Formula: x b b aca

= − ± −2 42

Arithmetic Sequence: a a n dn = + −( )1 1

Geometric Sequence: a a rnn= −

11

Finite Geometric Series: Sa r

rn

n

=−( )

−1 1

1

Degrees: 1 degree = π180 radians

Radians: 1 radian = 180

π degrees

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Answer Document

Name: __________________________________

Subpart 1 Sample Questions

1. 1.

2.

2. A B C D

Subpart 1 Practice Test Questions

1. A B C D

2.

3. A B C D

4.

5. A B C D

6. A B C D

7. A B C D

8. A B C D E

9. A B C D

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Answer Document


10. A B C D

11.

12.

13. A B C D

14.

15. A B C D E

16.

17. A B C D

18. A B C D

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Answer Document


19.

20.

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Answer Document

21.

22.

23.

24.

25.

26.

27.

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Answer Document

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29.

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Answer Key

Subpart 1 Sample Questions

1. 1. x x+ + =2 72

2. 35, 37

2. A B C D


1. A B C D

2. f w w w( ) ( )= +10 or any equivalent form

3. A B C D

4. 20

5. A B C D

6. A B C D

7. A B C D

8. A B C D E

9. A B C D


10. A B C D

11. 41

12. 0.43

13. A B C D

14. 0 and 2

15. A B C D E

16. 0 40 0 41. .−

17. A B C D

18. A B C D

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Answer Key


19. − + − − +3 9 8 2 124 3 2x x x x or any equivalent form

20.

21. 1

9

22. 3 154

+ i

3 154

− i

23. 60

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Answer Key

24. 2 8 722w w+ = or any equivalent equation

25. 0.8

26. f x x( ) ( )= + +4 1 62

27. y x= 3 2( )

28.

29. 19

30. f x x( ) ( )= + −3 4 232

Documents

EOC Integrated Math II Practice Test - Obion County Schools