Algebra 2 Enriched Final Exam Topics List

Chapter 5

  • 5.4 Analyzing Graphs of Polynomial Functions
  • 5.5 Solving Polynomial Equations
  • 5.6 The Remainder and Factor Theorems
  • 5.7 Roots and Zeros

Chapter 6

  • 6.1 Operations on Functions
  • 6.2 Inverse Functions and Relations
  • 6.3 Square Root Functions and Inequalities
  • 6.4 nth Roots
  • 6.5 Operations with Radical Expressions
  • 6.6 Rational Exponents
  • 6.7 Solving Radical Equations

Chapter 7

  • 7.1 Graphing Exponential Functions
  • 7.2 Solving Exponential Equations
  • 7.3 Logarithms and Logarithmic Functions
  • 7.4 Solving Logarithmic Equations
  • 7.5 Properties of Logarithms
  • 7.6 Common Logarithms
  • 7.7 Base e and Natural Logarithms
  • 7.8 Using Exponential and Logarithmic Functions

Chapter 8

  • 8.1 Multiplying and Dividing Rational Expressions
  • 8.2 Adding and Subtracting Rational Expressions
  • 8.5 Variation Functions
  • 8.6 Solving Rational Equations

Chapter 12

  • 12.1 Trigonometric Functions in Right Triangles

Please study from your old tests and quizzes along with doing the review packet for the final.

Chapter 5

  1. Sketch the graph. State the number of real zeros.

f(x)xx

  1. Sketch the general shape of the function.

f(x)xxx

  1. Find all zeros.

Factor each completely.

  1. xyxyx 5. mnmn

6a 7. m

8. x9.

Find all roots.

10. x(x)(x)(x)

Find all zeros.

11.

12. f(x)xx

13.

Use the remainder theorem to find the remainder for each division. Is the divisor a factor of the polynomial?

14. 15.

Use synthetic substitution to find f (4) and f (–2) for each function.

16. f (x) =

Chapter 6

5.

6.

7. Find the inverse and graph f(x) = 3x - 4

8. Find the inverse and graph f(x) = for x ≥ 3

9. Are the following inverses?

10. Graph, then state the domain and range

11. Graph

Simplify. Use absolute value signs when necessary.

Simplify.

15. 16. 17.

Simplify.

18. 19. 20.

Write in exponential form.

21. 22.

Write in radical form.

23. 24.

Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.

25. 26.

27.

Solve each equation. Remember to check for extraneous solutions.

28) 29)

Solve each equation.

Chapter 7

Recall that

1)Write each of the following as a logarithmic expression.

a) b) c)

d) e) f)

2)Write each of the following as an exponential equation.

a) b) c)

d) e) f)

3)Solve each of the following.

a) b) c)

d) e) f)

4)Evaluate each of the following.

a) b) c)

d) e) f)

5) Use the change of base rule to evaluate the following.

a) b) c)

d) e) f)

6)Evaluate each of the following.

a) b) c)

7)Expand each of the following logarithmic expression.

a) b)

8)Condense each of the following into a single logarithm.

a) b)

9)Solve each of the following.

a) b)

10)Solve each of the following.

a) b) c)

11)Solve each of the following.

a) b)

12)Solve and check for extraneous solutions.

a) b)

13)The population P of a city is given by where t is the time in years, with t = 0 corresponding to the population in 1950. In 1995, the population was 1,400 people. Find the value of k and use it to estimate the number of people in the year 2010.

14)Graph of y=4x

15)Graph y =

16)Use ≈ 0.6310, ≈ 1.4560, and ≈ 1.7712 to approximate the value of each expression.

A. B. C.

Chapter 7 Applications

Chapter 8

Simplify each and state the excluded value.

  1. 2. 3 .

Simplify each expression.

Solve each equation. Remember to check for extraneous solutions.

17.If f varies jointly as g and the cube of h, and f = 200 when g = 5 and h = 4, find f when g = 3 and h = 6.

18. If a varies jointly as b and c and inversely as the square of d, and a = 120 when b = 5, c = 2, and d = 9, find a when b = 12, c = 9 and d = 9.

19. Heather’s weekly pay is directly proportional to the number of hours she works at the record store. Her pay is $174 for 24 hours of work. Find the amount of pay for 40 hours of work.

20. The time, t, required to empty a tank varies inversely as the rate, r, of pumping. If a pump can empty a tank in 2.5 hours at a rate of 400 gallons per minute, how long will it take to empty a tank at 500 gallons per minute?

Chapter 12

14)

15)

16)

17)

Answers

Chapter 5
  1. 3 Zeros – See Graph
  2. See Graph Below
  3. No, 25
  4. Yes, None
  5. 758 and -46 ;
Graph for number 2 / Chapter 6
  1. 112
  2. 108
  3. 53
  4. -56
  5. -18
  6. -- See Last Page for Graph
  7. -- See Last Page for Graph
  8. Yes
  9. D: [ -5, ∞) R: [-1, ∞) See Last Page for Graph
  10. See Last Page for Graph

  1. n = -1 and -2
  2. m = 12
  3. x = 1
  4. n = -18
  5. m = 74

Chapter 7
  1. a. b.
c. d.
e. e.
  1. a. b. c.
d. e. f.
  1. a. 81 b. 2 c. 4
d. 8 e. 1/9 f.
  1. a. 2 b. 0 c. -4
d. 23 e. 1/3 f. 4
  1. a. 2.377 b. 1.969 c. 1.146
d. 0.5646 e. 2.833 f. 1.824
  1. a. x+4 b. 2 c. 4x+12
  1. a.
b.
  1. a. b.
  1. a. b. -10
  1. a. 1.1073 b. 53.65 c. 2.7095
  1. a. -4 b. 0.0166
  1. a. b. 2
  1. a. k = -0.0129 b. 1152.9/about 1153 people
  1. See Graph on Last Page
  1. See Graph on Last Page
  1. a. 3.5430 b. 3.8582 c. 0.9462
Chapter 7 Applications
1. a) $8713.76 b) about 23.1 yrs. c) 9.6 yrs.
2. a) about 8.2 yrs. b) about 13.9 yrs.
3.“B”
4. a) “k” is approximately .0125 b) about 97.58 min.
5. a) f(t) = 135,000(1.1)t b) 217,400 / Chapter 8







  1. a = 88
  2. b = 0
  3. n = -13
  4. x = 42
  5. k = 20 and 2
  6. 1296
  7. $290
  8. 120 min

Chapter 12
  1. 58° 2. 48° 3. 0.3256 4. 0.5000
  1. 0.8000 6. 0.7500 7. 31° 8. 24°
  1. 21.6 10. 22.4 11. 160.4 12. 5949.9
  1. 853.1 14. 24 km 15. 26.0 m 16. 80°
  1. 80 m high, 157 m away

Graphs:

Chapter 6 # 7Chapter 6 # 8

Chapter 6 # 10Chapter 6 # 11

Chapter 7 # 14Chapter 7 # 15