algebra ii 2014 2015 semester exams practice materials semester...

ALGEBRA II 2014–2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1

2014–2015 of 22 Revised July 2014 Clark County School District

1.2-1 What is the inverse of ?

(A)

(B)

(C)

(D)

1.2-2 If , what is ?

(A)

(B)

(C)

(D)

1.4-1 Which statement must be true if and are inverses of one another?

(A)

(B)

(C)

(D)

( ) 2 9f x x

1( ) 92

xf x

1 1( )

2 9f x

x

1 9( )

2

xf x

1 2( )

9f x

x

1 4( ) 8

3f x x ( )f x

3( ) ( 8)

4f x x

3( ) 8

4f x x

4( ) 6

3f x x

4( ) ( 8)

3f x x

f g

( )( ) ( )( )f g x g f x x

( )( ) ( ) ( ) ( )( ) ( ) ( )f g x f x g x g f x g x f x x

( )( ) ( ( )) ( )( ) ( ( ))f g x f g x g f x g f x x

1( )( )

( )( )f g x x

g f x



3.4-1 Simplify .

(A)

(B)

(C)

(D)

3.4-2 Simplify .

(A)

(B)

(C)

(D)

3.6-1 (3.3) Solve the quadratic equation by taking the square root.

(A)

(B)

(C)

(D)

(3- 4i) + (5- 6i)

8+10i

-9- 38i

8-10i

6-10i

(1- 3i) - (-3+ 7i)

4-10i

4+ 4i

18+16i

-2+ 4i

24 5 1x

6

2x

6

4x

6

2

ix

6

4x



3.7-1 (3.1, 3.5) A student has learned that test scores in math are determined by this

quadratic function:

In the function, is the score and is the number of hours that a student spends on

homework each week.

a) How many hours must a student spend on homework to achieve maximum score?

b) What is the maximum score?

c) Based on the function, what will be the score if a student does no homework?

3.7-2 (3.3) Show that is a root of .

3.7-3 (3.3, 3.6) Solve over the set of complex numbers.

(A)

(B)

(C)

(D)

3.7-4 (3.2, 3.5) Function A and Function B are continuous quadratic functions.

Function A Function B

Which function has a greater positive x-intercept?

(A) Function A

(B) Function B

2( ) ( 6) 99s t t

s t

( 3 )i 2 6 10 0x x

2 25 0x

25i

5

5i

25

2( ) 6f x x x



3.7-5 (3.1, 3.5) What is the equation of the parabola shown?

(A)

(B)

(C)

(D)

3.7-6 (3.3) Factor .

(A)

(B)

(C)

(D)

3.7-7 Solve the equation by factoring.

(A)

(B)

(C)

(D)

24y x

22y x

21

2y x

21

4y x

29 121x

(3 11)(3 11)x x

(3 11)(3 11)x x

(3 11 )(3 11 )x i x i

(3 11 )(3 11 )x i x i

26 24 126 x x

7 or 3x x

7 or 3x x

7 x

3x



3.7-8 What is the solution set of ?

(A)

(B)

(C)

(D)

3.7-9 Which of the following is a factor of ?

(A)

(B)

(C)

(D)

3.8-1 (3.3, 3.7) Which of the following quadratic equation has no real roots?

(A)

(B)

(C)

(D)

3.8-2 (3.2) Find the vertex of and state if it is a maximum or a minimum.

(A) (-1, -4); maximum

(B) (-1, -4); minimum

(C) (-4, -1); maximum

(D) (-4, -1); minimum

2 2 3 14y y y

7y

2 or 7y y

7 2y

2 7y

2 2( 1)a b

1a b

a b

1a

1a b

22 7 9 0x x

22 7x x

22 7 9 0x x

22 7 9 0x x

y = x2 + 2x - 3



3.8-3 (3.1) Consider the function

a) Determine the roots of the function. Show your work.

b) The vertex of is the point (3, 30). Write the function rule for in vertex

form.

c) Explain how transformed to become .

3.8-4 For what values of will have exactly one distinct real root?

(A)

(B)

(C)

(D)

3.9-1 Solve the equation by using the quadratic formula.

(A)

(B)

(C)

3.9-2 (3.8) Given the general form of a quadratic equation , determine

the effect of each condition on the solutions.

a) b) c) d) What is needed for the solutions to have imaginary parts?

2( ) 2 48.f x x x

g x g

f x g x

c 23 2 0x x c

3

2

1

3

1

3

2

3

22 5 3 0x x

x =1 or x = -6

x =

1

2 or x = -3

1 or 1

3x x

2 0x bx c

0b

0c

0c



3.13-1(3.5) Use the graph provided to choose the best description of what the graph

represents.

(A) A ball I dropped from a height of 42 feet and lands on the ground after 3

seconds.

(B) A ball is dropped from a height of 42 feet and lands on the ground after

1.5 seconds.

(C) A ball is shot up in the air and reaches a height of 42 feet after 1 second.

(D) A ball is shot up in the air, reaches a height of 42 feet, and lands on the

ground after 1.5 seconds.

3.14-1 (3.4, 3.7) The height of Carl, the human cannonball, is given by

where is in feet and is in seconds after the launch.

a) What was his height at the launch? b) What is his maximum height? c) How long before he lands in the safety net, 8 feet above the ground?

3.14-2 (3.5, 3.13) Several values of the quadratic function are given in the table.

2( ) 16 56 40h t t t h t

( )f x

Time (s)

Height (ft)



The function is given by . Which function has the greater

maximum for which value of ?

(A)

(B)

(C)

(D)

3.14-3 (3.8) Which statement best describes these two functions?

(A) The maximum of is less than the minimum of .

(B) The minimum of is less than the maximum of .

(C) The maximum of is greater than the minimum of .

(D) The minimum of is greater than the maximum of .

3.14-4 (3.1, 3.13) The amount of fuel (in billions of gallons) used by trucks from 1990

through 2009 can be approximated by the function where

represents 1990.

a) Describe the transformation of the common function . Then sketch

the graph over the interval

b) Find and interpret .

( )

4 96

2 24

0 0

4 96

9 486

x f x

( )g x 2( ) ( 2) 3g x x

x

( ); for 0f x x

( ); for 6f x x

( ); for 2g x x

( ); for 3g x x

2

2

4

3 3 7

f x x x

g x x x

( )f x ( )g x

( )f x ( )g x

( )f x ( )g x

( )f x ( )g x

F2( ) 20.5 0.035F f t t

0t

2( )f t t

0 19.t

(19) (0)

19 0

f f



c) Rewrite the function so that represents 2000. Explain how you got your answer.

d) Use the model from part (c) to predict the amount of fuel used by trucks in 2015. Does your answer seem reasonable? Explain.

4.2-1 What is the 4th term of the expanded binomial ?

(A)

(B)

(C)

(D)

4.2-2 Suppose and . What is ?

(A) 3

(B) 12

(C) 36

(D) 81

4.3-1 The table lists all the real roots of a 5th degree polynomial and the

multiplicity of each root.

Which general factorization correctly represents ?

(A)

0t

6(2 1)x

3240x

360x

3240 x

3160 x

9xy 2( ) 21x y 2 2x y

( )p x

Multiplicity

3 1

1 1

1 2

2 1

x

( )p x

2( 3)( 1) ( 2)a x x x



(B)

(C)

(D)

4.3-2 A 4th degree polynomial with real coefficients is found to have exactly two distinct

real roots. What must be true about the other two roots?

(A) One root is real and the other is imaginary.

(B) Both roots must be real.

(C) Both roots are imaginary roots that are complex conjugates.

(D) All the roots have been found.

4.4-1 Divide using long division.

(A)

(B)

(C)

(D)

4.4-2 The volume and height ( ) of the prism is given. Find a polynomial

expression for the area of the base ( ) in terms of . (Hint: )

3( 3)( 1) ( 2)a x x x

2( 3)( 1)( 1) ( 2)a x x x x

3( 3)( 1) ( 2)a x x x

4 3 2( 2 7) ( 1)x x x

2

2

62 1

1

x x

x

2

2

2 62 1

1

xx x

x

2

2

2 62 1

1

xx x

x

2

2

2 62 1

1

xx x

x

( )V x h

B x V Bh

2h x

3 2( ) 2 5 4V x x x



(A)

(B)

(C)

(D)

4.4-3 Write an expression that represents the width of a rectangle with length 5x and

area 3 212 47 60x x x .

(A) 3 27 12x x x

(B) 2 7 12x x

(C) 2 50

517 38

xx x

(D) 2 720

517 132

xx x

4.6-1 (4.3) Use the graph of ( )p x to answer questions

a) True or False: The leading term of , when written in standard form, is

positive.

22 2x x

22 4 4x x

6x

2 5 3x x

ALGEBRA II Honors 2013–2014 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1

2013–2014 Page 10 of 29 Revised November 2013

Clark County School District

28. Use the graph of ( )p x to answer questions.

a) True or False: The leading term of ( )p x , when written in standard form, is positive.

b) True or False: From the graph, ( 3) 0p - = . The multiplicity of the factor ( 3)x + is even. Explain

your answer.

29. If 4 3 2( ) 2 7 3 8 4f x x x x x= + + - - , find the possible rational roots of ( )f x .

(A) 1, 4x =

(B) 1, 4x = ±

(C) 1

, 1, 22

= ± ± ±x

(D) 1

, 1, 2, 42

= ± ± ± ±x

30. Given polynomial ( )q x , (4) 6q = . Which statement is correct?

(A) 4x = is not a root

(B) 4x = is a root

(C) ( 4)x - is a factor

(D) ( 4)x + is not a factor

( )p x



b) True or False: From the graph, . The multiplicity of the factor

is even. Explain your answer.

4.6-2 (4.3) Which graph represents ?

( 3) 0p

( 3)x

5 3( ) 6 9f x x x x






40. Which graph represents 5 3( ) 6 9f x x x x= - + ?

(A)

(B)

(C)

(D)



4.7-1 (4.6) Use the information in the table.

a) What are the three real zeros of the polynomial function ?

b) What can be said about the behavior of the graph of at ?

c) What is the least possible degree of ? Explain. Can the degree of ever be

even? Explain.

4.8-1 According to the Fundamental Theorem of Algebra, how many roots does the

following equation have?

(A) 2

(B) 4

(C) 6

(D) 11

4.9-1( 4.3, 4.6) Consider the graph of ( )p x below. Which general factorization correctly

represents ( )p x .


f

f 0x

f f

26 4 11x x




26. Consider the graph of ( )p x below. Which general factorization correctly represents ( )p x .

Which general factorization correctly represents ( )p x ?

(A) ( 3)( 2)( 4)a x x x+ - -

(B) ( 3)( 2)( 4)a x x x+ + +

(C) ( 3)( 2)( 4)a x x x- + -

(D) ( 3)( 2)( 4)a x x x- - -

27. The graph of ( )p x is shown below.


(A) 4( 3)( 2)( 4)x x x- - - -

(B) 6( 3)( 2)( 4)x x x- + +

(C) 1

( 3)( 2)( 4)4

x x x+ - -

(D) 4( 3)( 2)( 4)x x x+ + +

( )p x

Interval Value of f(x)

( , 2) Negative

( 2,1) Positive

(1,4) Negative

(4, ) Positive



(A)

(B)

(C)

(D)

4.9-2 (4.3, 4.6) The graph of is shown below.


(A)

(B)

(C)

(D)

4.9-3 (4.3) If , find the possible rational roots of .

(A)

(B)

(C)

(D)

( 3)( 2)( 4)a x x x

( 3)( 2)( 4)a x x x

( 3)( 2)( 4)a x x x

( 3)( 2)( 4)a x x x

( )p x




26. Consider the graph of ( )p x below. Which general factorization correctly represents ( )p x .


(A) ( 3)( 2)( 4)a x x x+ - -

(B) ( 3)( 2)( 4)a x x x+ + +

(C) ( 3)( 2)( 4)a x x x- + -

(D) ( 3)( 2)( 4)a x x x- - -

27. The graph of ( )p x is shown below.


(A) 4( 3)( 2)( 4)x x x- - - -

(B) 6( 3)( 2)( 4)x x x- + +

(C) 1

( 3)( 2)( 4)4

x x x+ - -

(D) 4( 3)( 2)( 4)x x x+ + +

( )p x

4( 3)( 2)( 4)x x x

6( 3)( 2)( 4)x x x

1( 3)( 2)( 4)

4x x x

4( 3)( 2)( 4)x x x

4 3 2( ) 2 7 3 8 4f x x x x x ( )f x

1, 4x

1, 4x

1, 1, 2

2 x

1, 1, 2, 4

2 x



4.9-4 (4.3) Given polynomial , . Which statement is correct?

(A) is not a root

(B) is a root

(C) is a factor

(D) is not a factor

4.9-5 (4.3)

a) Show that is a root.

b) Factor completely

c) If , what are the real roots of ?

4.9-6 (4.3) Given the polynomial :

a) Show that is a root.

b) What other root must also be a root of ? Explain.

c) Factor completely.

4.9-7 Write a cubic function that passes through the following points: (-2, 0) (3, 0) (-

1, 0) and (1, 2).

(A)

(B)

(C)

(D)

4.9-8 How many possible rational zeros exist for the polynomial function

?

(A) 9

(B) 12

( )q x (4) 6q

4x

4x

( 4)x

( 4)x

5 4 3 2( ) 3 13 19 17 16 4p x x x x x x

( 2)p

( )p x

( ) ( 3)f x p x ( )f x

4 3( ) 3 12 16p x x x x

(2 )p i

( )p x

( )p x

3 7 6y x x

3 7 6y x x

31 71

6 6y x x

31 71

6 6y x x

6 23 9 4 12y x x x



(C) 18

(D) 24

4.9-9 This polynomial function has at least one rational root.

a) What are all the possible integer values of ? Show your work or explain how you know.

b) What are all the possible real roots of the function? Show your work or explain how you know.

4.11-1 (4.3, 4.9) Consider .

a) Show that and are zeros of .

b) Completely factor where all the coefficients are rational numbers.

c) is translated 4 units right and 2 units up. What is the equation of

?

4.11-2 (4.3, 4.9) Consider .

a) Show that are roots of , then write as the appropriate

factorizations at this point.

b) Factor completely.

c) Let . List out the roots of .

d) Let be vertically stretched by 2, translated 2 units to the right and 4

units up. Write out the algebraic relationship between and .

4.11-3 (4.6) Consider the function .

a) Use the leading coefficient and degree of to describe the end behavior.

b) Write the rule for the function , and describe the transformation.

c) Describe the end behavior of . How does the end behavior of relate

to the transformation of ?

4 2( ) 9p x x kx

k

4 3 2( ) 2 11 5 5p x x x x x

5x 5x ( )p x

( )p x

( )h x ( )p x

( )h x

4 3 2( ) 2.5 7.5 15 9p x x x x x

6x ( )p x ( )p x

( )p x

( ) (4 )q x p x ( )q x

( )f x ( )p x

( )f x ( )p x

3 2( ) 3 9 3 9f x x x x

( )f x

( ) ( )g x f x

( )g x ( )g x

( )f x



4.12-1 (4.6, 4.7) The town of Frostburg experienced a bit of a heat wave during January

of this year. The graph below shows the curve of best fit that represents the low

temperature of every day in January.

A newspaper journalist is writing a story on the weather and needs to report some information. He needs a bit of guidance with interpreting the graph.

1) Write a few sentences describing the key characteristics of the graphs as it relates to the context of the problem. Be sure to include domain, range, intervals where the function increases and decreases, x and y intercepts, and any other important information



The graph below shows the curve of best fit that represents the low temperature of every day in February.

2) Three different models have been proposed that could be used to determine the temperature for a particular date in February. The models are given below:

Model 1:

Model 2:

Model 3:

Which model would best describe the low temperatures for February? Explain

why you chose that model.

The weather in July showed a related pattern to the weather in February. The curve of best fit for July is shown below:

3) Explain the relationship between the graph for February and the graph for

July. Use that relationship to create an equation for the temperatures in July.

2y ax bx c

2( 3)( 9)( 20)y a x x x

2( 3)( 9)( 20)y a x x x



5.2-1 (5.1) If f (x) = x2 -1 and g(x) = x -1 , which expression represents

f (x)

g(x)

for 1x ?

(A) x

(B) x -1

(C) x +1

(D)

1

x +1

5.3-1 Identify the x and y intercepts of the function 3( ) 8f x x .

(A) (8,0) and (0,-2)

(B) (2,0) and (0,2)

(C) (8,0) and (0,8)

(D) (-2,0) and (0,8)

5.3-2 Which is the domain of the function ( ) 5 4 3f x x ?

(A) { | 4}x x

(B) { | 3}x x

(C) { | 0}x x

(D) { | }x x

5.4-1 (5.3) Compare the graph of 36y x with the graph of its parent function

3( )f x x .

(A) Shifts 6 units down

(B) Reflects across the x-axis and shifts 6 units down

(C) Reflects across the x-axis and shifts 6 units up

(D) Reflects across the y-axis and shifts 6 units up



5.5-1 (5.1, 5.2) Which value of x makes this equation true?

9(x - 7)43 = 9

(A) 1

(B) 7

(C) 8

(D) 34

5.5-2 (5.1,5.2) Solve for x :

3 4 1 5x

(A) 31x

(B) 6x

(C) 31x

(D) No real solution

5.5-3 Solve for x .

7 1x x

(A) 5 and 10x x

(B) 5 x

(C) 10x

(D) No real solutions

5.5-4 Solve for x .

3 3x x

(A) 4x

(B) 6x

(C) 9x

(D) No real solutions



5.5-5 (5.2) If 3 12 28 4x , what is the value of 3x ?

(A) -8

(B) 3

(C) 12

(D) 27

5.6-1 Which is the inverse of 3( ) (2 1) 4f x x ?

(A) 3( ) 2 1 4a x x

(B) 3 4

( ) 12

xb x

(C) 3 4 1

( )2

xa x

(D) 3 1( ) 4

2a x x

algebra ii 2014 2015 semester exams practice materials semester...

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