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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