common assessment #3 algebra ii multiple choice
TRANSCRIPT
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
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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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