Name:___________________________________________ Date:_________________ Period:________________________________________________________________

Final Exam Review PacketA5a – I can convert between standard and factored form I’m ready for the final

I need more practice

Factor.

1. v2+2v−80 2. 2 p2−17 p−9 3. 16 x2−9

Expand (write each product as a sum).

4. (−3 x+3 ) (7x+1 )

A5b – I can solve quadratic equations I’m ready for the final

I need more practice

Solve using square roots.

1. 6 p2−7=47 2. (2k−4 )2+4=85

Solve using the Zero Product Property.

3. 2k2−20 k+32

Solve using the Quadratic Formula.

4. 4 n2−3n−10=0

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A5c – I can graph quadratic functions I’m ready for the final

I need more practice

Make a complete graph. Show all the steps.

1. y=−x2+2 x+15

A5d – I can model quadratic functions I’m ready for the final2

y-intercept ____________

x-intercept(s) ___________________

line of symmetry ____________

vertex ____________

mirror point ____________

I need more practice

The motorcycle in the picture is launching off a 5 foot ramp through the ring of fire (hopefully).

The path of the motorcycle can be approximated by the equation y=−16 x2+32 x+5 where xrepresents the time in seconds after launch and y represents the height off the ground in feet.

1. What was the highest point the motorcycle reached and how long did it take to get there?

2. How many seconds until the motorcycle hits the ground?

3. The bottom of the hoop is 15 feet off the ground and has a 10-foot diameter. Write an inequality to represent the height that the motorcycle must reach to pass through the ring of fire.

4. If the motorcyclist reaches the ring of fire after soaring for 0.5 seconds, will she make it through the ring safely?

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A6a – I can solve inequalities and represent them in multiple ways I’m ready for the final

I need more practice

Complete each missing representation.

1. Rule: ______________________

Graph:

Words: __________________________________________________________

Solve and graph each inequality.

2. −2n2+12<n2−15

3. −k−4 (8k−5 )≤−145

A6b – I can graph inequalities and identify the solution region I’m ready for the final

I need more practice

Graph the inequality.

1. y ≥ 74x−5

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Make a complete the graph of the system of inequalities. Show your steps.

2. y ≥−x2−4 x+2

y>x−2

Is the point (8,6) a solution to this system? Justify your answer.

3. A music company is trying to plan its next month’s work. The company makes CDs of both rock and rap groups. It costs them an average of $2500 to produce a rock CD and an average of $2000 to produce a rap CD. (The higher cost for rock comes from needing more instrumentalists for rock CDs.) The company can afford to spend up to $18000 on production next month. It takes 15 hours to produce a rock CD, while a rap CD takes 20 hours. According to the company’s agreements with the employee union, the company must spend at least 140 hours on production.

x = # of Rock CDs and y = # of Rap CDs

a) Write inequalities to represent the situation.

Hours: _________________________________ Cost: _________________________________

b) Graph the situation. c) What is one possible amount of rap and rock CDs the music company could make?

d) What is the largest number of CD that the company can make?

e) If the music company wanted to have the same amount of rap and rock CDs produced, how many CDs of each could they make?

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A7a - I can apply the properties of exponents I’m ready for the final

I need more practice

1. 6k5 ∙2 k5

2. (5b6 )3

3. 6n3

3n

4. x56

5. (2 y−4 )3

6. (2b4∙ b4 )4

7. 2x−3

4 x2∙2 x0

8. 3√64k

A7b - I can model exponential functions in multiple ways I’m ready for the final

I need more practice

1. Graph the equation y=13∙3x. 2. Use the table below to answer the following questions.

x y-2-10 20001 17002 14453

a) Write an equation that represents the data in the table.

b) What is the percent increase or decrease?

3. You wonder how small a piece of Red Vine you will have if you cut it in half over and over. The Red Vine starts at 12 inches long.

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a) Complete the table with the values for the first 5 cuts (don’t worry if the values get really small).

Cut Length012345

b) Write an equation modeling this situation.

c) How long will the piece be after 9 cuts?

d) After how many cuts will the piece be less than one inch?

less than 0.1 inches?

less than 0.001 inches?

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A5a1. (v+10)(v-8)2. (2p+1)(p-9)3. (4x+3)(4x-3)4. -21x2+18x+3

A5b

1. p = 3 and p= -32. k = 6.5 and k = -2.53. k = 8 and k = 24. n = 2 and k = -1.25

A5c

A5d

1. 21 feet off the ground in 1 second2. 2.14 seconds3. 15<x<254. She will be 17 feet off the ground. Yes, she will make it through the ring safely.

A6a1. X > -2; x is greater than or equal to -22. n>±33. k ≥5

A6b1.

2.

No (8,6) is not a solution to this system.

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3. a. 15 x+20 y ≥1402500 x+2000 y ≤18000b.

c. 2 rock, 6 rap (lots of correct answers here)d. 9 total CDse. 4 of each type

A7a1. 12k10

2. 125b18

3. 2n2

4. 6√ x5

5.8y12

6. 16b32

7.14 x5

8. 4 k13

A7b

1.

2.

X Y-2 2768-1 23530 20001 17002 14453 1228.25

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a. Y=2000(0.85)x

b. 15% decrease3.

b. y = 12(0.5)x

c. 0.0234 inchesd. 3 cuts, 7 cuts, 14 cuts

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Cut

Length

0 121 62 33 1.54 .755 .375