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?