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1 Test # 33 QUESTIONS MATH COLLEGE ALGEBRA Name atfm131bli website MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation b factoring. 1) = 0 A) - 3, - 3, C) - 1, - 1 Objective: (1.) Solve Quadratic Equations b Factoring ALVAREZ VIDEO M0-3,,, M-1, M,9,11,1 D) 3, - Solve the equation using the quadratic formula. ) = 0 A) {-7 + 3i, -7-3i} {-7-9i, i} C) {-7 + 3i} D) {-, -} Objective: (1.) Solve Quadratic Equations Using the Quadratic Formula ALVAREZ VIDEO M0-7 Solve the radical equation, and check all proposed solutions. 3) = + A) {-7} {} C) {-} D) {7} Objective: (1.) Solve Radical Equations ALVAREZ VIDEO 9 m9-3 m0-9 math #1 math # Use the graph of the given function to find an relative maima and relative minima. ) f() = ) ) 3) ) A) maimum: (0, 1); minimum: (, -3) maimum: (0, 1); minimum: none C) maimum: none; minimum: (, -3) D) no maimum or minimum Objective: (.) Use Graphs to Locate Relative Maima or Minima ALVAREZ VIDEO 1 M9- M-1, Graph the function. 1
2 ) f() = + 1 if < 1 if 1 ) - - A) (-1, ) (-1, ) (-1, ) (-1, ) C) D) (1, ) (1, ) (1, ) (1, ) Objective: (.) Understand and Use Piecewise Functions ALVAREZ VIDEO 17 m9- m0- math # math #
3 Find and simplif the difference quotient ) f() = + + f( + h) - f(), h 0 for the given function. h A) + h h + h + h + 1 h ) C) + h + D) 1 Objective: (.) Find and Simplif a Functionʹs Difference Quotient ALVAREZ VIDEO 1 m9-7 m0-11 math # math # Begin b graphing the standard absolute value function f() =. Then use transformations of this graph to graph the given function. 7) h() = ) A) C) D) Objective: (.) Use Horizontal Shifts to Graph Functions 3
4 ALVAREZ VIDEO 1 m9- Find the domain of the function. ) f() = 1 - A) (-, 1) (1, ) (-, 3 ] C) (-, 1] D) (-, 3 ) (3, ) Objective: (.) Find the Domain of a Function ) ALVAREZ VIDEO 3 m9-9 m0-1 math #30 math #7 Given functions f and g, perform the indicated operations. 9) f() = -, g() = 9 - Find f - g. A) C) 11-1 D) 7-9) Objective: (.) Combine Functions Using the Algebra of Functions, Specifing Domains VIDEO ALVAREZ M0-13 M9- M-31 M- ) f() = 3 +, g() = + Find fg. A) C) + + D) + 1 Objective: (.) Combine Functions Using the Algebra of Functions, Specifing Domains ALVAREZ VIDEO M0-13 For the given functions f and g, find the indicated composition. 11) f() = + 3 +, g() = 3 - (g f)() A) C) D) Objective: (.) Form Composite Functions ) 11) ALVAREZ VIDEO 31 m9-1 m0-1 math #3 math #9 Find the distance between the pair of points. 1) (-1, -3) and (-7, ) A) 0 C) 11 D) 0 1) Objective: (.) Find the Distance Between Two Points ALVAREZ VIDEO 33 m9-1 m0-1 math #3 math #
5 Graph the equation. 13) = 0 13) A) Objective: (.) Convert the General Form of a Circleʹs Equation to Standard Form ALVAREZ VIDEO 3 m9-17 m0-17 math #1 m,ath #1 Use the verte and intercepts to sketch the graph of the quadratic function. 1) f() = )
6 A) C) D) Objective: (3.1) Graph Parabolas ALVAREZ VIDEO 3 M0-0 M9-19 M-3 M-13,1,1,1 Solve the problem. 1) An arrow is fired into the air with an initial velocit of 10 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given b the function h() = -1t + 10t. Find the maimum height of the arrow. A) 100 ft 0 ft C) 00 ft D) 70 ft Objective: (3.1) Solve Problems Involving a Quadratic Functionʹs Minimum or Maimum Value ALVAREZ VIDEO 39 m9-0 math #,, Graph the polnomial function. 1) f() = ) 1)
7 A) C) D) Objective: (3.) Graph Polnomial Functions ALVAREZ VIDEO 3 m9- m0-3 math #0 math #1 Solve the polnomial equation. In order to obtain the first root, use snthetic division to test the possible rational roots. 17) = 0 17) A) {-, } {1 + i, 1 - i, i} C) {1 + i, 1 - i, } D) {1 + i, 1 - i, -} Objective: (3.) Solve Polnomial Equations ALVAREZ VIDEO 9 m9- m0- m-0 m-17 Find the vertical asmptotes, if an, of the graph of the rational function ) A) =, = = -, = - C) = - 9 D) =, =, = - 9 Objective: (3.) Identif Vertical Asmptotes 1) ALVAREZ VIDEO m9-7 m0- math # math #1 7
8 Find the slant asmptote, if an, of the graph of the rational function. 19) f() = A) = + = C) = + D) no slant asmptote Objective: (3.) Identif Slant Asmptotes ALVAREZ VIDEO 7 m9-30 m0- math # math #0 Find the domain of the logarithmic function. 0) f() = ln ( - ) A) (-, ) (-, ) C) (-, 0) D) (-, ) or (, ) Objective: (.) Find the Domain of a Logarithmic Function 19) 0) ALVAREZ VIDEO 3 m9-31 m0-30 math #1 math # Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 1) log 3 - ( + ) 1) A) log + log + 1 log ( - ) - log + log ( + ) 3 log + log + log ( - ) 1/3 - log - log ( + ) C) log ( 3 - ) - log (( + ) ) D) log + log + 1 log ( - ) - log - log ( + ) 3 Objective: (.3) Epand Logarithmic Epressions ALVAREZ VIDEO 7 m9-3 m0-31,3 m-,3, m-, #,3, math, Solve the equation b epressing each side as a power of the same base and then equating eponents. ) = - A) {} {} C) {37} D) {17} Objective: (.) Use Like Bases to Solve Eponential Equations ) ALVAREZ VIDEO 70 m9-33 m0-33 math # math #7 Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 3) 3 + = A) C) 1.31 D) -0.3 Objective: (.) Use Logarithms to Solve Eponential Equations ALVAREZ VIDEO 73 M0-3 M- M9-3 3)
9 Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. ) log ( - 1) + log ( - 7) = ) A) {9, -1} {9} C) {} D) {-1} Objective: (.) Use the Definition of a Logarithm to Solve Logarithmic Equations ALVAREZ VIDEO 7 m9-37 m0-3 math #7 math #30 ) log ( + ) - log = ) A) { 1 } {} C) { 1 } D) {1 } Objective: (.) Use the Definition of a Logarithm to Solve Logarithmic Equations ALVAREZ VIDEO 7 M0-37 ) log ( + ) - log ( - ) = log 3 A) {} 3 C) {-} D) Objective: (.) Use the One-to-One Propert of Logarithms to Solve Logarithmic Equations ALVAREZ VIDEO 79 M0-37 7) ln + ln ( -1) = ln 7 A) {9, -} {-} C) 73 D) {9} Objective: (.) Use the One-to-One Propert of Logarithms to Solve Logarithmic Equations ALVAREZLAB EXPONENZ (3,) INTERACTMATH SEC. EXE ALVAERZ VIDEO 0 m9-0,1 m0-3,37,3 math #1 math #3 Solve the problem. ) Find out how long it takes a $30 investment to double if it is invested at % compounded ) 7) ) semiannuall. Round to the nearest tenth of a ear. Use the formula A = P 1 + r n nt. A). ears 9 ears C). ears D) 9. ears Objective: (.) Solve Applied Problems Involving Eponential and Logarithmic Equations ALVAREZ VIDEO 1 M0-39 9) The function A = A0e models the amount in pounds of a particular radioactive material stored in a concrete vault, where is the number of ears since the material was put into the vault. If 900 pounds of the material are placed in the vault, how much time will need to pass for onl 19 pounds to remain? A) 00 ears 0 ears C) ears D) 00 ears Objective: (.) Solve Applied Problems Involving Eponential and Logarithmic Equations ALVAREZ VIDEO 3 M0-0, M9-3 M-3 30) The population of a certain countr is growing at a rate of.1% per ear. How long will it take for this countrʹs population to double? Use the formula t = ln, which gives the time, t, for a k population with growth rate k, to double. (Round to the nearest whole ear.) A) 33 ears 3 ears C) 3 ears D) 3 ears Objective: (.) Solve Applied Problems Involving Eponential and Logarithmic Equations 9) 30) ALVAREZ VIDEO m9- m0-3 math #7 math #37 9
10 Solve the sstem of equations. 31) + + z = - + z = z = 1 A) {(, -1, 1)} {(-1,, 1)} C) {(1,, -1)} D) {(1, -1, )} Objective: (.) Solve Sstems of Linear Equations in Three Variables ALVAREZ VIDEO 9 m9- m0- math #91 math #3 Find the indicated sum. 3) (i + ) i = 3 A) C) D) 30 Objective: (.1) Use Summation Notation ALVAREZ VIDEO 9 m9-7 m0- math #9 math #39 Write the first three terms in the binomial epansion, epressing the result in simplified form. 33) ( + ) 1 A) C) D) Objective: (.) Find a Particular Term in a Binomial Epansion 31) 3) 33) ALVAREZ VIDEO 0 m9-9 m0-9 math #0,1 math #0
11 Answer Ke Testname: AATM131BLIF33 1) A ) A 3) D ) A ) D ) C 7) A ) C 9) A ) A 11) B 1) A 13) B 1) A 1) C 1) C 17) D 1) A 19) C 0) A 1) D ) B 3) A ) B ) A ) A 7) D ) A 9) A 30) A 31) B 3) B 33) B 11
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