WBHS Algebra 2 - Final Exam

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1 Class: _ Date: _ WBHS Algebra 2 - Final Eam Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the pattern in the sequence. Find the net three terms. 1. 1, 20, 26, 2,... Add 6;, 50, 56. b. Add 6; 8,, 50. c. Multiply by 6; 192, 1152, d. Add 6; 26, 20, 1. 2., 9, 2, 81,... Multiply by ; 29, 2,18, 6,561. b. Add ; 8, 8, 90. c. Multiply by ; 2, 29, 2,18. d. Multiply by ; 2, 29, 2,18. Is the sequence arithmetic? If so, identify the common difference.. 10, 16, 22, 28,... yes, 6 b. yes, 6 c. yes, 10 d. no. Find the 50th term of the sequence 5, 2, 9, 16, b. c. 8 d. 1 Is the sequence geometric? If so, identify the common ratio. 5. 1, 2 9, 2, 8 81, 16 2,... yes, 2 b. yes, 1 9 c. yes, 1 6 d. not geometric Write the eplicit formula for the sequence. Then find the fifth term in the sequence. 6. a 1 =, r = -2 a n =! (-2) n ; 96 c. a n =! (2) n ; 8 b. a n = -2! () n - 1 ; 162 d. a n =! (-2) n - 1 ; 8. The sequence 2,, 6, 8,..., 2 has 12 terms. Evaluate the related series. 288 b. 156 c. 1 d. 12 1

2 8. Use summation notation to write the series for 12 terms. 5 Â (56 + n) c. Â (56 + n) n = 1 n = 1 12 b. Â (5 + n) d. Â (5 + n) n = 1 n = Â 9. For the series (n + 1), find the number of terms in the series. n = 2 terms b. 12 terms c. 8 terms d. 9 terms 10. Evaluate the series to S. 19,662 b. 8,62 c. 91 d Suppose that and y vary inversely, and = when y = 12. Write the function that models the inverse variation. y = 5 c. y = 19 b. y = 8 d. y = Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it. 9 1 y direct variation; y = 1 b. inverse variation; y = 208 c. neither 1. Suppose that y varies directly with and inversely with z y = 15 when = 20, and z = 8. Write the equation that models the relationship. Then find y when = 5 and z = 2. y = 6z ; 12 5 c. y = 6 z ; 15 b. y = z ; 8 5 d. y = z ; 10 2

3 Graph the function. 1. y = -1 c. b. d.

4 15. y = - c. b. d.

5 Sketch the asymptotes and graph the function y = c. b. d. Simplify the rational epression. State any restrictions on the variable. 1. q 2-2q + 1 q - 1 -q - 1; q " -1 c. q - 1; q " 1 b. q + 1; q " -1 d. -q + 1; q " 1 5

6 Multiply or divide. State any restrictions on the variables d 2 d + 2! d 2 + 5d + 6 d 2-1d d 2 + d d + d - 1, d " -2, 1 c. d - 1, d " -2, 1 b. d + d + d d - 1, d " -2, 0, 1 d. d - 1, d " -2, 0, 1 q + 1 q + 5 # q - 5 q 2 + 6q + 5 (q + 1)(q + 1) (q + 1)(q + 1), q " -5, 5 c., q " - 1, 5 q - 5 q - 5 b. (q + 1)(q - 5) (q + 1)(q - 5) (q + 5) 2 (q + 1), q " -5, - 1 d., q " -5, - 1, 5 (q + 5) 2 (q + 1) Add or subtract. Simplify if possible p p 2-9 8p - 8 (p - )(p + ) c. 16 (p - )(p + ) b. 16 p 2 + p - 2 d. 8p + 6 (p - )(p + ) 21. g 2-9g + 8 g 2-8g g - g - 1 g - c. b. g - 1 d. g 2-9g + g 2-8g + g - 8 g - 6

7 Solve the equation. Check the solution = b. -11 c. - d. 1 a 1 a a - 6 = a b. 6 c. 9 and 6 d. 6 Graph the eponential function. 2. y = 2 c. b. d.

8 25. An initial population of 820 quail increases at an annual rate of 1%. Write an eponential function to model the quail population. f() = 820(0.1) c. f() = ( 820! 0.1) b. f() = 820(1.1) d. f() = 820(1) Graph the function. Identify the horizontal asymptote. Ê 26. y = 1 ˆ Ë Á 8 c. b. asymptote: = d. asymptote: = 8 asymptote: = 0 asymptote: = 0 Write the equation in logarithmic form = 6 log 2 6 = 6 c. log 6 = 2 b. log 6 6 = 2 d. log 6 = 2! 6 8

9 Evaluate the logarithm. 28. log b. c. 2 d. 29. log b. c. d Write the equation log 2 8 = 5 in eponential form. 2 5 = 8 b. 5 8 = 2 c. Write the epression as a single logarithm. Ê Ë Á 5 ˆ 2 = 8 d. 8 5 = 2 1. log - 6 log ( + 2) 2 log + 2 c. log ( + 2) 2 b. log ( + 2) 6 d. none of these 2. log 6p Epand the logarithmic epression. 6 log p c. log 6 - log p b. log 6 + log p d. log 6! log p. Use the properties of logarithms to evaluate log 9 + log 6 - log. 2 b. c. 8 d. 1. Use the Change of Base Formula to solve 10 2 = 1. Round to the nearest ten-thousandth b c d Solve log(5 + 1) = 1. 2 b. - 5 c d Simplify ln e. 1 1 b. c. e d. e. Solve ln(2 + 1) = 2. Round to the nearest thousandth..195 b c d The amount of money in an account with continuously compounded interest is given by the formula A = Pe rt, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.8%. Round to the nearest tenth. 0.6 yr b. 1.2 yr c. 6.5 yr d. 12 yr 9

10 Find the real-number root. 0. Simplify 162a 10 b 6 1. a b 2 6a b. 6a b 2 a 1 8 b c Assume that all variables are positive. c. a b a b. 2 d. none of these d. - 5 c. 2 d. 2 Rationalize the denominator of the epression. Assume that all variables are positive. 2. b c d Simplify c b d. none of these ,68 b. 2 2 c. 29 d. 9 Multiply. Ê ˆ 5. - Ë Á Ê Ë Á + ˆ c b. 1 + d

11 6. Write the eponential epression Solve the equation. b. in radical form. c. d = 5 6 b. 18 c. 0 d ( - 10) = 9 1 b. ; 1 c. 19 d. 1; 1 9. Let f() = and g() = 2 -. Find 2f() g() c b d Let f() = - 6 and g() = - 2. Find f g and its domain. ; all real numbers b. ; all real numbers ecept = 2 c. 1; all real numbers d. ; all real numbers ecept = 51. Find the inverse of y = 2-5. y = ± b. y 2 = c. = d. y = ± y Write the polynomial in standard form c b d Write 2 ( 2 2 ) in standard form. Then classify it by degree and number of terms ; quintic trinomial c. 8 6 ; quintic binomial b ; quintic binomial d ; quartic binomial 5. Write in factored form. 6( + 2)( + 2) c. 2( + 2)( + 6) b. 2( + 6)( 2) d. 6( 2)( + 2) 55. Write a polynomial function in standard form with zeros at 5, 5, and 2. f() = c. f() = b. f() = d. f() =

12 56. Divide by c b , R 21 d , R 225 Divide using synthetic division. 5. ( ) # ( + ) c b d Factor the epression ( - 6)( ) c. ( - 6)( ) b. ( + 6)( ) d. ( + 6)( ) ( - )( - 5)( 2 ) c. no solution b. ( - )( - )( + 5)( + 5) d. ( - )( + )( - 5)( + 5) 60. A polynomial equation with rational coefficients has the roots 2 + 1, -. Find two additional roots. 1-2, + c , - b. 2-1, + d , - 12

Algebra II Honors Final Exam Review

Class: Date: Algebra II Honors Final Exam Review Short Answer. Evaluate the series 5n. 8 n =. Evaluate the series (n + ). n = What is the sum of the finite arithmetic series?. 9+ + 5+ 8+ + + 59. 6 + 9