VERSION A
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
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
VERSION A
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
Open Response
SHOW ALL WORK!
-2-
1. Rational Expressions
a. Add and simplify the following rational expression:
2
4
+
x + 5 x +1
b. Multiply and simplify the rational expression:
x 2 x 2 + 3x + 2
⋅
x + 1 x 2 + 3x
c. State any restrictions on the variable, x, for the rational expression in Part b.
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
b. Difference: (2 − 5i ) − (−3 + 4i )
c. Product: (2 − 5i )(−3 + 4i )
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)
b. Find and simplify f ( x ) − g ( x )
c. Find and simplify f ( x ) ⋅ g ( x )
d. Find and simplify ( f o g )( x )
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.
b. What is the maximum height of the ball?
c. What do the x-intercepts represent in the context of this problem?
d. What does the y-intercept represent in the context of this problem?
e. If the catcher does not catch the ball, how long will it take for the ball to hit the ground?
-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.
b. For how many years will Mike have to invest in this same account if he wanted to earn a total
of $2,250?
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:_______________________________________________________________
_______________________________________________________________
h:_______________________________________________________________
_______________________________________________________________
k:_______________________________________________________________
_______________________________________________________________
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.