VERSION A
Common Algebra 2 Assessment
Multiple Choice – KEY
Scoring Guideline: 2 point per problem
(partial credit allowed at teacher discretion)
62 total possible points for Multiple Choice
41 total possible points for Open Response
TOTAL Possible Points = 103
Formulas
Slope-Intercept Form of a Linear Equation
y  mx  b
Standard Form of a Linear Equation
Ax  By  C
Point-Slope Form of a Linear Equation
y  y1  m( x  x1 )
Exponent Rules:
a m  a n  a mn
am
 a mn
n
a
a 
m n
 a mn
Quadratic Formula:
x
b
 b  b 2  4ac
b 2  4ac

or x 
2a
2a
2a
Properties of Logarithms: For any positive numbers, M, N, and b (b  1):
log b MN  log b M  log b N
log b
M
 log b M  log b N
N
log b M x  x log b M
Interest Formulas:
I  Prt
A  Pe r t
Complex Numbers:
a  bi; i 2  1
Multiple Choice
-2-
1. Find the point-slope form of the equation of the line that passes through the points (4, 1) and (5, -1).
a.
b.
c.
d.
y  1  2( x  4 )
y  1  2( x  5)
y  1  2 ( x  4 )
y  1  2( x  4)
2. Which value is not in the domain of this function?
a. -3
b. -4
c. 1
d. 4
3. State the domain and range for the graph:
a.
b.
c.
d.
RSDomain: x  0
TRange: All real numbers
RSDomain: All real numbers
TRange: y  0
RSDomain: x  2
TRange: y  0
RSDomain: All real numbers
TRange: y  2
4. Solve the system:
a. (-5, -4)
b. (-1, -8)
c. (-4, -5)
d. (-1, -10)
RS y   x  9
T3x  y  11
f ( x) 
( x  3)( x  1)
( x  4)
Multiple Choice
5. Solve the system:
-3-
RS3x  y  7
T5x  3y  9
a. (3, 2)
b. (-3, 2)
c. (3, -2)
d. (-3, -2)
6. What region is the set of solutions for the given system of inequalities and graph?
y  x2 1

y  x  5
a. A
b. B
c. C
d. D
7. Given the following system of constraints and graph, find the value of x and y that maximizes the
objective function.
R|0  x  10
|S2  y  8
|| 1
|T y  2 x  6
Maximize for:
P  5x  2 y
a. (4, 8)
b. (6, 6)
c. (10, 8)
d. (10, 2)
Multiple Choice
-4-
d
8. Simplify: 3 2  16
i
a. 5 + 9i
b. 6 + 4i
c. 6 + 12i
d. 6 – 4i
27  75  12 .
9. Simplify:
a. 6 3
b.
90
c. 22 3
d. 9.4
10. Simplify:
3
8x 6 y8
a. 2 x 3 y 5
b. 2 x 18 y 24
c. 2 x 2 y 2
3
y2
d. 2 xy 3 2 x 3 y 5
11. Simplify:
a. 3
b. -3
c. 3i
d. -3i
3
27
Multiple Choice
12. Factor: x 2  6 x  55
a. ( x  5)( x  11)
b. ( x  5)( x  11)
c. ( x  11)( x  5)
d. ( x  11)( x  5)
13. Factor: 4 x 2  25
a. ( 2 x  5)( 2 x  5)
b. ( 2 x  5)( 2 x  5)
c. ( 2 x  5)(2 x  5)
d. ( 2 x  5) 2
14. Factor: 3x 2  26 x  35
a. ( x  5)(3x  7)
b. (3x  7)( x  5)
c. (3x  5)( x  7)
d. (3x  5)( x  7)
15. Factor: 4 x 3  16 x 2  84 x
a. 4 x ( x  7)( x  3)
b. 4 x ( x  3)( x  7)
c. (4 x  3)( x  7)
d. (4 x  7)( x  3)
16. Solve for x: 5x 2  25
a. x  5
b. x  25
c. x  5
d. x   5
-5-
Multiple Choice
-6-
17. Solve for x: x 2  6 x  42
a. x  6  51
b. x  3  42
c.
x  3  51
d. x   4 3
18. Find all the zeros of the polynomial: y  x 2 ( x  7)( 3x  1)
a.
1
, 1, 7
3
b.  1, 0, 7
c.
1
, 0, 7
3
d.
1
,7
3
19. Write a polynomial function with zeros at x = -2, 4, 6.
a. y  ( x  4)( x  2)( x  6)
b. y  ( x  4)( x  2)( x  6)
c. y  ( x  4 )( x  2)( x  6)
d. y  60( x  4)( x  2)( x  6)
20. Solve for x:
a.
x  7  x  1 . Check for extraneous solutions.
x  3, 2
b. x  3, 2
c.
x2
d. x  3
21. Between which two numbers is log 5 150 ?
a. 0 and 1
b. 1 and 2
c. 2 and 3
d. 3 and 4
Multiple Choice
-7-
22. Which of the following is equivalent to log 4  2 log x  log 25?
a. log(4  x )  25
FG 4 x IJ
H 25 K
2
b. log
c. log(100 x 2 )
 8x 
d. log 
 25 
23. Expand the logarithm log 3 x 4 y 7 .
a. 4 log 3 x  7 log 3 y
b. 11log 3 xy
c. 4 log 3 x  7 log3 y
d. 28 log 3 ( x  y )
24. Solve for x: log 2  log( x  5)  2 . Check for extraneous solutions.
a. x  15
b. x  55
c.
x6
d. x  55
25. Solve for t: 105t  2
a. t 
2
5
b. t  log 4 64
c. t  5 log 2
d. t 
log 2
5
26. Which equation models the graph?
a.
y   ( x  2) 2  1
b. y   ( x  1) 2  2
c.
y   x2  1
d. y  x 2  4 x  3
Multiple Choice
-8-
27. Which equation models the graph?
1
x  2 1
2
a.
f ( x) 
b.
f ( x)  2 x  2  1
c.
f ( x)  2 x  2  1
d.
f ( x) 
1
x  2 1
2
28. Which equation models the graph?
a.
f ( x )  x ( x  1)( x  3)
b.
f ( x )   x ( x  1)( x  3)
c.
f ( x )   x ( x  1)( x  3)
d.
f ( x )  x ( x  1)( x  3)
29. Which translations shift y  x to y  ( x  3)  7 ?
a. 7 units left, 3 units up
b. 3 units left, 7 units down
c. 3 units right, 7 units up
d. 7 units right, 3 units down
30. Suppose a number from 1 to 25 is selected at random. What is the probability that a multiple of 4 or
5 is chosen?
a.
2
25
b.
2
5
c.
11
25
d.
12
25
31. The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 10.
What percent of the scores are greater than 87?
a. 84%
b. 68%
c. 16%
d. 2.5%
VERSION A
Common Algebra 2 Assessment
Open Response – KEY
41 total possible points for Open Response
Formulas
Slope-Intercept Form of a Linear Equation
y  mx  b
Standard Form of a Linear Equation
Ax  By  C
Point-Slope Form of a Linear Equation
y  y1  m( x  x1 )
Exponent Rules:
a m  a n  a mn
am
 a mn
n
a
a 
m n
 a mn
Quadratic Formula:
x
b
 b  b 2  4ac
b 2  4ac

or x 
2a
2a
2a
Properties of Logarithms: For any positive numbers, M, N, and b (b  1):
log b MN  log b M  log b N
log b
M
 log b M  log b N
N
log b M x  x log b M
Interest Formulas:
I  Prt
A  Pe r t
Complex Numbers:
a  bi; i 2  1
Open Response
SHOW ALL WORK!
-2-
1. Rational Expressions = 9 points possible
a. Consider the rational expression:
x  5,  1
(2 points for correct restrictions)
2
4
. State any restrictions on the variable, x.

x  5 x 1
b. Add and simplify the rational expression:
2
4

x  5 x 1
6 x  22
( x  5)( x  1)
(2 points: 1 for work and 1 for correct answer)
c. Consider the rational expression:
x  3,  1, 0
(3 points for correct restrictions)
x 2 x 2  3x  2

. State any restrictions on the variable, x.
x  1 x 2  3x
d. Multiply and simplify the following rational expression:
x 2 x 2  3x  2

x  1 x 2  3x
x( x  2) x 2  2 x

x3
x3
(2 points: 1 for work and 1 for correct answer)
2. Complex Numbers = 6 points possible
Find the sum, difference, and product of the complex numbers (1  4i ) and 2  3i .
a. Sum: (1  4i )  (2  3 i )
(1  i )
(1 point for correctly combining like terms)
b
g
b. Difference: (1  4i )  ( 2  3 i )
3  7i
(2 points: 1 for distributing the negative and 1 for correctly combining like terms)
c. Product: (1  4i )( 2  3 i )
10  11i
(3 points: 1 for distributing correctly, 1 for correct i 2  1 and 1 for correctly combining like
terms)
3. Functions = 8 points possible
Use the functions f ( x )  x 2 and g ( x )  3x  2 .
a. Evaluate the expression f ( x )  g ( x ) and write your answer as a polynomial in standard form.
x 2  3x  2
(1 point for correctly subtracting the entire function g)
b. Evaluate the expression f ( x )  g ( x ) and write your answer as a polynomial in standard form.
3x 3  2 x 2
(1 point for correctly multiplying)
c. Evaluate the expression ( f  g )( x ) and write your answer as a polynomial in standard form.
9 x 2  12 x  4
(2 points: 1 for correct set up and 1 for simplifying correctly into standard form)
d. Find the value of ( f  g )(4) .
100
(2 points: 1 for correct set up and 1 point for finding correct value)
e. Find the value of f ( 3)  g ( 2) .
5
(2 points: 1 for correct set up and 1 for correct answer)
4. Quadratic Functions & Baseball = 8 points possible
A batter hits a baseball whose path can be modeled by the equation h(t )  16t 2  20t  4 where h(t)
represents the height of the ball in feet and t represents the time in seconds after the ball was hit.
Draw a sketch to model the situation. Label your axes.
(sketch not scored)
a. Find the height of the ball after it has traveled 1 second. Show your work.
8 ft.
(2 points: 1 for correct set up and 1 for correct answer)
b. What is the maximum height of the ball? Show your work algebraically and round your
answer to the nearest hundredth.
10.25 ft.
(2 points: 1 for showing algebraic strategy and 1 for correct maximum height)
c. What does the positive x-intercept represent in the context of this problem?
The time when the ball hits the ground (height = 0).
(1 point: correct description)
d. What does the y-intercept represent in the context of this problem?
The height where the player hit the ball (time = 0).
(1 point: correct description)
e. If the ball is not caught, how much time will it take for the ball to hit the ground? Show your
work algebraically and round your answer to the nearest hundredth.
1.43 seconds
(2 points: 1 for set up h(t)=0 and 1 for correct time)
5. Exponential Functions & Banking = 4 points possible
Mike earned money by working during the summer and wants to continue saving for his first year of
college. He decides to invest his money in a continuously compounded account.
a. Find the amount he would have in the account after 2 years with an interest rate of 3%, if he
invested $2,000. Round your answer appropriately.
$2123.67
(2 points: 1 for correct set up and 1 for correct amount)
b. Mike wants his account to grow to $2,300. Use algebraic processes including logarithms to
find the number of years, rounded to the nearest hundredth, to accomplish this.
4.66 years
(2 points: 1 for algebraic process and 1 for correct number of years)
6. Function Transformations = 6 points possible
2
Consider the vertex form of a quadratic function: f ( x )  a  x  h   k .
a. How do the values of a, h, and k affect the graph of f ( x)  2( x  4) 2  3 as compared to the
parent function f ( x)  x 2 ? Be as specific as possible.
a: The graph is reflected over the x-axis and is stretched by a factor of 2.
(2 points: 1 for the reflection and 1 for the stretch)
h: The graph is translated 4 units to the right.
(1 point for the correct horizontal translation)
k: The graph is translated 3 units up.
(1 points for the correct vertical translation)
b. Write an equation so that the graph of f ( x)  x 2 has been translated 5 units up, 7 units to the
left, and with a vertical stretch of 3.
f ( x)  3( x  7) 2  5
(2 points for correct equation – key components: 3, +7, +5, quadratic)