In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4
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1 Semester Final Eam Review Packet Name Chapter 8: Eponents and Eponential Functions In #1-4 simplify the epression. Write your answer using eponents. 1) ( ) ( )( ) 5 ) ( 6 ) 5 4 ) ) In #5-7 simplify the epression 1 5) 6) 8 5 ( 4 n m ) 7) r In #8-11, Simplify the epression. Write your answer using only positive eponents. 8) yz 1 ab 9) a c 10) ( 6m) (m ) 4 (mn) (m) 11) 4 4m n 1) In the following, use the function y = a) Complete the table for the function b) Graph the function c) Identify the domain and range. Domain: Range:
2 1) Write in scientific notation 14) Write 1,08,000 in scientific notation 15) A company is offering its employees a retirement benefit of $4,000 per year and guarantees an annual cost of living increase of % of the benefit. a) Write a function that models the retirement benefit over time. Assume that the retirement benefit only increases by the cost of living increase. y a 1 r t b) Use the function to find the amount of the retirement benefit after 6 years. 16) You buy a new car for $,000. It depreciates at the rate of 1% per year. a) Write a function that models the value of your car over time. y a 1 r t b) Use the function to find the amount the car is wroth after 5 years. In 17 and 18, Tell whether the graph represents eponential growth or eponential decay. Then write a rule for the function. 17) 18)
3 In 19 and 0, simplify the epression. 19) when = 5 0) 1 when = Chapter 9: Polynomials and Factoring In 1 and, find the sum of the polynomials. 1) ( 7 5 ) ( ) ) (7a a 14) (9a 11a) In and 4, find the difference of the polynomials. ) (17y 6y 5) (11y y 8) 4) ( b b 6b 1) (b 11b ) In #5-8, find the product of the polynomials. (double-distribute/foil) 5) ( 9r )(r 1) 6) (7t )( t 5t ) 7) ( 5b) a 8) ( 9z )(9z )
4 In #9-4, factor the polynomial. 9) ) 4 y y 6 1) ) 11 ) 7 0 4) 9 y 66 y 11 In #5-6, what are the -intercepts? (Also called Zeros/Roots/Solutions) 5) ( 7)( ) y 6) (5 )( 11) y In #7-4, solve the equation. z z 7) ) 9) ) ) 5 5 4) m 6m m 1
5 4) A rectangle has the length of (+) inches, a width of (+4) inches, and an area of 15 square inches. Find the value of. (hint: draw a picture!) Chapter 10: Quadratic Equations and Functions Find the verte of the following quadratics: 44) ) ) Given the following information about the parabola, answer the questions. y 8 a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maimum or minimum? d) Find and draw the ais of symmetry ( Also known as the coordinate of the verte) e) Find a plot the verte. Find more points on the graph and graph the parabola y Verte
6 47) Given the following information about the parabola, answer the questions. y 4 a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maimum or minimum? d) Find and draw the ais of symmetry ( Also known as the coordinate of the verte) e) Find a plot the verte. Find more points on the graph and graph the parabola y Verte In solve the equation. Round to the nearest hundredth, if necessary 48) ) ) Use the Quadratic Formula to solve. 7 5
7 Use the discriminant to tell whether the equation has two, one, or zero solutions. 51) ) w 9w w 4 5) The discriminant of 5 c is -7. What is the value of c? Chapter 11: Radicals and Geometry Connections In # 54-61, simplify the epression ) 4 55) 18 56) 5 57) 75 np 4 m 58) k 59) 6 49d 60) ) 5 500
8 In #6-64, solve for. 6) 6 4 6) ) 4 0 Chapter 1: Rational Equations and Functions 65) Given that y varies inversely with, use the specified values to write an inverse variation equation that relates and y. Then find y when = 6. = 4, y = 66) Given that y varies inversely with, use the specified values to write an inverse variation equation that relates and y. Then find y when = 18. = 6, y = 9 Graph the function. 67) y y Und.
9 Simplify the epressions. 68) ) ) ) ( ) ) ) 1 n n n n
10 Name: Date: Hour: Algebra Practice Eam Chapters 8-1 Multiple Choice Please select the choice that best answers the question and mark your answer on the provided Scantron sheet. 74. What is the equation of the graph? a.) y = b.) y = c.) d.) y 1 y Simplify 5a 5 b a b 6a b 5 15a 5 b. a.) b.) c.) d.) a 5 b 4 15a 5 6b a 5 b 15a 5 b Rewrite in standard form. a.) b.) c.) 65,000,000 d.) 6,500,000
11 77. Which of the models below are eponential decay models? I. y = 1.19 II. y = 0.1 III. y 5 IV. y a.) I and II b.) II and III c.) I and III d.) II and IV 78. You buy a used tractor for $55,10. It depreciates at the rate of 8.8% per year. What is the value of the tractor after 6 years? a.) $16, b.) $91,48.71 c.) $1, d.) $,4,69.8 y a 1- r t 79. You deposit $700 in an account that pays 8% interest compounded yearly. How much money is in the account after 10 years? a.) $1,000 b.) $ c.) $ d.) $964,06.15 y a 1 r t Simplify a.) 4 8 b.) 4 16 c.) 4 10 d.) ? 81. Which number represents 65,006,000 in scientific notation? a.) b.) c.) d.)
12 8. Which of the following is equal to ? a.) 7 8 b.) c.) d.) Which of the following is equal to (6a 4b)? a.) 6a 48ab 16b b.) 6b 48ab 16a c.) 6a 16b d.) 16b 49a Which of the following is equal to the epression ? a.) ( 7)(6 + 5) b.) (5 + 6)( 7) c.) (6 + 7)( + 5) d.) (5 7)(5 + 6) 85. Which of the following is a solution of the equation 7 11 = 4 +97? a.) 0 b.) -5 c.) -6 d.) What is the -coordinate of the verte of the graph of the equation y = ? a.) b.) - c.) d.) 1
13 87. What are the zeros of the function y 4 6? a.) - and b.) and c.) - and 6 d.) 6 and 88. What is the discriminanat of the equation y = 1? a.) 0 b.) 9 c.) -7 d.) Name the type of model that the graph suggests. a.) Quadratic b.) Eponential Decay c.) Eponential Growth d.) Linear 90. What is the correct factorization of ? (Factor the epression) a.) ( + 5)( 7) b.) -( + 5)( 7) c.) -( 5)( + 7) d.) ( 5)( 7)
14 91. What is the simplest form of (5 + )(5 )? a.) 5-4 b.) 10 c.) d.) What are the -intercepts for the graph of y = ( )( + ) a.) and b.) - and c.) - and d.) - and - 9. Which of the following is , in simplified form? a.) 5 9 b.) c.) 6 18 d.) Solve = 58. a.) 710 b.) 4 c.) 14 d.) Which function is graphed? a.) y = 0 b.) y 1 c.) d.) y =
15 96. Which epression is equivalent to 7? a.) 70 b.) 6 c.) 6 d.) 97. Find the area of the rectangle. (A = l * w) 4 a.) 4 b.) 16 c.) 1 d.) Which of the following equations models inverse variation?? a.) y = b.) y = c.) y = + d.) y =
In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4
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