2011-2012
Common Algebra 2 Assessment
Multiple Choice
Formulas Reference
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 )
a m  a n  a mn
Exponent Rules
am
 a mn
n
a
a 
m n
 a mn
b
b 2  4ac

2a
2a
OR
x
Quadratic Formula
x
 b  b 2  4ac
2a
log b MN  log b M  log b N
Properties of Logarithms:
For any positive numbers, M, N, and b (b  1)
log b
M
 log b M  log b N
N
log b M x  x log b M
I  Prt
Interest Formulas
Complex Numbers
A  Pe r t
a  bi; i 2  1
2011-2012
Multiple Choice
1.
-2-
Which point-slope equation matches 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)
2011-2012
Multiple Choice
-3-
5. 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
6. 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)
2011-2012
Multiple Choice
-4-
d
7. Simplify: 3 2  16
i
a. 5 + 9i
b. 6 + 4i
c. 6 + 12i
d. 6 – 4i
27  75  12 .
8. Simplify:
a. 6 3
b.
90
c. 22 3
d. 9.4
9. 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
10. Simplify:
a. 3
b. -3
c. 3i
d. -3i
3
27
2011-2012
Multiple Choice
11. 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
12. 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)
13. 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)
14. Solve for x: 5x 2  25
a. x  5
b. x  25
c. x  5
d. x   5
15. Solve for x: x 2  6 x  55
a.
x  5, x  11
b. x  5, x  11
c.
x  3  55
d. x  61
-5-
2011-2012
Multiple Choice
-6-
16. Solve for x: x 2  6 x  42
a. x  6  51
b. x  3  42
c.
x  3  51
d. x   4 3
17. 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
18. Which polynomial function has 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)
19. Solve for x:
a.
x  7  x  1 . Remember: check for extraneous solutions.
x  3, 2
b. x  3, 2
c.
x2
d. x  3
20. Between which two numbers is log 5 150 ?
a. 0 and 1
b. 1 and 2
c. 2 and 3
d. 3 and 4
2011-2012
Multiple Choice
-7-
21. 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 
22. 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 )
23. Solve for x: log 2  log( x  5)  2 . Remember: check for extraneous solutions.
a. x  15
b. x  55
c.
x6
d. x  55
24. Solve for t: 105t  2
a. t 
2
5
b. t  log 4 64
c. t  5 log 2
d. t 
log 2
5
25. 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
2011-2012
Multiple Choice
-8-
26. 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
27. 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)
28. 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
29. Find P(female | vanilla).
Preferred Ice Cream Flavor
a. 0.286
c. 0.222
b. 0.125
d. 0.778
Vanilla
Chocolate
Female
12
28
Male
42
14
30. 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%
2011-2012
Common Algebra 2 Assessment
Open Response
Formulas Reference
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 )
a m  a n  a mn
Exponent Rules
am
 a mn
n
a
a 
m n
 a mn
b 2  4ac
b

2a
2a
OR
x
Quadratic Formula
x
 b  b 2  4ac
2a
log b MN  log b M  log b N
Properties of Logarithms:
For any positive numbers, M, N, and b (b  1)
log b
M
 log b M  log b N
N
log b M x  x log b M
I  Prt
Interest Formulas
Complex Numbers
A  Pe r t
a  bi; i 2  1
2011-2012
Open Response
SHOW ALL WORK!
-2-
1. Rational Expressions – Addition
a. Consider the rational expression:
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
2. Rational Expressions – Multiplication
x 2 x 2  3x  2
a. Consider the rational expression:

. State any restrictions on the variable, x.
x  1 x 2  3x
b. Multiply and simplify the following rational expression:
x 2 x 2  3x  2

x  1 x 2  3x
3. Complex Numbers
Find the sum, difference, and product of the complex numbers (1  4i ) and 2  3i .
a. Sum: (1  4i )  (2  3 i )
b
b. Difference: (1  4i )  ( 2  3 i )
c. Product: (1  4i )( 2  3 i )
g
2011-2012
4. Functions
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.
b. Evaluate the expression f ( x )  g ( x ) and write your answer as a polynomial in standard form.
c. Evaluate the expression ( f  g )( x ) and write your answer as a polynomial in standard form.
d. Find the value of ( f  g )(4) .
e. Find the value of f ( 3)  g ( 2) .
2011-2012
5. Quadratic Functions & Baseball
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.
a. Find the height of the ball after it has traveled 1 second. Show your work.
b. What is the maximum height of the ball? Show your work algebraically and round your
answer to the nearest hundredth.
c. What does the positive x-intercept represent in the context of this problem?
d. What does the y-intercept represent in the context of this problem?
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.
2011-2012
6. 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. Round your answer appropriately.
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.
7. Graphing Systems
a. Graph the solution set for the following system of inequalities.
1

y  3 x 1


y  x  2


b. Give an ordered pair that is in the solution set to the system of inequalities.
c. Using algebra, show that your ordered pair is a solution to the system of inequalities.
2011-2012
8. Function Transformations
2
Consider the vertex form of a quadratic function: f ( x )  a  x  h   k .
Word Box
horizontal
shrink
reflect
translate
stretch
vertical
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 and use words from the word box
provided.
a: _________________________________________________________________________
_________________________________________________________________________
h: _________________________________________________________________________
_________________________________________________________________________
k: _________________________________________________________________________
_________________________________________________________________________
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.