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Name:______________________________________________ Date:_______________Block:_______
Algebra 2
Final Exam Review
Day 1 – Polynomials & Statistics
Simplify completely.
1. (x )
2. 3 x  8 x
4. ( x 2 ) 6
5.
3 0
5
 x2 y5z 

3. 
3 
2
x


6
36 x 7 y 5
4x 4 y 2
6. (3x 1 y 2 z 2 )(3x 5 yz 4 )
7. (  4 x 4  3 x 2  3x ) + (  12 x 4  3x 3  5x 2  8x  1)
8. ( 3x 2  7 x  4) - (  4 x 2  12 x  8)
9. (3x – 7)(2x + 1)
2
10. (x -1)(x + 3)(x + 4)
11. (3x – 1)2
Factor the following polynomials.
12.) x 2  5 x  36
13.) x 2  64
14.) 4 x 2  3x  1
15.) x 2  49
16.) x 3  5 x 2  x  5
17.) x 3  4 x 2  x  4
Divide the polynomials using BOTH long and synthetic division.
18. ( x 3  x 2  2 x  24)  ( x  3)
19. (4 x 3  52 x  15)  ( x  5)
Find all of the zeros of the given function using both long division and synthetic division.
20.) f ( x)  x 3  9 x 2  4 x  36 ; x = 2 is a zero
21.) f ( x)  2 x 3  11x 2  18x  9 ; x = -3 is a zero
Perform the indicated operations. Then state the domain.
Let f ( x)  x 2  4 x  5 and g ( x )  x  9
22.) f ( x)  g ( x)
23.) g ( x)  f ( x)
24.) f ( x)  g ( x)
25.) f ( g ( x ))
Statistics
26.) The data, shown below, was collected regarding the class size of Miss Sweeney’s courses at
RBRHS this year.
Class Size
6
14
16
18
Tally
|
||
||
|
Frequency
1
2
2
1
a. Calculate the mean, median, mode, and range of the data.
Mean =
Mode =
Median =
Range =
b. Which of the following statements are true? Circle all the apply!
A) range > median
B) mean = median
C) median > mean
D) median < mean
Name:______________________________________________ Date:_______________Block:_______
Algebra 2
Final Exam Review
Day 2 – Quadratics, Roots & Rational Expressions
Identify the form of the quadratic equation and determine if the graph opens up or down. Then find
the vertex, axis of symmetry, roots, complete the table and graph the function.
Form:_______________________  or 
1.) y  x 2  5x  6
x
y
Form:_______________________  or 
2.) y  ( x  2) 2  3
x
y
Evaluate the expression.
3.)
3
125
27
4.)
4
81
16
5.) 2433 5
Simplify the expression.
6.) 2 x 1 / 4  x 9 / 4
1
64 x 3 y 6 z 12
1
8.) 16 2  16 4
10.)
3
7.)
9.)
3
5
4
11.)
80
 256x y 
8 2
14
Solve the equation. Check for extraneous solutions.
12.) x1 / 2  3  8
14.) x  6  x  6
13.) 5  7 x  3
5
2
15.) ( x  9)  1  31
State the domain.
16.) h( x) 
2
3x  1
17.) h( x) 
7
4
x3
Find the inverse of the equation.
18.) y  2 x  3
19.) y  x  3
Simplify.
20.)
x2  x
x 1
Multiply/Divide.
21.)
9x
2x  8

8 x  32 3x
22.)
x5
x5

x
2x
23.)
x 2  5x  4
x4

2
x
x
24.)
x 2  4x  4
x2
x3
26.)
1
2x

x2
x5
29.)
1 5 3


x 4x 2
Add/Subtract.
25.)
x4
4 x

6x
6x
27.)
2
3

x  3 x 1
Solve.
28.)
x 5 x
 
2 6 3
Name:______________________________________________ Date:_______________Block:_______
Algebra 2
Final Exam Review
Day 3 – Logarithms, Exponentials & Trigonometry
Logarithms
Rewrite the equation in exponential form.
1.
2.
Simplify the expression.
3.
4.
5.
Use a property of logarithms to evaluate the expression.
6..
7..
8..
9..
Use
and
10.
to approximate the value of the expression.
11..
12.
Expand the expression.
14.
15.
Condense the expression.
16.
17.
Use the change-of-base formula to evaluate the expression.
18.
19.
Solve the equation.
20.
21.
22.
23.
24.
25.
Solve the equation. Check for extraneous solutions.
26.
27.
Exponentials
Graph the function and label at least three points on the graph, identify if its growth or decay. State the
domain and range.
1
2. y  4   
2
1. y  3 x
Domain:
Range:
x
Domain:
Range:
x
1
2. What is the domain of y  2    - 4? What is the range? How was the function shifted?
3
3. What is the domain of
4. What is the domain of
? What is the range? How was the function shifted?
? What is the range? How was the function shifted?
5. Jacob deposited $1800 in an account that pays 2.75% annual interest. Find the balance after 3 years
if the interest is compounded:
a) Annually:
c) monthly:
b) Quarterly:
d) Daily:
Trigonometry
1 
Given the equation y  3 cos x   2 graph it and find:
2 
Amplitude:
Period:
Vertical shift:
Given the equation y  2 cos2x  1 graph it and find:
Amplitude:
Period:
Vertical shift:
Determine the amplitude, period and write the equation for each function given
amplitude:
period:
equation:
amplitude:
period:
equation:
Determine the amplitude and period for each function given
A) y = 2 sin(x)+ 2
B) y = -3 cos (2x-1)
C) y = cos x
amplitude:
amplitude:
amplitude:
period:
period:
period:
shift:
shift:
shift: