EOI Algebra II - Oklahoma State Department of Education

Oklahoma School Testing Program

Oklahoma Core Curriculum Tests

2011–2012 Released Items End-of-Instruction ACE Algebra II

Oklahoma State Department of Education Oklahoma City, Oklahoma

Copyright © 2011 by the Oklahoma State Department of Education. All rights reserved. Any other use or reproduction of this document, in whole or in part, requires written permission of the Oklahoma State Department of Education.

Section 1

1

Section 1 Directions Read each question and choose the best answer. 1

(5)

Which expression is equivalent to 3

A

4

57 7 3

B

7

54 4 3

C

7 ⎞ ⎛ −⎜ 4 3 ⎟ ⎝ 57 ⎠

D

4 ⎞ ⎛ −⎜ 7 3 ⎟ ⎝ 54 ⎠

−4 7

?

2

17x − 20 68 x What is the simplified form of this expression? F

−39 17x

G

−21 85x

H

−20 85x

J

−19 17x

GO ON 2

Section 1

3 x

5

4

− 2 x + 3x + 7 2 x +1

What are the quotient and remainder when this division is performed? A

Quotient: x

3

− 3x 2 + 6

Remainder: 1 B

Quotient: x

3

− 3x 2

Remainder: 7 C

Quotient: 4 x + 5 3 2 Remainder: x − 2 x − x + 2

D Quotient: x

3

− 2x 2 − x + 2

Remainder: 4 x + 5

GO ON 3

Section 1

4

5

1 x − 3 Which expression is equivalent to 2 ? x − x − 6

F

x +2

G

1 x + 2

H

1 2 ( x − 3) ( x + 2)

J

1 ( x − 3)( x + 3)( x − 2)

What is the product of (3 − 5i ) and (2 + 4i )? A 14 − 2i B 14 + 2i C

26 − 2i

D 26 + 2i

GO ON 4

Section 1

6

f (x) = x 2 − 49 g(x) = x

What is the value of

F

2

+ 3 x − 18

⎛ f ⎞ (−6)? ⎝ g⎠

− 13

36

G

0

H

85 72

J

undefined

GO ON 5

Section 1 Use the information below to answer Number 7 on the next page. The graph shows y = f (x).

y 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5

1 2 3 4 5

x

GO ON 6

Section 1

7

Which graph shows y = f A

−1

(x)?

y

B

5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5

C

1 2 3 4 5

5 4 3 2 1

x

-5 -4 -3 -2 -1 -1 -2 -3 -4 -5

y

D

5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5

1 2 3 4 5

y

1 2 3 4 5

x

1 2 3 4 5

x

y 5 4 3 2 1

x

-5 -4 -3 -2 -1 -1 -2 -3 -4 -5

GO ON 7

Section 1

8

Which graph represents the solution set to the system of inequalities below?

⎧y < 2 x + 2 ⎪ 3 ⎨ ⎪y < 2 x − 1 3 ⎩ F

y

G

3 2 1 -3 -2 -1 -1 -2 -3

H

1 2 3

3 2 1

x

-3 -2 -1 -1 -2 -3

y

J

3 2 1 -3 -2 -1 -1 -2 -3

1 2 3

y

1 2 3

x

1 2 3

x

y 3 2 1

x

-3 -2 -1 -1 -2 -3

GO ON 8

Section 1

9

9x 2 + 6 x + 1 = 0 What is the solution set of this equation? A

{3 }

B

{

C

{0, 3}

D

{− }

1 , −1 3 3

}

1 3

10 The height of a projectile, h(t ), is modeled as a function of time, t, in seconds.

h(t )= −32t 2 + 128t How long is the projectile in the air? F

0 seconds

G 2 seconds H 4 seconds J

8 seconds

GO ON 9

Section 1

11

y 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5

1 2 3 4 5

x

What is the equation of this graphed hyperbola?

A

( x − 1) 2 (y − 3) 2 − =1 4 4

B

( x − 1) 2 (y − 3) 2 − =1 2 2

C

(y − 3) 2 ( x − 1) 2 − =1 4 4

D

(y − 3) 2 ( x − 1) 2 − =1 2 2

GO ON 10

Section 1

( )

12 Which graph represents y = 1

3

F

?

y 7 6 5 4 3 2 1 -7-6-5-4-3-2-1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

H

x

G

7 6 5 4 3 2 1

x

-7-6-5-4-3-2-1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

y 7 6 5 4 3 2 1 -7-6-5-4-3-2-1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

y

J

y 7 6 5 4 3 2 1

x

x

-7-6-5-4-3-2-1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

x

GO ON 11

Section 1

13 Karen hears a scream that has a relative intensity, R, of 90 decibels. The relative intensity of a sound, R, in decibels is given by the formula

R = (10)log I , where I is the intensity of a sound and I 0 is the I0

threshold for hearing. How does the intensity of this scream, I, compare to the intensity of the threshold for hearing, I 0? A

3,486,784,401 times as loud

B

1,000,000,000 times as loud

C

900 times as loud

D 9 times as loud

14

2 x 3 + x 2 − 5x + 2 = 0 Given that (x + 2) and (x − 1) are factors of this polynomial equation, what is the third factor? F

2x − 1

G 2x − 5 H 2x + 3 J

2 x 2 + 3x + 12

GO ON 12

Section 1

15 Kylie is making a box with an open top from a square piece of cardboard that measures 11 inches on each side.

x

x

x

x

x

x x

x Key = fold

First, she cuts out squares of uniform side length, x, from each corner of the cardboard. Then she folds the cardboard to form the lateral faces of the box. Which function models the volume of the box?

V = Bh A

V (x) = (11 − 2 x) 2

B

V (x) = x(11 − 2 x) 2

C

V (x) = (11 − x) 2

D

V (x) = x(11 − x) 2

GO ON 13

Section 1

16

2x + 5 = 3 2

x

What are the solutions of this equation?

F

x = 3 and x = 2

G

x = 4 and x = −2

H

x = 3 and x = −2

J

x = 4 and x = 2

4

3

4

3

GO ON 14

Section 1

17 Tanisha used this table to compare the number of school yearbooks purchased (y) in Mr. Bach’s class each year (x) that he was a teacher.

Teaching Year

1

2

3

4

5

6

7

Number of Yearbooks

23

22

23

24

23

22

23

Which scatter plot represents the data in the table? A

B

Yearbooks Purchased in Mr. Bach’s Class

Yearbooks Purchased in Mr. Bach’s Class

24 23 22 21 20 0

1 2 3 4 5 6 7 8 Teaching Year

x

24 23 22 21 20 0

D

Yearbooks Purchased in Mr. Bach’s Class

x

1 2 3 4 5 6 7 8 Teaching Year

Number of Yearbooks

y

24 23 22 21 20 0

1 2 3 4 5 6 7 8 Teaching Year

Yearbooks Purchased in Mr. Bach’s Class

y Number of Yearbooks

C

y Number of Yearbooks

Number of Yearbooks

y

x

24 23 22 21 20 0

1 2 3 4 5 6 7 8 Teaching Year

x

GO ON 15

Section 1

18

x

y

-3

3

-2.5

2

-1

1.5

-0.5

1

1

-0.5

1.5

-1

2

-2.5

3

-3

Which type of function best models the data in this table? F

exponential

G logarithmic H quadratic J

linear

GO ON 16

Section 1

19

4, 6, 9, 13.5, 20.25, . . . Which formula can be used to determine the 50th term of this sequence?

Arithmetic Sequences & Series nth term: an = a1 + (n − 1)d Sum: sn =

n 2

(a + an) 1

Geometric Sequences & Series nth term: an = a1r Sum: sn =

A

a50 = 4 + (50 − 1)(1.5)

B

s 50 = 50 (4 + 80.5)

C

a50 = 4(1.5) 49

D

s 50 =

(n−1)

a1(1 − r n) (1 − r )

2

4 − 4(1.5) 1 − 1.5

50

STOP 17

STOP END OF SECTION 1

18

535743

1 2 3 4 5 A B C D E

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