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Algebra II Honors Final Exam Review Name: __________________________________________ Period: __________ Date: __________________ To prepare for the final exam review all notes, quizzes, and tests in chapter 7 & 8 and pre-calc chapters 4 & 5. Chapter 7 Solve the equation. Check for extraneous solutions. 1.) 2 x 1 16 x 2 2.) e x 4 3.) 3 2 x 5 13 6.) log 3 (2 x 5) 2 5.) 5 x 32 9.) 3 log( x 4) 6 7.) ln x ln( x 2) 3 10.) log 4 x log 4 ( x 6) 2 Graph the function. State the domain and range. 12.) y 3 x 13.) y 2 4 x2 1 16.) y 2 3 x2 Use change-of-base to evaluate the logarithm. 22.) log 5 50 23.) log 6 23 8.) 7 2 x 30 11.) log 3 (5 x 3) 5 14.) f ( x) 5 2 x 3 3 15.) y 40.25 x x 2 17.) g ( x) 2 3 Evaluate the logarithm without using a calculator. 1 19.) log 5 25 20.) log 2 32 4.) 3 x 1 5 10 18.) y log 2 x 21.) log 6 1 24.) log 9 45 25.) From 1996 to 2001, the number of households that purchased lawn and garden products at home gardening centers increased by about 4.85% per year. In 1996, about 62 million households purchased lawn and garden products. Write a function giving the number of households H (in millions) that purchased lawn and garden products t years after 1996. 26.) You deposit $2,500 in an account that pays 3.5% annual interest compounded continuously. What is the balance after 8 years? 27.) The model y 7.7e 0.14 x gives the number y (in thousands per cubic centimeter) of bacteria in a liquid culture after x hours. After how many hours will there by 50,000 bacteria per cubic centimeters? Round your answer to the nearest tenth of an hour. Chapter 8 1.) The number n of photos your digital camera can store varies inversely with the average size s (in megapixels)of the photos. Your digital camera can store 54 photos when the average photo size is 1.92 megapixels. Write a model that gives n as a function of s. How many photos can your camera store when the average photo size is 3.87 megapixels? Simplify the complex fraction. x 6 3 2.) 4 10 x 15 3.) 2 x 16 x2 4.) 4 6 x 1 x x 4 5 Perform the indicated operation and simplify. x 2 3x 4 x 6 3x 2 y 6y2 5.) 6.) 4 x 3 y 5 2 xy3 x 2 3x 18 x 1 x 2 11x 28 2 8.) x 16 x 2 5x 4 11.) 3x 6 x x 12 x 4 2 9.) 3x 4x 1 x5 x5 12.) 7.) x 2 8 x 15 x4 2 2 x 12 x 32 x 25 10.) 4 2 x3 x6 15.) x2 x2 x 1 x 4 4 2x 2 x 5 x 25 Solve the equation. Check for extraneous solutions. 3 x3 1 x 1 13 13.) 14.) x 2 2x 4 x6 x x6 Pre-Calculus Chapter 4 Convert the angle measure from degrees to radians (# 1 &2) or radians to degrees (# 3 & 4). 3 7 1.) 115 2.) 642 3.) 4.) 2 12 Evaluate (if possible) the sine, cosine, and tangent of the real number. 7 11 5 5.) t 6.) t 7.) t 4 6 3 Solve for the variable. 8.) 9.) 10.) A 30-meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of approximately 75 with the ground. (a) Draw a right triangle to represent the problem. Shown the known quantities on the triangle and use a variable to indicate the unknown height of the balloon. (b) Use a trigonometric function to write an equation involving the unknown. (c) What is the height of the balloon? 11.) You are standing 75 meters from the base of the Jin Mao Building in Shanghai, China. You estimate that the angle of elevation to the top of the building is 80 . What is the approximate height of the building? Suppose one of your friends is at the top of the building. What is the distance between you and your friends? Evaluate the expression. 12.) arccos 1 2 13.) arccos 0 Sketch the graphs. Include two full periods. 16.) f ( x) 2 sin x 17.) g ( x) 4 sin x 20.) y 3 cos6 x 21.) y 1 sin x 2 2 14.) arcsin 2 15.) arctan 18.) y sin x 4 19.) f ( x) 4 cos x 22.) y 8 cosx 23.) y 6 cos x 6 3 3 Pre-Calculus Chapter 5 Verify the identity. 1.) sin t csc t 1 2.) tan y cot y 1 csc 2 x 3.) csc x sec x cot x 4.) cot 2 y(sec 2 y 1) 1 5.) cos 2 sin 2 1 2 sin 2 6.) tan 2 6 sec 2 5 7.) 2 csc 2 z 1 cot 2 z 8.) cos x sin x tan x sec x 9.) Solve the equation for 0 x 2 . 10.) 2 cos x 1 0 11.) 2 sin x 1 0 12.) cot 3 x cos x(csc 2 x 1) csc x 3 sec x 2 0 13.) cot x 1 0 Find the exact value of the trigonometric function given that sin u 5 13 , where 0 u 2 and cos v 3 5 , where 2 v . 14.) sin( u v) 15.) cos(v u ) 16.) cos(u v) 17.) sin( u v) Find the exact value of the trigonometric function given that sin u 7 25 , where 2 u and cos v 4 5 , where 3 2 v 2 . 18.) cos(u v) 19.) sin( u v) 20.) sin( v u ) 21.) cos(u v) Find all solutions of the equation in the interval [0,2 ). 1 22.) sin x sin x 1 23.) sin x sin x 3 3 6 6 2 24.) cos x cos x 1 4 4 25.) cos x cos x 1 6 6 Find the exact values of sin 2u , cos 2u , and tan 2u using the double-angle formulas. 3 2 1 3 26.) sin u ,0 u 27.) cos u , u 28.) tan u , u 5 2 7 2 2 2