# Advanced Algebra 2 Final Review Packet KG Page 1 of Find the slope of the line passing through (3, -1) and (6, 4).

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1 Advanced Algebra Final Review Packet KG 0 Page of 8. Evaluate (7 ) 0 when and Solve the equation.. Solve the equation.. Solve the equation. 6. An awards dinner costs \$ plus \$ for each person making reservations. The total bill is \$7. How man people made reservations? 7. For 980 through 990, the population, P, (in thousands), of Hawaii can be modeled b P = 7(t + 6.6) where t = 0 represents 980. What was the population in 987? 8. Solve the inequalit. Then graph our solution Is = a solution of the inequalit ( 7)? 0. Is = 7 a solution of the inequalit 7 ( 7)? Solve:. or. Solve the inequalit. Then graph our solution.. Solve the inequalit. Then graph our solution.. Solve the inequalit. Then graph our solution. 8. Determine whether the relation is a function. (0, ), (, ), (, ), (, 6), (, 6) 9. Determine whether the relation is a function. (, 0), (, ), (, ), (6, ), (6, ) 0. Find 7 8 ( ) 7 ( ) f. f () 8. Find the slope of the line passing through (, -) and (6, ).. In 980 the Wincom river was feet below the bridge. Because of silt build-up in the river bottom, the river was onl 7 feet below the bridge b 987. Write an equation for the distance of the river from the bridge, d, with t = 0 representing 980. If nothing is done about the silt, what ear will the river reach the bridge?. For the scatter plot shown, state whether and have a positive correlation, a negative correlation, or no correlation For the following data: A. Make a scatter plot of the data. B. Approimate the best fitting line for the data. C. Find an equation of our line of best fit Graph the inequalit in a coordinate plane Graph the function. 8. Graph the equation. 9. Graph the equation The population, P (in thousands), of a town can be modeled b P t 8, where t = 0 represents 990. During which two ears does the f, 0, 0 =

2 Advanced Algebra Final Review Packet KG 0 Page of 8 town have a population of 8000?. Solve the sstem graphicall:. Solve the linear sstem:. Solve the sstem.. Solve the linear sstem. 7 = + = + =. The Modern Grocer has cashews that sell for \$.0 a pound and peanuts that sell for \$.00 a pound. How much of each must Albert, the grocer, mi to get 60 pounds of miture that he can sell for \$.00 per pound. Epress the problem as a sstem of linear equations and solve using the method of our choice to find the solution of the problem. 6. Sketch the graph of the sstem of linear inequalities.. A florist sells bouquets of daffodils and jasmine. The florist pas \$0. each for daffodils and \$0.87 each for jasmine. He must also pass along his overhead costs of \$0.8 per bouquet to pa his rent, refrigeration, and workers salaries. Write an equation that models the total cost (TC) of a bouquet of flowers as a function of the number of daffodils and jasmine used. Complete the table which details the total cost for several different numbers of daffodils and jasmine. daffodils 0 jasmine. Solve the sstem:. Solve the linear sstem. z + z = + + z = 6. Solve the linear sstem. + z = = z = 7. Solve the linear sstem. z z z z z z 6 8. Tast Baker sells three kinds of muffins: chocolate chip muffins at cents each, oatmeal muffins at 0 cents each, and cranberr muffins at cents each. Charles bus some of each kind and chooses three times as man cranberr muffins as chocolate chip muffins. If he spends \$9.60 on muffins, how man oatmeal muffins did he bu? 9. Write the augmented matri for the linear sstem. z 7 z + z 8 0. Does the parabola open up or down? 6. Does the parabola open up or down? 7. Sketch the graph of the equation.. The surface of a cube is 80 square inches. How long is each edge? (Round to two decimal places.)

3 Advanced Algebra Final Review Packet KG 0 Page of 8. Solve b factoring:. The base of a triangle is five feet longer than the height. The area of the triangle is 7 square feet. Find the height and base of the triangle. 6. Find the zeros of the equation. = 7. Solve: 8. Solve the equation. 60. The height, h (in feet), of a falling object on Mars is given b h 6t s, where t is the time in seconds and s is the initial height in feet. If an object were dropped from a height of 7 feet, how long would it take to travel half the distance to the ground? (Round to two decimal places.) 6. The height, h (in feet), of a falling object on Mars is given b h 6t s, where t is the time in seconds and s is the initial height in feet. If an object were dropped from a height of feet, how long would it take to reach the ground? (Round to two decimal places.) 6. Solve: 6. Solve the equation. 6. Solve the equation Write the epression as a comple number in standard form. 6. i i (6 ) = Solve the equation b completing the square Solve the equation b completing the square Find the value of c that makes 0 c a perfect square trinomial. Write the new epression as the square of a binomial. 7. Write the quadratic equation in verte form. What is the verte? Write the equation in the form a( h) k. Then graph the equation. = Use the quadratic formula to solve the equation Solve: 80. A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given b d 6t t. How long after the rock is thrown is it 0 feet from the ground? 8. Graph: Sketch the graph of the inequalit An arrow shot into the air is 08t.9t meters above the ground t seconds after it is released. During what period of time is the arrow above 76. meters? Round our answer to the nearest.0 second. 8. Write a quadratic function in verte form that has the given verte and passes through the given point. Verte: ( 9, 8); Point: (, 0) ( 7i)( i) i i Simplif: 8. (s t u) 86. ( )

4 Advanced Algebra Final Review Packet KG 0 Page of Solve for. 88. Solve for. 89. Evaluate the polnomial when w = : w w w Graph: Multipl: 9. Factor: 9. Factor completel with respect to the integers Factor completel with respect to the integers Find all real-number solutions Find all real zeros of the function. g() Write a polnomial function that has the zeros,, and and has a leading coefficient of. Then graph the function to show that,, and are solutions. 99. Solve for : ( )( ) = Graph the function You are given a piece of cardboard inches long and inches wide. You want to create an open topped bo b cutting -inch squares out of the corners and folding up the sides so the edges ou just cut form right angles. What is the maimum volume of the bo (rounded to the nearest tenth of a cubic inch)? What are the approimate dimensions of the bo (rounded to the nearest quarter-inch)? (Remember: 0 6) 0. Which equation s graph passes through the points, 0,,, and? [A] [B] [C] [D] 0. Simplif: 0. Evaluate. 0. Use a calculator to evaluate (6) /. Round the result to three decimal places. 06. Rewrite using radical notation Evaluate 980 to three decimal places using a calculator. Simplif: /6 09. / 0., 0 6, 0 0, 8 f () f () 8 f () 8 f () / 7 /. Write the epression in simplest form. 6 7z. The surface area of a tennis ball is. in. The surface area of a billiard ball is. in. Find the ratio of the volumes of a tennis ball to a billiard ball. Surface Area = r and Volume =. r. Let f () and g(). Find f () g().. A large cit is growing b a rate of 0.% annuall. If there were,60,000 residents of the cit in 997, predict how man (to the nearest thousand) will be living in the cit in 00. Use,60,000(.7) 0.00t, where t 0 represents 997.

5 Advanced Algebra Final Review Packet KG 0 Page of 8. What is the equation for the inverse of the function f () = +? 6. Find the inverse of the relation. (, 7), (, ), (, ), (, ) 7. Find the inverse of the relation. (, ), (, ), (, ), (, ) 8. Find the inverse of the relation. (, ), (, ), (, ), (, ) 9. Write an equation for the inverse of the relation Sketch the graph of the function and its inverse on the same coordinate plane. f (). The sales of a certain product after an initial release can be found b the equation s 7t, where s represents the total sales and t represents the time in weeks after release. How man weeks will pass before the product sells about 00 units? Round our answer to the nearest week. Solve the equation. Check for etraneous solutions Find the mode of the set of data. 0, 8, 9,, 8, 9, 0,, 9, 9. Graph: f () 0. Find the value of \$000 deposited for 0 ears in an account paing 7% annual interest compounded earl.. The projected worth (in millions of dollars) of a large compan is modeled b the equation 6.0. The variable represents the number of ears since 997. What is the projected annual percent of growth, and what should the compan be worth be in 00?. Sketch the graph of the function and its inverse on the same coordinate plane. f (). A compan had total sales of \$,00,000 in 98. Each ear between 98 and 99 the sales increased b %. Approimate the sales for 99 to the nearest \$00,000.. A piece of equipment costs \$8,000 new but depreciates % per ear in each succeeding ear. Find its value after 0 ears.. Evaluate: log 9 Find the inverse of the function.. log 8 6. log / Refer to the function g().. What is the domain of g()? 8. Evaluate log 6 0 to three decimal places. 9. Evaluate log 78 to three decimal places.

6 Advanced Algebra Final Review Packet KG 0 Page 6 of 8 0. Graph the function. State the domain and range. log ( ). Epand the epression.. Solve: = 9 6. Epand using the properties of logarithms: log a z 7 log ( ). Sketch the graph of the function. f () 8. Perform the operations and simplif Simplif: 60. Solve: f f = 0 6. Find the distance between point A 8, and point C7, 9, then find the midpoint of AC. 6. Write the standard form of the equation of the circle that passes through the point (, ) with its center at the origin.. Identif all horizontal and vertical asmptotes of the graph of the function. f () 8 6. Divide: 9 7. The length of a rectangle is m, while its width is m. Which of the following is true? [A] [B] [C] [D] perimeter: area: ( ) m 8 ( ) m perimeter: 8 ( ) m area: 6 ( ) m The pool at a park is circular. You want to find the equation of the circle that is the boundar of the pool. Find the equation if the area of the pool is 900 square feet and (0, 0) represents the center of the pool. 6. Graph: Graph the equation and identif the asmptotes: 9 = 66. Determine the foci and vertices of the graph of = 67. Write the equation in standard form and classif the conic section = Solve the sstem b substitution: Find the common difference of the arithmetic sequence.,, 6,,...

7 Advanced Algebra Final Review Packet KG 0 Page 7 of 8 7. Find the common difference of the arithmetic sequence.,, 7, 6, Find the common difference of the arithmetic sequence..6,.9,.,., Find the common ratio of the geometric sequence., 8,, 8, In a financial deal, ou are promised \$700 the first da and each da after that ou will receive 6% of the previous da s amount. When one da s amount drops below \$, ou stop getting paid from that da on. What da is the first da ou would receive no pament and what is our total income? 8. A photographer points a camera at a window in a nearb building forming an angle of with the camera platform. If the camera is m from the building, how high above the platform is the window, to the nearest hundredth? m 87. Given triangle ABC with a = 7, C =, and B = 6, find c. Round the answer to two decimal places. 88. Solve ABC with A = 68, b =, and c = Epand s t. 79. Half of a circle is inside a square and half is outside, as shown. If a point is selected at random inside the square, find the probabilit that the point is also inside the circle. r r 80. Eight balls numbered from to 8 are placed in an urn. One ball is selected at random. Find the probabilit that it is NOT number. 8. A and B are independent events. P(A) = 0.6 P(B) = 0.8 Find P A and B. 8. A fair coin is tossed times. What is the probabilit of obtaining eactl head? Epress the answer both in terms of C n k and as a four-place decimal.

8 Advanced Algebra Final Review Packet KG 0 Page 8 of 8 [] [] [] [] 0 9 [] 0 [6],08,00 [7] < [8] < [9] No [0] Yes [] [A] 8 or [] [] [] or or [] [6] < or > [7] It is. [8] It is not. [9] [0] [] [] d = t; 998 [] No correlation [] = []

9 Advanced Algebra Final Review Packet KG 0 Page 9 of 8 [6] [7] [8] 0 [9] [0] (, ) [] [] 996, 000 [] (, ) [] no solution 6 f( ) f( ) 0 f( ) 0 0 [] (, 8) 0 [6] [7] 9 [8] [C] 0 [9] = 0 pounds of cashews = 0 pounds of peanuts [0] [] jasmine, [] [B] [] (,, ) [] (,, ) [] (,, ) [6] [D] daffodils [7] (,, ) [8] [B] [9] [B] 7 TC the value of z is 8 0 =, =

10 Advanced Algebra Final Review Packet KG 0 Page 0 of 8 [0] [] [] ais of smmetr: verte:, [] Down 0 0 [] Verte: (, ); Ais: = 0 0 (, ) [60] verte:, 0 ais of smm: The onl - intercept is at the verte. 0 [] Up [6] [7] [A] [8] [9] [B] [6] verte: smm: ,. ; ais of.; - intercepts at.6, 0. [6] 7.96 in. [6] ( )( ) [6] 9 [6] = or = 7 [66] = or = 6 [67] Base: ft; Height: 0 ft [68], [69] [70] [7]. seconds

11 Advanced Algebra Final Review Packet KG 0 Page of 8 [7].6 seconds [7] [C] [C] ma = [7] [7] [76] i [77] i [8] verte = (, 6) [8] ma = [86] ma = [87] [88] i i [78] i [79] 8 9 i [80], 7 [8] 6 [8] c ; [8] 8 9 verte = ( 8, 9) 6 = ( ) + [89] [90] [9] [9] [9] [9] [9] [96] [97] 0 sec (, ) 0 [98] between 0.87 and or 0 < or > 9, 8 9,

12 Advanced Algebra Final Review Packet KG 0 Page of 8.8 seconds [99] f 9 [00] f 8 [] [0] [0] [0] [0] [0] [06] [07] [08] = [09] [0] 7 [] c d 8 s 6 t 8 u [] [] The function is a cubic polnomial with degree and leading coefficient. [] The function is a quartic polnomial with degree and leading coefficient. [6]The function is a quadratic polnomial with degree and leading coefficient. [7] [8] f 8 f f [9] [0] [] [] [] [] [] ( 7 ) 7 0( )( )( ) ( )( ) ( )( )

13 Advanced Algebra Final Review Packet KG 0 Page of 8 [], [6] [7] ; [8] [9] [0] [] [] [] [] [] [6],, - [7], -, - [8], - [9] [0],, [] 6, 6,, c 7c =,, and, 0 [] = 7 6 [] [B] [B] [] [6], [7] [8] (, 0), (, 0), (, 0) [9] ( =.) Volume = 60. = f ()

14 Advanced Algebra Final Review Packet KG 0 Page of 8 length = 9. width = 7. height =. [0] [C] [C] f () 8 [] 9 [] 6 [] [] 0.97 [] 6 [6] 8 [7].77 [8] [9] [60] 7 7 v w 9 z [6] 9z [6].0 [6] [6] [6] [66],,000 [67] [68] [69] [70] (7, ), (, ), (, ),(, ) [7] (, ), (, ), (, ), (, ) [7] (, ), (, ), (, ), (, ) [7] [7] [7] = = g() = f( ) f () f - ()

15 Advanced Algebra Final Review Packet KG 0 Page of 8 g( ) 6 [8] [8] f() g() h() [76] [77] No f( ) [78] Shift the graph of left units, and down units. [79] [80] 0 f () f - () [8] [8] [8] 8 weeks [86] 9 [87] [88] [B] [B] 0 [89] = 7 [90] = 6 [9] [A] [A] [9] [9] \$967. [9] %; \$69.86 million [9],7,000 [96] \$6,00,000 [97] \$6,7.

16 Advanced Algebra Final Review Packet KG 0 Page 6 of 8 [98] [C] [C] [99] 8 [00] [] f( ) 6 6 [0] [0] [0] [0] [0].898 [06].68 0 [07] Domain: ; Range: all real numbers [08] [A] [A] [09] log a log a log a log a z log log 9 [0] [A] [A] [] [] f() = 0(.) ; [] [B] [B] 6. ppm [] =, = [6] [B] [B] [7] [8] [9] [0] [] [] [] [] distance = midpoint = [] area: 7 8 ( ) m 6 8, 7

17 Advanced Algebra Final Review Packet KG 0 Page 7 of 8 [6] [7] [8] [9] [0]center (, ); r = [] 0 = ( ) + ( ) = 6 [] vertices = ( 0, 6) ; foci = (0, ) [] ( ) + ( ) = ; The figure is a circle. [] (, ) [], 0, 8, 88 [6] [7] [8] 0. [9] 768, 07,,88 [0] 6 [] [] [] [] 6 a n a n 8 n n [] a n [6] [C] [C] 7th da; \$ total income [7] 6 [8] 0 [9] 0,0 [0]! = 0 [] 6! = 70 [] 6 n

18 Advanced Algebra Final Review Packet KG 0 Page 8 of 8 [] 6 [] 6 [],00 [6] [7] [8] q 6q r qr 8r 8s 6s t st 7t 8 [9] [A] [A] [60] 0.8 [6] [6] [A] [A] 8.6 m [6] [B] [B] 8. [6] [D] [D] [6] 6.9t and [66].6 m 7 8 C (.) a.0, B 60.7, C.8 0.8t

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