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Honors Geometry / Algebra II B Final Review Packet
2018-19
Name _____________________________ Per__ Date______
This review packet is a general set of skills that will be assessed on the midterm. This review packet MAY NOT
include every possible type of problem that is assessed on the final exam.
Unit 7: Radical Functions
Simplify.
1. 20 125 45 2. 2 6 2 2 3i i 3. 5 3
4 3
4. 6 36 5. 41
81 6. 3 6 456h k
7. 5
3125 8. 3
3
15
81
9.
5 3
5
3
256
n
n
10. 37 49 11. 3
24k
12. 3 100
13. 55 64 4 2 14. 3
3
8 2
9 15.
3
2
5
1 33 2
n
n n
Solve each equation.
16. 6 3 0z 17. 5 2 4 0x x
18. 12 2y y 19. 1 6 1b b
20. 3 2 3 4x 21. 34 2 11 2 10x
22. 2 9 6 10 2x x 23. 2 281 27x x
24.
3
25( 2) 320x 25.
4
3( 1 2 ) 81h
Unit 8: Polynomial Functions
Simplify by using long division.
1. 14 3 25 31 25 29 20 5k k k k k
2. 4 310 5 20 11 10 5p p p p
Simplify by using synthetic division.
3.
3 25 41 41
9
y y y
y
4. 4 24 2 12 2p p p p
State whether the given graph is an even-degree polynomial or odd-degree polynomial, state the number of
real zeros of the polynomial. Describe the end behavior using arrow notation.
5.
For each polynomial function:
a) List each real zero and their multiplicities.
b) Sketch the curve WITHOUT A CALCULATOR.
6. 2( ) ( 4) ( 5)f x x x x b)
a)
7. 3 2( ) 6 9 54f x x x x b)
(Hint: Factor by grouping)
a)
Given the polynomial function, use a graphing calculator to:
a) Find each real zero.
b) Find each relative maximum and minimum.
c) Sketch the function.
16. 4 2( ) 4 2 4f x x x x c)
a) ________________________________
b) ________________________________
Unit 9: Rational Functions
Simplify.
1. 2
1711
a
b 2.
7 4
8 8y y
3.
2
2
4 3 6
m
m m
4. 2 2
6 5
3 2 4x x x
5.
2 2
1 5
9 20 10 25h h h h
6.
2
1 2
9 3 3
x
x x x
7. 4 216 4
4 8 4
x x
x x
8.
2
2
6 5 4
4 4 35 2
x x x
x x x
9.
2 2
2 2
5 6 2 8
3 4 4 3
x x x x
x x x x
Solve each equation. Remember to check for extraneous solutions.
10. 2
2 2
2 13 15 11
3 6
a a a
a a
11.
2
3 1 7
5 6 2 3
x
x x x x
12. 2
2 1
36 6 6
a
a a a
13.
2
1 3 1
5 25 5
x x x
x x x
Write the equation of the function graphed below. (The enlarged point represents a hole)
14.
For each rational function, find the x- and y-intercepts, horizontal asymptotes, vertical asymptotes, and holes.
Then, graph the function.
15. 3 2
3 2
2 8( )
3 4
x xf x
x x x
x-intercept(s): _______________
y-intercept: _______________
HA: _______________
VA: _______________
Hole(s): _______________________
16. 2
4( )
3 3 36
xg x
x x
x-intercept(s): _______________
y-intercept: _______________
HA: _______________
VA: _______________
Hole(s): ________________________
Unit 10: Exponential/Logarithmic Functions
Evaluate each expression.
1. 12
1log
144 2. 8log 32,768 3.
7
5log 5 4. ln 42e
Use 3log 28 3.0331 and 3log 4 1.2619 to approximate the value of each expression.
5. 3log 36 6. 3log 7 7. 3log 256
Write each expression as a single log.
8. 5 5 52log log 8 log 3x 9. 6 6 6log 11 log 2logx y
Solve each equation. Don’t forget to check your solution(s).
10. 3log 6x 11. 2
10log 1 1x 12. 25
3log
2n
13. 2
2 2log 10 log 2y y 14. log 121 2b 15. 3 3 32log log 4 log 25x
16. 2 2log log ( 2) 3x x 17. 3 3 3log ( 3) log (4 1) log 5x x 18. 5 5log ( 3) log (2 1) 2x x
19. 4 42log ( 1) log (11 )x x 20. 6 6log (2 5) 1 log (7 10)x x 21. 2 2 24log log 5 log 405x
22. ln ln 3 12x x 23. 2ln( 12) ln ln 8x x 24. 2 15x
25. 411 57x 26.
3 2 17 35x x 27. 8 50xe
28. ln(5 3) 3.6x 29. 16 3 21xe 30. 41
819
n
n
Show all work to solve each word problem.
31. For a certain strain of bacteria that grows continuously, k is 0.872 when t is measured in days. How long will it
take 9 bacteria to increase to 738 bacteria?
32. Jessica decides to plant asparagus in her kitchen garden. Her first harvest had 10 stalks in 2006. By 2008 she
produced 30 stalks. Assume that the number of stalks she harvests varies exponentially with the number of years
since she started harvesting the plants.
a. Find the particular equation of this function expressing number of stalks in terms of the time since she harvested.
b. Jessica will need 100 stalks to enter the “gardening” contest at the local fair. When can she enter the contest?
c. According to your model, when did she harvest the first stalk?
d. What will be her production in the year 2020?
33. Radium-226 decomposes radioactively. Its half-life, the time it takes for half of the sample to decompose, is
1800 years. Find the constant k in the decay formula for this compound.
34. To the nearest year, how old is a fossil remain that has lost 90% of its Carbon-14? Use the formula.00012ty ae .
Unit 10.5: Graphing Logarithmic, Exponential, and Piecewise Functions
Graph each function without the use of a graphing calculator. List three points and the asymptote of each
graph.
1. 3( ) 2log 1 3f x x
Points: ____________________________
_____________________________
_____________________________
Asymptote: _____________________
2. 2( ) 3 5xf x e
Points: ____________________________
_____________________________
_____________________________
Asymptote: _____________________
Write the equation for the exponential function from the graph.
3.
Graph each piecewise function.
4. 2
13
3
( ) 4 3 3
log 3 3
if xx
f x x if x
x if x
5.
3
2 1 1
( ) 2 3 1 3
32
x
x if x
f x if x
xif x
Write the equation for the piecewise function from the graph.
6.
Unit 11: Trigonometric Functions
Rewrite the radian measure in degrees.
1. 9
2.
6
3.
19
12
Rewrite the degree measure in radians.
4. 400 5. 225 6. 10°
Draw and angle with the given measure in standard position. Then state one positive and one negative
coterminal angle.
7. 11
6
8. 640
_____________ ______________ _____________ ______________
Find the exact value of each trigonometric expression.
9. sin 840 10. 8
cot3
11. sec 225
12. tan 3 13. 11
cos6
14.
7csc
6
15. sec60 tan135 cot 60 sin 60 16. sec cos tan cot3 3 3 3
Draw a diagram if necessary.
17. If the 7
tan13
B and cos 0B , find sec B .
18. The terminal side of passes through the point 5, 2 . Find the exact value of the six trigonometric ratios.
Show all work to solve each problem.
19. In a tourist bus near the base of the Eiffel Tower at Paris, a passenger estimates the angle of elevation to the top
of the tower to be 60 . If the height of the Eiffel Tower is about 984 feet, what is the distance from the bus to the
base of the tower?
20. Matt is standing 20 m from a tower that has a flagpole mounted at the top. He estimates the angles of elevation
to the top and bottom of a flagpole as 60 and 50 , respectively. Calculate the height of the flagpole.
Unit 12: SAT Problem Solving and Data Analysis
1. To determine the mean number of athletes per household in a community, Samantha surveyed 25 families at a
local indoor sports facility. For the 25 families surveyed, the mean number of athletes per household was 2.8. Which
of the following statements must be true?
A) The mean number of athletes per household in the community is 2.8.
B) A determination about the mean number of athletes per household in the community should not be made
because the sample size is too small.
C) The sampling method is flawed and may produce a biased estimate of the mean number of athletes per
household in the community.
D) The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of the
mean number of athletes per household in the community.
2.
3. Mobile users in India have gone up by 20% in a year. There are 540 million users today. How many mobile users
were there in India last year?
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