Algebra 2 Semester 2



Algebra 2 Semester 2 – Final Review

Unit 4.1

Perform the indicated operations and simplify. All answers should be stated in standard form.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. [pic] 12. [pic]

13. The length of a rectangle is [pic]. The width of the rectangle is [pic]. Find the area in terms of [pic].

14.[pic] 15. [pic] 16. [pic]

17. [pic] 18. [pic] 19. [pic]

20. [pic] 21. [pic]

22. [pic] 23. [pic] 24. [pic]

25. [pic] 26. [pic] 27. [pic]

Unit 4.2 -Properties of Exponents

Write each expression in expanded form.

1. [pic][pic] 2. [pic] 3. [pic]

Write in radical form.

4.[pic] 5. [pic] 6. [pic]

Write in exponential form.

7. [pic] 8. [pic] 9. [pic]

Simplify each expression. Properties of Exponents page 35

10. [pic] 11.[pic] 12. [pic]

13.[pic] 14.[pic] 15. [pic]

16. [pic] 17. [pic] 18. [pic]

19. [pic] 20. [pic] 21. [pic]

22. [pic] 23. [pic] 24. [pic]

Unit 4.3 - Exponential functions/ Growth/ Decay

Identify each of the following exponential functions as exponential growth or decay.

EXPLAIN HOW YOU KNOW

1. f(x) = 25(1.03)x 2. y =1000 (½ ) x 3.

________________ ________________ ________________

4. 5. 6.

|x |y |

|-1 |.25 |

|0 |1 |

|1 |4 |

|2 |16 |

________________ ________________ ________________

Write an equation for each of the below situations

7. Tex City has been declining in population at a rate of 3.2% each year. The present population is 12,000.

8. A particular virus infects the cells in a lizard by infecting the number of healthy cells at a rate of 20% every hour. There were 50 infected cells in the animal when the scientist began studying the data

9. Johnny invested $500 in an account that pays 7.5% annually. He wants to determine the amount in the account after 10 years.

Unit 5.1 - Logs/ Exponents/ Inverses

Find the inverse of the following equations:

1. f(x) = 2x – 3 2. f(x) = ¼(x + 2) 3. f(x) = 8x + 3 4. f(x) = ½x – 6

Write the exponential equation in logarithmic form.

5. [pic][pic] 6. [pic] 7. [pic]

Write the logarithmic equation in exponential form.

8. [pic] 9. [pic] 10. [pic]

Evaluate the logarithm without using a calculator.

11. [pic] 12. [pic] 13. [pic]

Evaluate using a calculator:

14. [pic] 15. [pic] 16. [pic]

Write as a single logarithm, then simplify if possible.

17. [pic] 18. [pic] 19. [pic]

20. [pic] 21. [pic] 22. log 2 – log x

Unit 5.2 - Natural Log/ Compound Interest

1. a) The formula for CONTINUOUSLY compounding interest is:

b) The formula for compound interest is:

c) What is P: ______ A:_______ n:_______r:________t:_______ e:_______

2. What is the total amount for an investment of $2345 invested at 6% for 14 years compounded monthly?

3. What is the total amount for an investment of $380 invested at 7.25% for 18 years and compounded weekly?

4. What is the total amount for an investment of $5000 invested at 3.25% for 10 years and compounded semi-annually?

Unit 5.3 - Rational Expressions

Add and subtract

1. [pic] 2. [pic] 3. [pic] 4. [pic]

5. [pic] 6. [pic]

Simplify each rational expression.

7. [pic][pic] 8. [pic] 9. [pic] 10. [pic]

Multiplying Rational Expressions: (leave in simplest form)

11. [pic] 12. [pic] 13. [pic]

Dividing Rational Expressions: (leave in simplest form)

14. [pic] 15. [pic] 16. [pic]

Solving Rational Expressions:(check your solutions)

17. [pic] 18. [pic] 19. [pic] 20.[pic] [pic]

Unit 6.1 - Circle Area/ Circumference/ Arc Length/ Sector Area

What is the formula for the area of a circle?

1. What is the approximate area of a circle with a radius 4? ________

2. What is the approximate area of a circle with a diameter of 7? ________

What is the formula for the circumference of a circle? __________

3. What is the approximate circumference of a circle with a radius 2? _________

4. What is the approximate circumference of a circle with a diameter of 5? _________

5. What is the approximate circumference of a circle with a diameter of 8? ________

6. What is the approximate area of a 75° sector with a radius of 3? __________

7. What is the approximate area of a 115° sector with a radius of 4.5? __________

8. What is the approximate area of a 30° sector with a radius of 2? ________

9. What is the approximate arc length of a 78° sector with a radius of 9? _________

10. What is the approximate arc length of a 105° sector with a radius of 2.75? ________

11. 12.

13) (2004 Summer Exit) The shaded area in the circle below represents the section of a park

used by the chamber of commerce for a fund-raising event. What is the approximate area

of the section of the park used for the fund-raiser?

A) 339 square feet

B) 1,357 square feet

C) 4,071 square feet

D) 12,214 square feet

14. What is the area of the shaded region in terms of [pic]? The figure below circle P and circle Q. PQ, QR, and RS are each 5 units long.

15. Find the Area and Perimeter of the figure.

[pic]

A = _______ P = ________

17. Find the Area of the figure.

19. A skate park consists of a two adjacent rectangular regions as shown. Find the perimeter and area of the park.

20. The radius of a spherical beach ball is 20 centimeters. If another spherical beach ball has a radius 5 centimeters longer, about how much greater is its surface area, to the nearest square centimeter?

Unit 6.2 - Solids

1 2

P =________ B=_________ h=_______ P =________ B=_________ h=_______

LSA = ________ TSA = ________ V = ________ LSA = ________ TSA = ________V = ________

3. P =________ B=_________ h=_______ 4. P =________ B=_________ h=_______

LSA = ______ SA = _______ V = ______ LSA = ________ TSA = ________

V = ________

5. How many faces, edges, and vertices does a square pyramid have?

6. The NBA uses basketballs with a 9.39 in diameter. How much material is needed to make the ball?

7. Chemical plants use spherical storage tanks to hold highly flammable or toxic gasses. If a tank has a diameter or 10 meters, what is the volume?

8. Find the volume of the composite figure

Unit 6.3 - Completing the Square/ Circle Equations/ Ellipse Equations

Complete the Square to Change the Equation from General Form to Standard Form.

1) x2 + 8x + y2 + 4y = 61 2) x2 – 4x + y2 + 6y = 12

Identify the center and the radius and graph the circle:

3. [pic] 4. [pic]

C:________ C:________

r =_______ r =_______

Write the circle equation for each of the following:

5. Center at the origin and a radius of [pic] 6. Center is at (-3, -1) and radius [pic].

Equation Equation:

7. [pic]

Direction Center_______

a = b = c =

Verticies ( , ) and ( , )

Co-Verticies( , ) and ( , )

Foci ( , ) and ( , )

8. Major Axis________

Center ______________________

Vertices _________________________

Co-vertices ____________________

Equation ________________________

-----------------------

A = _______

18. Find the Area of the shaded region.

A = [pic]

5 cm.

9 cm.

Parent function ________

Description____________

_____________________

Possible Function_______

Parent function ________

Description____________

_____________________

Possible Function_______

12 cm.

A = _______

16. Find the Area of the figure.

[pic]

The spread of a dangerous virus is infecting the population of a rare species of tigers. The number of tigers affected has doubled every month for the past 2 years.

What is the area of the paper left after the circle is cut out?

5 in

14 in.

2 in

10ft

8ft.

5 in

3 in

10 in

4 cm

12 cm

|x |-1 |0 |1 |2 |3 |

|y |500 |100 |20 |4 |.8 |

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