Algebra II with Trigonometry

Algebra 2 Honors Final Exam Review Guide

To prepare for your midterm exam, please follow these suggested steps. The more practice you do, the better prepared you will be for the exam. Be sure to have your calculator ready the day of the exam with WORKING batteries, a straightedge, and more than one sharpened pencil. Do not expect to borrow materials.

1. Review key vocabulary terms at the beginning of each chapter or use the list at the end of the chapter in the review.

2. Read the chapter summary at the end of each chapter several times. Write down any ideas that are unclear.

3. Review the quizzes and tests you have already taken and be sure that you would get 100% if you took the same test today.

4. Complete the chapter review and chapter test practice at the end of each chapter.

5. Use pages 1015-1016, 1021-1023 (chapters 6-7, 12, ch.13, 14.1-14.2) for extra practice problems for each chapter.

6. For additional practice on areas you may use previous homework assignments. Your homework should be a solution key to check your work.

7. Answer the remaining questions in this packet. Do not rely simply on these questions. These questions are only a basic outline of what you should be familiar with for the exam.

*REMINDER: Bring all quizzes and tests to the exam for extra credit on the final!! You must have all of them or no credit.

1 Algebra II with Trigonometry Honors Final Exam Review – 2014

CHAPTER 6 – RATIONAL EXPONENTS AND RADICAL FUNCTIONS

 Properties of rational exponents  Properties of radicals  Simplifying expressions with rational exponents  Simplifying expressions with radicals  Solving radical equations  Domain and range  Function operations - addition, subtraction, multiplication, division, composition  Inverse functions

1. Simplify each of the following using exponent rules (positive exponents only). a) b) c)

d) e) f)

2. State the domain and range of f(x) = .

3. Simplify each radical expression.

2 c) d)

4. If f(x) = x + 3 and g(x) = 4x – 1, find the following: a) f(x) – g(x) b) f(x)  g(x) c) f(g(x)) d) g(f(x))

5. Solve each of the following equations. a) b)

c) d) 3 e) f)

6. Find the inverse of the function f(x) = 4x - 2. Is the inverse a function?

7. Verify that f and g are inverses of each other. (Show f(g(x)) = g(f(x)) = x) f(x) = 6x - 5 and g(x) =

CHAPTER 7 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

 Converting between logarithmic and exponential forms  Evaluating logarithmic expressions  Change of base formula  Using properties of logarithms to condense and expand expressions  Solving logarithmic and exponential equations

1. Write in logarithmic form. a) 72 = 49 b) 34 = 81 c) 641/3 = 4

4 2. Write in exponential form.

a) log6 216 = 3 b) log 100000 = 5 c) log5 x = 6

3. Expand each of the following. 3 a) log6 2x b) log5 8x

4. Condense each of the following.

a) log x + 2 log y – 3 log z + ½ log w b) 3log 2 4 - log 2 p - 4 log q

5. Solve each of the following exponential equations. a) 3x 35 = 37 b) (5x)3 = 512 c) 4x = 43x - 6

6. Solve each exponential equation. a) 82+x = 2 b) 2x = 13

5 c) 3x+2 + 1 = 15 d) 8(3x) - 1 = 22

7. Solve each of the following logarithmic equations.

a) log (5x) = 4 b) log4 x= -1.5

c) logx 5 = 1/2 d) log3 x = 4 log3 2 + log3 5 - log3 4

e) 2 logm (x + 1) - logm 4 = 0 f) log b (3x – 4) – log b (x + 2) = log b 4

2 g) log 4 (x – 17) = 3

CHAPTER 13 - TRIGONOMETRY

 Angles  SOHCAHTOA  Laws of sines and cosines  Converting degrees and radians  Evaluating trig functions

1. Given the triangle below, find each trig function.

sin  = ______tan  = ______

cot  = ______cos  = ______

6 sec  = ______csc  = ______

2.Given csc  =, find the following.

cos  = ______sec  = ______cot  = ______

3. Evaluate the six trigonometric ratios for  if the terminal ray of  contains the point P(-6, -8).

4. Evaluate the five remaining trigonometric ratios for  given that cot  = and  lies in Quadrant III.

5. Find the missing value. Round angles to whole degree and sides to tenths.

7 6. Convert each of the following. a) –120 b) 440 c) d)

7. Find the reference angle for the given angle: A) 156 B) C) -172

8. Find one positive and one negative coterminal angle for each of the following angles. a) 15 b) 421 c) d)

8 9. Draw an angle with the given measure in standard position.

A) 207 B) -320 C)

D) E) F) 505

10.Evaluate each of the following providing EXACT answers. Strategy: use unit circle.

A) tan 135 B) sec -315 C) sin 240

D) sin E) cos F) tan

G) sin H) cos I) tan

J) tan K) cot L) sec

M) cot N) sec O) csc

11.Solve each of the following special right triangles. Give side lengths in simplest radical form. a) C = 90, B = 60, a = 8 b) C = 90, B = 45, a = 8

9 12.Solve each of the following right triangles. Give sides to the nearest tenth. a) C = 90, B = 31, a = 7 b) C = 90, A = 63, a = 12

13.Solve each of the following problems. a) A ladder that is 6 meters long leans against a house so that its lower end is 1.5 meters from the building’s base. What angle does the ladder make with the ground?

b) From the top of the lighthouse 180 feet above the ground, the angle of depression to a boat at sea is 33. Find the boat’s distance from the foot of the lighthouse.

c) A vertical pole 30 ft high casts a shadow 18 ft long. What is the angle of elevation to the sun?

14.Find the requested information for the given triangles. Draw diagrams. a) a = 4, b = 6, c = 5, find B

10 b) C = 16, b = 92, c = 32, find all sides and angles

c) A = 130, a = 20, b = 16, find all sides and angles

d) B = 35, c = 42, a = 25, find b

GRAPHING REVIEW  Graph a given function  Identify domain and range  Identify function shifts  Identify equations of asymptotes 11  Describe right and left end behaviors of functions  Find vertices, axes of symmetry, end points, turning points, etc for a given function

1. Graph a) b) c)

2. Sketch the graph and complete the following information for:

Horizontal Shift ______

Vertical Shift ______

Domain ______

Range ______

Table of Values 12 3. Sketch the graph and complete the following information for:

Horizontal Shift ______

Vertical Shift ______

Domain ______

Range ______

Table of Values

13 4. Sketch the graph and complete the following information for:

Equation of Asymptote ______

x-intercept ______

y-intercept ______

Domain ______

Range ______

Table of Values

5. Sketch the graph and complete the following information for: 14 Equation of Asymptote ______

x-intercept ______

y-intercept ______

Domain ______

Range ______

Table of Values

6. Sketch the graph and complete the following information for:

15 Equation of Asymptote ______

x-intercept ______

y-intercept ______

Domain ______

Range ______

Table of Values

Match each function below to the correct graph.

______

(A) (B) (C) (D)

16 (E) (F) (G) (H)

(I) (J) (K) (L)

CHAPTER 12 – SEQUENCES AND SERIES

 Arithmetic and Geometric sequences  Writing rules (explicit formulas) for sequences  Write recursive formulas for sequences  Find sums of series and infinite geometric series  Binomial Expansion 1. Find the sum of the series

17 Write a rule for the nth term of the arithmetic sequence. 2. 4, 7, 10, 13, … 3. d = 6, 31

4. CARS Chris buys a $20,000 car. He makes a $4,400 down payment and then pays a $325 monthly payment. Write a rule for the total amount of money paid on the car after n months.

Write a rule for the nth term of the geometric sequence. 5. 512, 64, 8, 1, … 6. r = 3,

7. Find the sum of the series

8. Find the sum of the infinite geometric series, if it exists:

9. Write the repeating decimal as a fraction in lowest terms: 0.546546546…

18 10. Write the first five terms of the sequence.

11. Write a recursive rule for the sequence. 7, 13, 19, 25, 31,…

12. Expand . Show all work.