KEY
Common Algebra 2 Assessment
Multiple Choice
Formulas
Exponent Rules:
a m ⋅ a n = a m+n
am
= a m−n
an
(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
VERSION A
Multiple Choice
-2-
1. Find the point-slope form of the equation of the line that passes through the points (-7, 1) and (-4, 6).
5
y − 1 = − ( x + 7)
3
5
b. y − 1 = ( x − 6)
3
5
c. y − 1 = ( x + 7)
3
3
d. y + 4 = − ( x + 7)
5
a.
2. What value is not a member of the domain of this function?
a. -3
b. -5
c. 1
d. 5
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 + 5)
Multiple Choice
5. Solve the system:
-3-
RS3x − 4 y = −7
T2 x − y = −8
a. (5, 2)
b. (5, -2)
c. (-5, 2)
d. (-5, -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 P = 5x − 2 y .
R|0 ≤ x ≤ 10
|S2 ≤ y ≤ 8
|| 1
|T y ≤ 2 x + 6
a. (4, 8)
b. (6, 6)
c. (10, 8)
d. (10, 2)
Multiple Choice
-4−27
3
8. Simplify:
a. 3
b. 3i
c. -3
d. -3i
d
9. Simplify: 3 2 + −25
i
a. 6 + 15i
b. 6 + 6i
c. 5 + 5i
d. 6 + 5i
27 + 75 − 12 .
10. Simplify:
a. 6 3
b.
90
c. 22 3
d. 9.4
11. 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
12. Divide 3x 3 − 3x 2 − x − 10 by x − 2
a. 3x 2 + 3x + 5
b. x 2 − x − 3
c. 3x 2 − 9 x − 7
d. 3x 2 − 3x − 5
Multiple Choice
13. Factor: x 2 − 13x − 48
a. ( x + 16)( x − 3)
b. ( x − 4)( x − 12)
c. ( x − 16)( x + 3)
d. ( x − 16)( x − 3)
14. Factor: 9 x 2 − 16
a. (3x + 4)( −3x − 4)
b. (3x + 4)(3x − 4)
c. ( −3x + 4)(3x − 4)
d. (3x − 4) 2
15. 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)
16. 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)
17. Solve for x: 3x 2 = 21
a.
x=7
b. x = 21
c.
x = ±7
d. x = ± 7
-5-
Multiple Choice
-6-
18. Solve for x: x 2 + 6 x = 42
a.
x = −6 ± 51
b. x = −3 ± 42
c.
x = −3 ± 51
d. x = ± 4 3
19. Find all the zeros of the polynomial: y = x 2 ( x − 5)(2 x + 1)
a.
1
, 1, 5
2
b. 0, 1, 5
c.
−1
, 0, 5
2
d. 1, 2, 5
20. Write a polynomial function with zeros at x = -3, 4, 5.
a.
y = ( x − 4)( x + 3)( x − 5)
b. y = ( x + 4)( x − 3)( x + 5)
c.
y = ( x + 4)( x + 3)( x + 5)
d. y = −60( x − 4)( x − 3)( x − 5)
21. 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
22. Between which two numbers is log5 150 ?
a. 0 and 1
b. 1 and 2
c. 2 and 3
d. 3 and 4
Multiple Choice
-7-
23. Which of the following is equivalent to log 3 + 2 log x − log 20 ?
a. log(3 + x ) − 20
FG 3x IJ
H 20 K
2
b. log
c. log(60 x 2 )
d. log(6 x − 20)
24. Expand the logarithm log 4 x 3 y 5 .
a. 3 log 4 x + 5 log 4 y
b. 8 log 4 xy
c. 3 log 4 x ⋅ 5 log 4 y
d. 15 log 4 ( x + y )
25. 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
26. Solve for t: 105t = 2
a. t =
2
5
b. t = log 4 64
c. t = 5 log 2
d. t =
log 2
5
27. 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-
28. 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
29. 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)
30. 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
KEY
Note:
Departments can
choose to use their own
common scoring process.
Data collection will be done
with student work. All
teachers should use their
professional judgment
when scoring the problems
and accepting answers that
may differ from those given
here.
Common Algebra 2 Assessment
Open Response
Formulas
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 2 − 4ac
−b
− b ± 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 = Pr t
A = Pe r t
VERSION A
Open Response
SHOW ALL WORK!
-2-
1. Rational Expressions
a. Add and simplify the following rational expression:
2
4
+
x + 5 x +1
6 x + 22
( x + 5)( x + 1)
b. Multiply and simplify the rational expression:
x 2 x 2 + 3x + 2
⋅
x + 1 x 2 + 3x
x 2 + 2x
x+3
c. State any restrictions on the variable, x, for the rational expression in Part b.
x ≠ −3, − 1, 0
2. Complex Numbers
Find the sum, difference, and product of the complex numbers (2 − 5i ) and −3 + 4i .
a. Sum: (2 − 5i ) + (−3 + 4i )
b
−1 − i
b. Difference: (2 − 5i ) − (−3 + 4i )
5 − 9i
c. Product: (2 − 5i )(−3 + 4i )
14 + 23i
g
Open Response
SHOW ALL WORK!
3. Functions
Use the functions f ( x ) = x 2 and g ( x ) = 2 x + 3 .
a. Find and simplify f (3) + g ( −2)
8
b. Find and simplify f ( x ) − g ( x )
x 2 − 2x − 3
c. Find and simplify f ( x ) ⋅ g ( x )
2 x 3 + 3x 2
d. Find and simplify ( f o g )( x )
(2 x + 3) 2 = 4 x 2 + 12 x + 9
4. Quadratic Functions & Baseball
The height, y (in feet), above the ground of a baseball thrown from the outfield after a time, x (in
seconds), is given by the equation y = −16 x 2 + 30 x + 6 .
a. Find the height of the ball after it has traveled 0.5 seconds.
17 feet
b. What is the maximum height of the ball?
20.0625 feet
c. What do the x-intercepts represent in the context of this problem?
One x-intercept will be negative and is not realistic in this situation as it is
would be where the ball would hit the ground behind the player. Another
x-intercept will be positive and represents where the ball will hit the
ground after being thrown from the outfield.
d. What does the y-intercept represent in the context of this problem?
The y-intercept, (0, 8), represents that at time 0 the ball is in the players
hand as it is being thrown.
e. If the catcher does not catch the ball, how long will it take for the ball to hit the ground?
~2.057 seconds
-3-
Open Response
SHOW ALL WORK!
-4-
5. Exponential Functions & Banking
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.
$2,123.67
b. For how many years will Mike have to invest in this same account if he wanted to earn a total
of $2,250?
t ≈ 3.926
~ 4 years
6. Function Transformations
Consider the general absolute value function f ( x ) = a x − h + k .
a. How do the values of a, h and k affect the graph of the parent function f ( x ) = x ?
a: If |a| > 1, then the parent function vertically stretches. If |a| < 1, then the parent
function vertically shrinks. If a < 0, then the parent function reflects over the x-axis.
h: If h > 0, then the parent function translates to the right. If h < 0, then the parent
function translates to the left.
k: If k > 0, then the parent function translates up. If k < 0, then the parent function
translates down.
b. Write an equation so that the graph of f ( x ) = x has been translated 5 units up, 7 units to the
left, with a vertical stretch of 3, and reflected across the x-axis.
f ( x) = −3 x + 7 + 5