SCHOLAR NAME ___________________________

Common Assessment #3

Algebra II

MULTIPLE CHOICE

Administered Spring 2018

INSTRUCTIONS:- This test will last 75 minutes. At the end of 75 minutes, your teacher willcollect your test regardless of whether or not you have finished.

- This time limit includes answering the multiple choice questions, bubbling inthe answer sheet, and completing the constructed response questions.

- You may use scratch paper provided by your teacher. However, onlyanswers bubbled on the answer sheet and written on the constructedresponse pages will be scored.

- You may use only the formula chart, equations, and reference materialsprovided in this assessment.

- Calculators may be used on this test.

Some questions (c) 2017 by Region 10 Educational Service Center.

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STAAR ALGEBRA IIREFERENCE MATERIALS State of Texas

Assessments of Academic Readiness

STAAR®

FACTORING

Perfect square trinomialsa ab b a b2 2 22+ + = +(

a ab b a b2 2 22− + = −(

Difference of squares a b a b a b2 2− = − +( )( )

Sum of cubes a b a b a ab b3 3 2+ = + − +( )(

Difference of cubes a b a b a ab b3 3 2− = − + +( )( 2)

2)

PROPERTIES OF EXPONENTS

Product of powers a a am n m n= +( )

Quotient of powers a

aa

nm n= −( )

Power of a power ( )a am n mn=

Rational exponent a amn mn=

Negative exponent aa

nn

− =1

m

QUADRATIC EQUATIONS

−

)

)

)

)

Standard form f x ax bx c( ) = + +2

Vertex form f x a x h k( ) ( )= − +2

Parabola( ) (x h p y k− = −2 4

( ) (y k p x h− = −2 4

Quadratic formula xb b ac

a=− −2 4

2

Axis of symmetry x ba

=2

This page is intentionally left blank

1 Write 34 = 81 in logarithmic form.

A log34 = 81

B log381 = 4

C log481 = 3

D log43 = 81

2 Carolanne was subtracting the two

polynomials shown below.

(3x2 – 4x – 1) – (8x2 – x + 6)

Which of the following best describes her

answer in simplest form?

F 1 1x2 – 3x –7

G 5x2 – 5x + 5

H -5x2 – 3x – 7

J -5x2 – 5x + 5

3 Which is the complete factorization of

27x3 – 8?

A (3x – 2)(9x2 + 6x + 4)

B (3x + 2)(9x2 − 6x + 4)

C (3x – 2)(3x + 2)(3x − 2)

D (3x – 2)(9x2 − 6x + 4)

4 Which equation moves y = logbx to the

left 4?

F y = logb x - 4

G y = logb (x - 4)

H y = logb x + 4

J y = logb (x + 4)

5 Solve for x in the equation below:

A 5

B 25

C ±25

D 125

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6 For an activity in class, the teacher gave

each student a small card with a

binomial on it and had them pair with

another student. Elinor’s card had

3x + 4 on it. She paired with Mike whose

card showed −2x – 1. The teacher asked

the students to add, subtract, and then

multiply the binomials on their two

cards together. Which of the following

could NOT be one of Elinor and Mike's

answers?

F 5x + 3

G x + 3

H 5x + 5

J −6x2 – 11x – 4

7 Simplify completely:

A

B

C

D

8 What is the complete factored form of

x3 – 5x2 – x + 5?

F (x2 – 1)(x – 5)

G (x + 1)(x – 1)(x − 5)

H (x – 1)(x – 1)(x – 5)

J (x + 1)(x – 1)(x + 5)

9 Given an initial investment of $500 at a

rate of 4% interest compounded

annually, and no additional deposits,

Mrs. Ramirez wanted to determine how

long she would have to leave the money

in her investment account for her

money to grow to $1000. To solve the

problem Mrs. Ramirez uses the equation

500(1.04)t = 1000, where t represents

the number of years. How long will she

need to plan to invest her money?

A Approximately 0.3 years

B Approximately 17.7 years

C Approximately 117.4 years

D Approximately 2 years

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10 Solve the equation

for the value(s)

of x.

F x = −3

G x = −2

H Both of the above

J None of the above

1 1 Which of the following shows the

correct exponential form of the

logarithmic equation below?

A

B

C

D

12 The parent exponential function,

f(x) = 2x, has been transformed and is

shown in the graph below.

Which function below represents the

algebraic transformation on the

function?

F f(x + 5) + 3

G f(x) − 5 + 3

H f(x – 5) + 3

J f(x) + 5 + 3

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13 Which of the following graphs best reflects the transformation of the exponential parent

function, f(x) = 2x, to the form 3f(x + 2) – 4?

A

B

C

D

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14 Simplify completely:

F

G

H

J

15 Solve the equation below:

8x-3 = 2-3

A

B 4

C

D 1

16 Sara was solving the following problem

in class.

(7x2 – 4x + 5) (3x2 + 6x – 9)

What is Sara's final answer?

F 21x4 + 54x3 – 102x2 + 66x – 45

G 21x4 + 30x3 - 72x2 + 66x – 45

H 21x2 – 24x – 45

J 10x2 + 2x – 4

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17 Joe converted the exponential equation

to logarithmic form as

. Which reason best

explains whether Joe is correct, or if he

is incorrect, the way he should have

written the equation?

A Joe is incorrect; The correctly

converted equation is .

B Joe is incorrect; The correctly

converted equation is .

C Joe is incorrect; The correctly

converted equation is .

D Joe is correct in his answer.

18 Use the properties of logarithmic

equations to solve

log5 6 + log5 2x2 = log5 48 for the

value(s) of x.

F

G

H

J none of the above

19 Which expression is equivalent to b in

the equation below?

A

B

C

D

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20 Caitin solved the equation

log9x + log9(x - 8) = 1 and got two

answers; x = 9 and x = −1. Which best

explains Caitin’s solutions?

F Caitin is correct. Both answers are

solutions to the equation.

G Caitin is incorrect. Neither answer

is a solution to the equation. She

made an error in solving the

problem.

H Caitin is half correct. Only x = 9

can be a solution to a log equation

because negative numbers have no

logs.

J Caitin is half correct. Only x = −1 is

a solution to a log equation because

the number 9 cancels out with the

base.

21 Max is trying to completely factor the

polynomial 8x4 + 16x3 + x + 2. His

work so far is shown below.

What does Max need to do to finish

completely factoring this problem?

A Nothing, this is as far as Max can

work.

B Write the answer as 8x3(x + 2)2.

C Factor out a 1 from the second

factor to be able to write the final

answer as (8x3 + 1)(x + 2).

D Factor out a 1 from the second

factor to get (8x3 + 1)(x + 2) and

factor (8x3 + 1) as a sum of cubes.

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22 When the parent function f(x) = 2x is

transformed to , which of

the following attributes of the graph is

not changed?

F horizontal asymptote

G y-intercept

H range of the graph

J domain of the graph

23 Three students were factoring a

challenge problem for a bonus on their

math test. They were to completely

factor 45x3 + 18x2 – 5x – 2. Their

answers are shown below.

Student A: (9x2 – 1)(5x + 2)

Student B: (3x + 1)(3x – 1)(5x + 2)

Student C: (9x2 + 1)(5x + 2)

Which student factored correctly?

A Student A

B Student B

C Student C

D None of the students

24 Jonathan was solving an equation in his

math class. His work is shown below.

Jonathan is stuck in the problem

solving process. Which information

does he need to know so he can

continue solving?

F To get rid of the rational exponent

he should have used the inverse

exponent of 3/5 instead of 5/3.

G In the first step, you cannot

combine the -6 and the -5 to make

-11 because the 5 is being

multiplied with the parenthesis

and not added.

H There are 2 mistakes; both F and

G above.

J None of the above. Next take the

third root of 466 and then raise

that value to the 5th power, which

is 28,009.79054 and keep solving.

BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERSON YOUR ANSWER DOCUMENT STOPPage 10

SCHOLAR NAME ___________________________

Common Assessment #3

Algebra II

CONSTRUCTED RESPONSE

Administered Spring 2018

1 A rectangular kitchen rug has a length of 5x2 + 4x and a width of 3x + 7.

A) What is the perimeter of the rug in simplest form?

B) What is the area of the rug in simplest form?

2 A swimming pool's volume is represented by x4 - 3x2 + 10. If the swimming pool has a

height of x2 - 2, find the area of the base of the pool (V = Bh, where B is area of the base and

h is height). Show all work.

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3 Find all the factors for the polynomial x3 – 2x2 – 7x – 4, if (x + 1) is one factor. Show all

work.

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4 A) Sketch a general graph of y = 2x showing growth.

B) Identify the x-intercept, y-intercept, domain, range, and asymptotes of the function.

C) The exponential function is translated 4 units left and 3 units up. Write the equation of

the transformed function.

D) Determine which of the properties from part B were effected by the transformation.

E) The function from part C is then reflected over the x-axis. Write the equation of the new

function.

F) Determine which properties listed in part B are effected by this transformation.

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