ALGEBRA II WARMUP CST QUESTIONS
STANDARD 1: Students solve equations and inequalities involving absolute value
1. What is the complete solution to the equation: 3  6 x  1 ?
A) x 
1
1
; x
2
3
B) x  
1
1
; x
2
3
C) x 
1
1
; x
2
3
D) x  
1
1
; x
2
3
C) x 
7
; x  7
3
D) x  
7
; x  7
3
2. Which of the following are solutions to 3x  7  14 ?
A) x 
7
; x7
3
B) x  
7
; x7
3
3. Which of the following is equivalent to 2 x  9  3 ?
A) 3  x  6
B) 3  x  6
C) 3  x  6
D) 3  x  6
4. Which of the following is equivalent to 3x  5  19 ?
A) x  
14
or x  8
3
B) x  8 or x 
14
3
C) x  8 or x 
14
3
D) x  
14
or x  8
3
STANDARD 2: Students solve systems of linear equations and inequalities (in two or three variables) by
substitution, with graphs, or with matrices
1. For a wedding, Julie bought several dozen roses and several dozen carnations. The roses cost $15 per dozen,
and the carnations cost $8 per dozen. Julie bought a total of 17 dozen flowers and paid a total of $192. How
many roses did she buy?
A) 6 dozen
B) 7 dozen
C) 8 dozen
D) 9 dozen
2. A cashier at a restaurant made the chart below for popular lunch combinations. What is the individual price
of soup?
Soup + Salad = $4.25
A) $1.50
B) $1.75
Soup + Sandwich = $4.75
C) $2.25
Salad + Sandwich = $5.50
D) $2.50
3. What is the solution to the system of equations shown below?
2 x  y  3z  8

x  6 y  z  0
 6 x  3 y  9 z  24

10
A) (0,4,4)
B) (1,4, )
C) no solution
D) infinitely many solutions
3
ALGEBRA II WARMUP CST QUESTIONS
STANDARD 3: Students are adept at operations on polynomials, including long division.
1. 2 x  7 2 x 4  21x3  35x 2  37 x  46
4
2x  7
4
C) x 3  7 x 2  7 x  6 
2x  7
A) x3  7 x 2  7 x  6 
B) 2 x 3  14 x 2  14 x  12 
D) x 3  7 x 2  7 x  6 
4
2x  7
4
2x  7
2. What is the quotient of (4 x3  11x 2  9 x  5)  ( x  4) ?
C) 4 x 2  5 x  11 
39
4 x  11x 2  9 x  5
3
39
x4
401
D) 4 x 2  27 x  99 
x4
B) 4 x 2  5 x  11 
A) 4 x3  5 x 2  11x  39
3. Which polynomial represents (3x 2  x  4)( 2 x  5) ?
A) 6 x 3  13x 2  13x  20
B) 6 x 3  13x 2  13x  20
C) 6 x 3  13x 2  3x  20
D) 6 x 3  13x 2  3x  20
4. Which polynomial represents ( x 2  x  3)( x 2  4 x  2) ?
A) x 4  3x 3  5 x 2  14 x  6
B) x 4  3x 3  5 x 2  14 x  6
C) x 4  3x 3  5 x 2  14 x  6
D) x 4  3x 3  5 x 2  14 x  6
5. Which polynomial has the factorization (2 x  1)( 4 x 2  2 x  1) ?
A) 8 x 3  1
B) 2 x 3  1
C) 4 x 3  1
D) 8 x 3  1
6. (2 x 2  6 x  1)  2(4 x 2  3x  1)
A) 6 x 2  1
B)  10 x 2  1
D)  10 x 2  12 x  1
C) 6 x 2  12 x  1
7. What is the sum of 2 x 4  5 x 3  8 x 2  x  10 and 8 x 4  4 x 3  x 2  x  2 ?
A) 10 x 4  x 3  9 x 2  12
B) 10 x 4  x 3  9 x 2  2 x  12
C) 10 x 4  x 3  7 x 2  2 x  12
8. (3x3  x  11)  (4 x3  x 2  x)
A)  7 x 3  x 2  2 x  11
C) 7 x 3  x 2  2 x  11
D) 10 x 4  9 x 3  7 x 2  2 x  12
B) x3  x 2  2 x  11
D)  x 3  2 x
STANDARD 4: Students factor polynomials representing the difference of squares, perfect square
trinomials, and the sum and difference of two cubes.
1. 8a 3  c 3
A) (2a  c)( 2a  c)( 2a  c)
C) (2a  c)( 4a 2  4ac  c 2 )
B) (2a  c)( 4a 2  2ac  c 2 )
D) (2a  c)(4a 2  2ac  c 2 )
ALGEBRA II WARMUP CST QUESTIONS
2. Which of the following is the factorization of x 3  8 ?
A) ( x  2)( x 2  4 x  4)
B) ( x  2)( x 2  2 x  4)
C) ( x  2)( x 2  4 x  4)
D) ( x  2)( x 2  2 x  4)
3. The total area pf a rectangle is 4 x 4  9 y 2 . Which factors would represent the length times width?
A) (2 x 2  3 y)( 2 x 2  3 y)
B) (2 x 2  3 y)( 2 x 2  3 y)
C) (2 x  3 y )( 2 x  3 y )
D) (2 x  3 y )( 2 x  3 y )
4. Factor: 16 x 4  1
A) (2 x  1)( 2 x  1)( 4 x 2  1)
C) (2 x  1)( 2 x  1)( 2 x  1)( 2 x  1)
B) (2 x  1)( 2 x  1)( 2 x  1)( 2 x  1)
D) (2 x  1)( 2 x  1)( 4 x 2  1)
5. Factor: 32 x 6  2 x 2
A) 2 x 2 (2 x  1)( 2 x  1)( 2 x  1)( 2 x  1)
C) 2 x 2 (2 x  1)(2 x  1)( 4 x 2  1)
B) 2 x 2 (2 x  1)( 2 x  1)( 2 x  1)( 2 x  1)
D) 2 x 2 (2 x  1)( 2 x  1)( 4 x 2  1)
STANDARD 5: Students demonstrate knowledge of how real and complex numbers are related both
arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
1. If i  1 , what is the value of i 26 ?
A) 1
B) i
C) -1
D)  i
3. If i  1 , which point shows the location of
5  2i on the plane?
i
A) Point A
A
B) Point B
B
C) Point C
C
D) Point D

D
4. Find the absolute value of 5 – 2i
A) 3
B) 29
C)
21
D) 7
STANDARD 6: Students add, subtract, multiply, and divide complex numbers
1. Simplify: 16  2i    3  4i 2 
A) 9  2i
B) 13  2i
C) 15  2i
D) 17  2i
ALGEBRA II WARMUP CST QUESTIONS
2. Simplify:  3  6i   2  i  7   4
A) 1  4i
3. Multiply:
 4  3i 
A)
6. Divide:
D) 3  4i
B) 4  48i
C) 4  36i
D) 32  36i
B) 7  24i
C) 25  24i
D) 7 12i
B) 5  3i
C) 5  3i
D) 3  5i
B)  i
C) i
D)
2
A) 7
5. Divide:
C) 11  2i
3  7i  6  2i 
A) 18  22i
4. Multiply:
B) 11  6i
6  10i
2i
3
5
i
4  i
1  4i
A) 
8
i
17
8
i
17
STANDARD 7: Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with
monomial and polynomial denominators and simplify complicated rational expressions, including those
with negative exponents in the denominator.
1.
x3
6
 2

x  5 x  3 x  10
x2  x
x 2  3x  10
x 2  x  12
C) 2
x  3x  10
A)
2.
7x  9
x  3 x  10
x2  x  1
D) 2
x  3x  10
B)
2
2x 1
3
 2

x  8 x  16 x  16
2
A)
2( x 2  5 x  8)
( x  4)( x  4) 2
B)
2( x 2  5 x  8)
( x  4)3
C)
2( x 2  5 x  8)
( x  4)( x  4) 2
D)
2( x 2  5 x  8)
( x  4)3
ALGEBRA II WARMUP CST QUESTIONS
x  x 3
3x


x  12 x  32 x  8
2
3.
2
(4 x  1)( x  3)
( x  8)( x  4)
(4 x  1)( x  3)
C)
( x  8)( x  4)
(4 x  1)( x  3)
( x  8)( x  4)
(4 x  1)( x  3)
D)
( x  8)( x  4)
A)
B)
8x  3
7
 2
?
x  2 x  35 x  25
4. What is the difference
2
2(4 x 2  15 x  17)
A)
( x 2  2 x  35)( x  5)
2(4 x 2  15 x  32)
B)
( x 2  2 x  35)( x  5)
2(4 x 2  15 x  17
C)
( x 2  2 x  35)( x  5)
2(4 x 2  15 x  32)
D)
( x 2  2 x  35)( x  5)
5. Which is the simplified form of
A)
3a 5
b 3c 5
B)
3ab
c5
3a 2b3c 2
?
(a 1b 2c)3
C)
3
bc
2 5
D)
3
ab 3c 5
C)
1
16 x 4 y10
6. Which is the simplified form of (4 x 2 y 5 ) 2 ?
A) 16 x 4 y 7
B) 16 x 4 y10
5 x3 y 9
7. Simplify
:
20 x 2 y  2
1
A) 4xy11
B) xy11
4
C)
1
4 xy11
D) xy 11
20 x 4 8 x 3

8. What is
?
27 y 2 15 y  5
32 y 3
A)
81x
32
B)
81xy7
25 y 3
C)
18 x
B)
x  11
x2
25
18 xy7
x 2  9 x  22
?
x 2  121
x2
C)
D) x  2
x  11
9. What is the quotient ( x  2) 
A) x  11
D)
D)
1
16 x 4 y 7
10.
4x  8
3x  6

x  3x  2 x  1
2
A) 12( x  2) B)
11.
ALGEBRA II WARMUP CST QUESTIONS
4
3( x  2)
C)
3
4( x  2)
x2 y 2
3
C) 3x 2 y 2
D) x  2
12 xy 7 x 5 y 2

7 x4
4y
3
2 2
x y
A)
B)
D) x 2 y 2
STANDARD 8: Students solve and graph quadratic equations by factoring, completing the square, or
using the quadratic formula. Students apply these techniques in solving word problems. They also solve
quadratic equations in the complex number system.
1. What are the solutions of x 2  12 x  61  0
A) 1, 11
B) 6  5i
C) 6  97
D) 6  i 61
2. Solve for x by using the quadratic formula: 3x 2  x  14
2
7
x  14
A) 7,
B) , 2
C)
3
3
3x
1 i 167
D)  
6
6
3. Solve for x by completing the square: x 2  2 x  10  0
A) 7, -1
B) 1  3i
C) 1  3i, 1  3i
D) 4, -2
STANDARD 9: Students demonstrate and explain the effect that changing a coefficient has on the graph
of a quadratic function; that is students can determine how the graph of a parabola changes as a, b, and c
2
vary in the equation y  a  x  b   c
1. Which of the following most accurately describes the translation of the graph y   x  3  2 to the graph of
2
y   x  2  2 ?
2
A) up 4 and to the right 5
C) down 2 and 3 to the left
B) down 2 and 2 to the right
D) up 4 and to the left 2
2. Which of the following sentences is true about the graphs of y  3  x  5   1 and y  3  x  5   1 ?
A) Their vertices are maximums
B) The graphs have the same shape with different vertices
C) The graphs have different shapes with different vertices
D) One graph has a vertex that is a maximum, while the other graph has a vertex that is a minimum.
2
2
ALGEBRA II WARMUP CST QUESTIONS
STANDARD 10: Students graph quadratic functions and determine the maxima, minima, and zeros of
the function.
1. What are the zeros of y  x 2  13x  40 ?
A) -5, -8
B) 5, -8
C) 4, 10
D) 5, 8
2. Find the minimum point on the graph of f  x   x2  4 x  14
A) (2,18)
B) (-2,18)
C) (-2,26)
D) (2,10)
3. Find the maximum point on the graph of f  x   3x2  12 x  1
A) (6,-5)
B) (-2,-19)
C) (2,13)
D) (1,14)
4. Which is the graph of y  2  x  1  1 ?
A
2
B
C
STANDARD 11: (11.1) Students understand the inverse relationship between exponents and logarithms,
and use this relationship to solve problems involving logarithms and exponents.
1
log 3 x  2
2
1. What is the solution of the equation:
A) 4
B) 81
1
64
C) 64
D)
C) b 2  37
D) None of these
2. Write the exponential form: logb 37  2
A) 37 2  b
B) 2b  37
3. If log10 x  2 , what is the value of x?
A) x  
1
10
1
10
B) x 
4. Which equation is equivalent to log 3
3
1
 x3
A)
9
3
C) x 
1
100
D) x  100
1
 x?
9
1
B)    x
9
1
C) 3 
9
x
1
9
D) 3  x
ALGEBRA II WARMUP CST QUESTIONS
(11.2) Students judge the validity of an argument according to whether the properties of real numbers,
exponents, and logarithms have been applied correctly at each step.
1. Jeremy, Michael, Shanan, and Brenda each worked the same math problem at the whiteboard. Each
student’s work is shown below. Their teacher said that while two of them had the correct answer, only one of
them had arrived at the correct conclusion using correct steps.
Jeremy’s Work
x3
x3 x 7  7
x
Shanan’s Work
x3
x3 x 7  7
x

 x10 , x  0
Michael’s Work
x3
3 7
x x  7
x
Brenda’s Work
x3
3 7
xx  7
x
 x 4 , x  0
Which is a completely correct solution?
A) Jeremy’s work
 x4 , x  0
B) Shanan’s work
C) Michael’s work
2. Which is the first incorrect step in simplifying log 4
Step 1: log 4
Step 2:
Step 3:
A) Step 1
1
, x0
x4
D) Brenda’s work
4
?
64
4
 log 4 4  log 4 64
64
 1 16
= -15
B) Step 2
C) Step 3
D) Each step is correct
STANDARD 12: Students know the laws of fractional exponents, understand exponential functions, and
use these functions in problems involving exponential growth and decay.
t
 1  300
1. A certain radioactive element decays over time according to the equation y  A   , where A = the
2
number of grams present initially and t = time in years. If 1000 grams were present initially, how many grams
will remain after 900 years?
A) 500 grams
B) 250 grams
C) 125 grams
D) 62.5 grams
ALGEBRA II WARMUP CST QUESTIONS
2. Bacteria in a culture are growing exponentially with time as shown in the table below.
Day Bacteria
0
100
1
200
2
400
Which of the following equations expresses the number of bacteria, y, present at any time, t?
A) y  100  2t
B) y  100  2t
C) y  2t
D) y   200  2t
3. If the equation y  2 x is graphed, which of the following values of x would produce a point closest to the x
axis?
1
3
5
8
A)
B)
C)
D)
4
4
3
3
STANDARD 13: Students use the definition of logarithms to translate between logarithms in any base.
1. Which of the following is equivalent to log 2 7 ?
A) 7 2
B) 2 7
C) 7 log 2
D)
log 7
log 2
2. Use the change of base formula to identify the expression that is equivalent to log3 10
A)
ln 3
ln10
B) 10 log 3
C) ln
10
3
D)
1
log 3
STANDARD 14: Students understand and use the properties of logarithms to simplify logarithmic
numeric expressions and to identify their approximate values.
1. Evaluate log a 16 given that log a 2  0.4307
A) 0.0344
B) 1.7228
C) 4.4307
D) 1.8168
2. Evaluate log a 18 given that log a 2  0.2789 and log a 3  0.4421
A) 1.1631
B) 0.2466
C) 0.0349
D) 1.4420
3. Evaluate log a 24 given that log a 2  0.4307 and log a 3  0.6826
A) 0.8820
B) 1.9747
C) 0.2940
D) 1.1133
4. What is the value of log 2
A) 4
1
?
16
B) - 4
C) 8
D)
1
2
ALGEBRA II WARMUP CST QUESTIONS
5. Evaluate: log16 4
A) 64
B) 4
C)
1
2
D)
1
4
STANDARD 15: Students determine whether a specific algebraic statement involving rational
expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true,
or never true.
x 2  16
1. On a recent test, Jeremy wrote the equation
 x  4 . Which of the following statements is correct
x4
about the equation he wrote?
A) The equation is always true
C) The equation is never true
B) The equation is always true, except when x = 4
D) The equation is sometimes true when x = 4
3x  9
 x  3 true?
3
B) some values of x
D) impossible to determine
2. If x is a real number, for what values of x is the equation
A) all values of x
C) no values of x
3. Given the equation y  x n where x > 0 and n < 0 which statement is valid for real values of y?
A) y > 0
B) y = 0
C) y < 0
D) y  0
STANDARD 18: Students use fundamental counting principles to compute combinations and
permutations.
1. Natalie wants to create several different 8-character screen names. She wants to use arrangements of the
first three letters of her first name (nat), followed by arrangements of the 5 digits in her zip code (92562). How
many different screen names can she create in this way?
A) 15
B) 360
C) 720
D) 126
2. Andrew needs to create a 7-character password. He wants to use the arrangements of the first 3 letters of his
first name (and) followed by arrangements of the letters in his middle name (john). How many different
password can he create in this way?
A) 30
B) 36
C) 72
D) 144
3. Allison went to a buffet restaurant for lunch. She had to choose from four main courses, three side dishes,
three drinks, and two desserts. How many different combinations could she have created?
A) 1728
B) 12
C) 144
D) 38
STANDARD 19: Students use combinations and permutations to compute probabilities
1. Jack and Jill are among 12 students who have applied for a trip to Washington D.C. Two students from the
group will be selected at random for the trip. What is the probability that Jack and Jill will be the two students?
1
2
2
1
A)
B)
C)
D)
66
66
12
6
ALGEBRA II WARMUP CST QUESTIONS
2. Alex’s math teacher told the class that if he rolled three dice and they all turned up one, he would let them
skip their homework for a month. What is the probability of this actually happening?
1
2
A)
B)
1
18
C)
1
6
D)
1
216
3. Suppose you have the following five books in your backpack: Chemistry, Biology, Calculus, Physics, and
Psychology. Without looking, you pick a book. You replace the book and repeat this process. What is the
probability that the first time you pick Physics or Chemistry, and the second time you picked Physics?
3
10
A)
B)
3
25
C)
2
25
D)
3
5
STANDARD 20: Students know the binomial theorem and use it to expand binomial expressions that are
raised to positive integer powers
3
1.  3 y  4  
2.
3.
A) 27 y 3  54 y 2  81y  64
B) 27 y3  108 y 2  144 y  64
C) 27 y 4  108 y3  144 y 2  64 y
D) 27 y3  144 y 2  108 y  64
 4 y  1
4

A) 256 y 4  256 y 3  96 y 2  16 y  1
B) 256 y 4  256 y 3  96 y 2  16 y  1
C) 256 y 4  64 y 3  96 y 2  16 y  1
D) 256 y 4  96 y3  16 y 2  96 y  256
 3 y  1
5

A) 243 y5  486 y 4  270 y3  90 y 2  45 y  1
B) 243 y5  405 y 4  270 y3  90 y 2  45 y  1
C) 243 y5  405 y 4  270 y 3  90 y 2  15 y  1
D) 243 y 5  405 y 4  270 y 3  90 y 2  15 y  1
STANDARD 22: Students find the general term and the sums of arithmetic series and of both finite and
infinite geometric series.
1 1 1 1
1. What is the sum of the infinite geometric series     ...
2 4 8 16
A) 1
B) 1.5
C) 2
D) 2.5
2. Find the ninth term of the arithmetic sequence with a1  4 and d  10 . Assume that the series begins with
1.
A) 94
B) 84
C) 46
D) 49
9 27 81
3. Find the common ratio of the geometric series: 4,3,  , ,  ,...
4 16 16
3
3
4
4
A) 
B)
C)
D) 
4
4
3
3
ALGEBRA II WARMUP CST QUESTIONS
STANDARD 24: Students solve problems involving functional concepts, such as composition, defining
the inverse function and performing arithmetic operations on functions.
1. Which expression represents f  g  x   if f  x   x2 1 and g  x   x  3 ?
A) x 3  3 x 2  x  3
B) x 2  6 x  8
C) x 2  x  2
D) x 2  8
C) x 2  25
D) x 2  5 x 2
C) 10
D) 32
2. Given f  x   x2 and g  x   x  5 , find g  f  x   .
A)
 x  5
2
B) x 2  5
3. If f  x   x  4 and g  x   3x , find f  g  2   .
A) 36
B) 16
STANDARD 25: Students use properties from number systems to justify steps in combining and
simplifying functions.
2
1. If f  x   x2  2 x  1 and g  x   3  x  1 , which is an equivalent form of f  x   g  x  ?
A) x 2  4 x  2
10 x 2  20 x  10
B) 4 x 2  2 x  4
C) 4 x 2  8 x  4
D)
C) 2 x 2  7
D) 2 x 2  5
C)   x  3
D) 0
2. Given f  x   6 and g  x   2 x2  1 , find f  x   g  x  ?
A) 2 x 2  5
B) 2 x 2  7
3. Given f  x   2 x  4 and g  x   1  3x , find f  x   g  x  ?
A) 5x  3
B) x  3
STANDARD P.S. 2: Students know the definition of conditional probability and use it to solve for
probabilities in the finite sample spaces.
1. A box contains 4 large red marbles, 8 large yellow marbles, 2 small red marbles, and 6 small yellow marbles.
If a marble is drawn at random, what is the probability that it is red given that it is one of the small marbles?
A)
3
10
B)
1
4
C)
1
10
D)
3
7
2. A jar contains 2 red, 3 blue, and 4 green marbles. Niki draws one marble from the jar and then Tom draws a
marble. What is the probability that Niki will draw a green marble and Tom will draw a blue marble?
A)
4
27
B)
7
9
C)
1
6
D)
7
81
3. What is the probability that a family will have four children, all of them girls?
A)
1
4
B)
1
8
C)
1
16
D)
1
32