Algebra 2 Semester 2 – Final Review

Unit 4.1

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

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

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

14.15. 16.

17. 18. 19.

20. 21.

22. 23.24.

25.26.27.

Unit 4.2 -Properties of Exponents

Write each expression in expanded form.

1. 2. 3.

Write in radical form.

4.5. 6.

Write in exponential form.

7. 8. 9.

Simplify each expression. Properties of Exponents page 35

10. 11.12.

13.14.15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

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)x2. y =1000 (½ ) x3.

______

4. 5.6.

x / y
-1 / .25
0 / 1
1 / 4
2 / 16

______

Write an equation for each of the below situations

7. TexCity 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 – 32. f(x) = ¼(x + 2)3. f(x) = 8x + 34. f(x) = ½x – 6

Write the exponential equation in logarithmic form.

5. 6. 7.

Write the logarithmic equation in exponential form.

8. 9. 10.

Evaluate the logarithm without using a calculator.

11. 12. 13.

Evaluate using a calculator:

14. 15. 16.

Write as a single logarithm, then simplify if possible.

17. 18. 19.

20. 21. 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 at7.25% 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. 2. 3.4.

5.6.

Simplify each rational expression.

7. 8. 9. 10.

Multiplying Rational Expressions: (leave in simplest form)

11. 12. 13.

Dividing Rational Expressions: (leave in simplest form)

14. 15. 16.

Solving Rational Expressions:(check your solutions)

17. 18. 19. 20.

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? ______
  1. What is the approximate area of a circle with a diameter of 7? ______

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

  1. What is the approximate circumference of a circle with a radius 2? ______
  1. What is the approximate circumference of a circle with a diameter of 5? ______
  1. What is the approximate circumference of a circle with a diameter of 8? ______
  1. What is the approximate area of a 75° sector with a radius of 3? ______
  2. What is the approximate area of a 115° sector with a radius of 4.5? ______
  1. What is the approximate area of a 30° sector with a radius of 2? ______
  1. What is the approximate arc length of a 78° sector with a radius of 9? ______
  1. 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 ? 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.

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

12

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 = 612) x2 – 4x + y2 + 6y = 12

Identify the center and the radius and graph the circle:

3. 4.

C:______C:______

r =______r =______

Write the circle equation for each of the following:

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

EquationEquation:

7.

DirectionCenter______

a = b = c =

Verticies ( , ) and ( , )

Co-Verticies( , ) and ( , )

Foci ( , ) and ( , )

8. Major Axis______

Center ______

Vertices ______

Co-vertices ______

Equation ______