ALGEBRA 2 FINAL EXAM REVIEW

1 Name: _____ Class: _____ Date: _____ ID: A1 ALGEBRA 2 FINAL EXAM REVIEWM ultiple ChoiceIdentify the choice that best completes the statement or answers the Classify 6x5 + 4x3 + 3x2 + 11 by ____2. Classify 8x4 + 7x3 + 5x2 + 8 by number of of 5 of 4 termsConsider the leading term of each polynomial function. What is the end behavior of the graph?____3. 5x8!2x7!8x6+ leading term is 5x8. Since n is even and a is positive, the end behavior is down and leading term is 5x8. Since n is even and a is positive, the end behavior is up and leading term is 5x8. Since n is even and a is positive, the end behavior is up and leading term is 5x8.

2 Since n is even and a is positive, the end behavior is down and !3x5+9x4+5x3+ leading term is !3x5. Since n is odd and a is negative, the end behavior is up and leading term is !3x5. Since n is odd and a is negative, the end behavior is down and leading term is !3x5. Since n is odd and a is negative, the end behavior is up and leading term is !3x5. Since n is odd and a is negative, the end behavior is down and the polynomial in factored x3 + 9x2 + (x + 1)(x + 3) (x + 6)(x 3) (x + 6)(x + 1) (x + 3)(x + 6)Name: _____ ID: A2 What are the zeros of the function? Graph the y=x(x!2)(x+5) , , 2, , 2, , 5, 2____7.

3 Divide 4x3+2x2+3x+4 by x + !14x+ !14x+59, R +18x!53, R +18x!53 Divide using synthetic Divide !6x3+18x2!7x!10 by (x!2).a.!6x2+6x+5c.!6x2+30x!19, R !6x! !30x+19, R 20 Name: _____ ID: A3____9. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3!6x2+4x+9=0. Do not find the actual 9, 1, 1, 9c. 9, 3, 1, 1, 3, , 3, rootsUse Pascal s Triangle to expand the (d!2) +12d5+60d4+160d3+240d2+192d++ !6d5+15d4!20d3+15d2!6d+ !12d5+60d4!160d3+240d2!192d+ +6d5+15d4+20d3+15d2+6d+1____11. Find all the real square roots of and and and and the real-number !

4 !125343c.!1251029d.!57 Multiply and simplify if 114" 7xx!77 ! ! !49xd.!42xWhat is the simplest form of the expression?____15. of theseName: _____ ID: A4 What is the simplest form of the product?____16. 50x7y7" is the simplest form of the quotient?____17. is the simplest form of the radical expression?____18. 32a!62aa.!62ac.! possible to simplifyWhat is the simplest form of the expression?____19. 20+45! is the product of the radical expression?____20. 7!2 8+2 + + ! +562____21. 5!2 5+2 : _____ ID: A5 How can you write the expression with rationalized denominator?

5 ____22. 3!63+6a.!1!2183c.!3+22b.!3! !218____23. 2+ + + + + 313" Write the exponential expression 3x38 in radical is the solution of the equation?____27. 2x+8!6=! 3____28. x+6()35= : _____ ID: A6____29. Let f(x)=4x!5 and g(x)=6x!3. Find f(x) ! g(x). 2c. 2x 8d. 2x 2____30. Let f(x)=3x+2 and g(x)=7x+6. Find f"g and its +4x+42; all real numbers except x = ! +4x+42; all real +32x+12; all real +32x+12; all real numbers except x = !67 ____31. Let f(x)=x2!16 and g(x)=x+4. Find fg and its +4; all real numbers except x# +4; all real numbers except x#! !4; all real numbers except x# !4; all real numbers except x#!

6 4____32. Let f(x)=x+2 and g(x)=x2. Find g f !5(). 10 What is the inverse of the given relation?____33. y=7x2! x+ ! + x!37____34. y=3x+ + + ! !3 Name: _____ ID: A7 Graph the exponential y= Suppose you invest $1600 at an annual interest rate of compounded continuously. How much will you have in the account after 4 years?a.$ $6, $10, $1, How much money invested at 5% compounded continuously for 3 years will yield $820?a.$ $ $ $ the equation in logarithmic 25= " : _____ ID: A8 Evaluate the log51625a. log 10b. the expression as a single 3logbq+6logbv (q3v6) +6()logbq+v +6 +v6 ____43.

7 Log34!log32 the logarithmic ! ! !log3d____45. " + ! Use the Change of Base Formula to evaluate log728. : _____ ID: A9 Solve the exponential 116=644x! 44x= the logarithmic equation. Round to the nearest ten-thousandth if 3log2x= Find the horizontal asymptote of the graph of y=!4x6+6x+38x6+9x+ = = = ! horizontal asymptoteSimplify the rational expression. State any restrictions on the p2!4p!32p+4a.!p+8;p#!4c.!p!8;p# !8;p#! +8;p#4____52. q2+11q+24q2!5q! +8q!8;q#!3,q#! +8q!8;q#!3,q#8b.!(q+8)q!8;q#8d.!(q+8)q!8 ;q#!3,q#8 Name: _____ ID: A10 What is the product in simplest form? State any restrictions on the 4a57b4" ,a#0,b# ,a#0,b# ,a#0,b# ,a#0,b#0 What is the quotient in simplified form?

8 State any restrictions on the x+2x!1 x+4x2+4x!5a.(x+2)(x+5)x+4,x#!5,!4c.(x+2) (x+4)(x!1)2(x+5),x#1,!5,!4b.(x+2)(x+4)(x !1)2(x+5),x#1,!5d.(x+2)(x+5)x+4,x#1,!4 Simplify the 7a+8+7a2! !49(a!8)(a+8) (a!8)(a+8) +a! +63(a!8)(a+8)Simplify the b2!2b!8b2+b!2!6b! ! !4b! !2b!14b2+b! !10b!1 Name: _____ ID: A11 Simplify the complex 25t!33t12t+12ta.!35b.!4c.!53d.!14____58. 4x+31x+ +4x2+ +10x+ + hereSolve the equation. Check the !2x+4=4x+3a.!136b.!11c.!83d.!113____60. aa2!36+2a!6=1a+6a. 9b. 6c. 9 and ID: A1 ALGEBRA 2 FINAL EXAM REVIEWA nswer SectionMULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L2 REF: 5-1 Polynomial FunctionsOBJ: To classify polynomials STA: | : 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial | polynomial function | standard form of a polynomial functionDOK: DOK 1 2.

9 ANS: D PTS: 1 DIF: L2 REF: 5-1 Polynomial FunctionsOBJ: To classify polynomials STA: | : 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial | polynomial function | standard form of a polynomial functionDOK: DOK 1 3. ANS: C PTS: 1 DIF: L2 REF: 5-1 Polynomial FunctionsOBJ: To graph polynomial functions and describe end behaviorSTA: | TOP: 5-1 Problem 2 Describing End Behavior of Polynomial FunctionsKEY: polynomial | end behavior DOK: DOK 1 4. ANS: C PTS: 1 DIF: L3 REF: 5-1 Polynomial FunctionsOBJ: To graph polynomial functions and describe end behaviorSTA: | TOP: 5-1 Problem 2 Describing End Behavior of Polynomial FunctionsKEY: polynomial | end behavior DOK: DOK 1 5.

10 ANS: D PTS: 1 DIF: L2 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: To analyze the factored form of a polynomial STA: | | | TOP: 5-2 Problem 1 Writing a Polynomial in Factored Form KEY: DOK: DOK 2 6. ANS: C PTS: 1 DIF: L3 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: To analyze the factored form of a polynomial STA: | | | TOP: 5-2 Problem 2 Finding Zeros of a Polynomial Function DOK: DOK 2 7. ANS: C PTS: 1 DIF: L2 REF: 5-4 Dividing PolynomialsOBJ: To divide polynomials using long division STA: | | TOP: 5-4 Problem 1 Using Polynomial Long Division KEY: DOK: DOK 2 8.