Math 100 Final Exam PRACTICE TEST Solve the equation. 1) 9x + 7(-3x - 3) = -31-2x A) 1 B) 5) -5 x A) [0, 8] D) - 1 B) (0, 8)

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1 Math 0 Final Eam PRACTICE TEST Solve the equation. ) 9 + 7(-3-3) = ) [0, 8] (0, 8) Solve. ) (000 - ) = 0. {30} {300} {0} {0} [, -] Solve the investment problem. 3) Mardi received an inheritance of $0,000. She invested part at 8% and deposited the remainder in ta-free bonds at %. Her total annual income from the investments was $0. Find the amount invested at 8%. $0,000 $9,000 $,900 $,000 Solve the inequalit, giving its solution set in both interval and graph forms. ) -3 9 [-3, ) (-, -3] [3, ) (-, -3) (, -) For the compound inequalit, give the solution set in both interval and graph forms. ) - or (-, ) (-, -] [, ) [-, ] (-, ) Epress the set in simplest interval form. 7) (-8, 9] (-, ) (-8, ) (-8, 9] (-, 9] [-, 9] 8) (-7, ) [-3, ] (-7, -3] [-3, ) [-3, ] (-7, ]

2 Solve the given equation or inequalit. If an equation is given, then write the solution set in set notation. If an inequalit is given, then write the solution set in interval notation. (-, 0); (0, ) 9) = no solution 0, 0 -, 0 Find the - and -intercepts. Then graph the equation. ) - 8 = 8 (, 0); (0, -) Find the slope of the line through the pair of points. ) (9, -3) and (-, 3) - - Find the slope of the line. ) (-, 0); (0, ) (, 0); (0, -) - - -

3 3) Write the equation in slope-intercept form, state the slope and -intercept, and graph the equation. 7) - = -0 = - - ; slope: -, -intercept (0, - ) Undefined - -8 ) = - ; slope:, -intercept (0, - ) Undefined = - + ; -8 Decide whether the pair of lines is parallel, perpendicular, or neither. ) The line through (-0, ) and (-, 7) and the line through (-, ) and (7, ) Parallel Neither Perpendicular ) = and + 8 = 3 Perpendicular Neither Parallel slope: -, -intercept (0, )

4 = + ; slope:, -intercept (0, ) Find an equation of the line satisfing the conditions. Write the equation in slope-intercept form ) Through (-3, 8); perpendicular to -3 + = -3 = = 3 + = = Graph the compound inequalit. 9) - > and

5 0) < + or < Decide whether the relation is a function. ) {(-, -8), (-, 9), (-, -), (-, 7)} Function Not a function Give the domain and range of the relation. ) {(, ), (, ), (8, -), (-7, ), (, -3)} Domain: {, -, -3,, }; Range: {,, 8,, -7} Domain: {, -, 8,, -7}; Range: {, -, -3,, } Domain: {,, 8,, -7}; Range: {, -, -3,, } Domain: {, 8,, -7}; Range: {, -, -3,, } Decide whether the relation is a function, and give the domain and range. 3) Function; domain: (-, 3] ; range: (-, ) Not a function; domain: (-, 3] ; range: (-, ) - ) Not a function; domain: (-, ); range: (0, ) Function; domain: (-, ); range: (0, )

6 Solve the problem. ) Find f(-) when f() = ) Find f(k) when f() = k + k + 9k + k + 3k + k + 3k + k + Decide whether the ordered pair is a solution of the given sstem. 7) (-, -) 3 + = + 3 = Yes No Solve the sstem b substitution. 8) + 7 = = 3 {(-, 3)} {(3, 7)} {(, -)} {(7, )} Solve the sstem b elimination. If the sstem is inconsistent or has dependent equations, sa so. 9) + 7 = = -8 Inconsistent: no solutions {(, -3)} {(-3, -3)} {(-, -)} Appl the product rule for eponents, if possible. 30) (-3)(-) Evaluate the epression. Assume all variables represent nonzero numbers. 3) Appl the quotient rule for eponents, if applicable, and write the result using onl positive eponents. Assume all variables represent nonzero numbers. - 3) Simplif the epression. Write our answer with onl positive eponents. Assume that all variables represent nonzero real numbers. 33) (-3) Simplif the epression so that no negative eponents appear in the final result. Assume all variables represent nonzero numbers. 3) r 3(r) 3 (r) r r Combine terms. 3) q3 - q + q + q - q3 q + q3 + q -9q8 - q + q 9q + q3 - q -9q - q3 + q Add or subtract as indicated. 3) ( ) - ( ) r r

7 For the given polnomial function, find the requested value. 37) f() = ; find f(-) Find the product. Divide ) ( ) ) (-7 + )(- - + ) ) (7 - ) ) ) Use long division to find (9z - z3 + z + z + 7) (z - z + ) z - 9 9z - 3z + + z - z + -z + 9 9z + 3z - + z - z + 9z + 3z - z - 9 9z + 3z - + z - z + Factor out the greatest common factor. ) ( ) ( ) ( ) ( ) ) m( - m) + 7n( - m) m( + 7n)( - m) (m - 7n)( - m) (m + 7n)( - m) (m + n)( - m) Factor b grouping. ) 0r + r - 8r - 9 (8r + 9)( - r) (8r + 9)( - r) (8r + 9)(r - ) (9r + 8)(r - ) ) Factor the trinomial completel. 7) + - ( - )( + ) ( + )( - ) ( - )( + ) Prime ) + + (3 - )( - 3) (3 + )( + 3) ( + )( - ) ( + )( + 3) Factor the polnomial completel. 9) 3k - m (k + m)(k - m) (k - m) (3k + m)(k - m) (k + m) 7

8 0) m + m + (m - ) (m + )(m - ) (m + ) Prime ) ( + )(3 + ) ( - )(3 + + ) ( + )(3 - + ) ( + )( - + ) ) 8a3-7b3 (a + 3b)(a - ab + 9b) (a - 3b)(a + ab + 9b) (a - 3b)(a + 9b) (a + 3b)(a - ab + 9b) Find all solutions b factoring. 3) - = - -8, - -8,, 8 {8, } Write the rational epression in lowest terms. 7) m - 9m 9 - m Alread in lowest terms m + 3 -m m Perform the indicated operation and epress in lowest terms. 8) k + 9k + k + 3k + k + k k - k - k + k k - 7 k - 7 9) z + z + 9 z + z + z + 7z z + z + k k + 3k + k k - 7 z + 8 z + 8 z z z + z + z + 8 z + 8z ) ( + )( + ) = -3 {-9, } {-7, -9} {, -} {-, -3} Find all numbers not in the domain of the function. - ) f() = + - 8, -8 7, , 3 Epress the rational epression in lowest terms. ) ) 3 r + r + ) ) 7r + r(r + ) -r - 7 r(r + ) r + r(- - r) -r - 7 r(- - r)

9 Simplif the comple fraction. 3) Solve the equation. ) + = - ) {-} {} {-} = ,, - 3, { is a real number } { -, } Solve the problem. ) A formula for electric circuits is a = b +. If a = 8 and b = 9, find c. c Solve the formula for the specified variable. 7) PV T = pv for P t P = pvv tt P = pv ttv P = pvt tv P = tvt pv Simplif the root. 9) Simplif the epression involving rational eponents. 70) /3 7) 78,, 3 -/ Not a real number Write with radicals. Assume that all variables represent positive real numbers. 7) (m + k) / m + k m + k m + k m + k Use the rules of eponents to simplif the epression. Write the answer with positive eponents. Assume that all variables represent positive real numbers. 73) (3km) / km 3km k m 3k m 8) S = πrh + πr for h h = π(s - r) h = hs - r h = S πr - h = S - πr πr 7) / 3/ -3 7/ / 7/ / 9

10 Multipl using the product rule. Assume all variables represent positive real numbers. 7) Epress the radical in simplified form. 7) 78 Simplif. Assume that all variables represent positive real numbers. 8) 3 - (3 - ) Cannot be simplified Epress in simplified form. Assume that all variables represent positive real numbers. 77) 8 83) ) Simplif the radical. Assume that all variables represent positive real numbers. 79) Perform the indicated operations and simplif. Assume that all variables represent positive real numbers. Multipl, then simplif the product. Assume that all variables represent positive real numbers. 8) (3 + 3) Rationalize the denominator. Assume that all variables represent positive real numbers. 8) Simplif. Assume that all variables represent positive real numbers. 8) 80) )

11 Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. 87) 7 - Multipl or divide as indicated. 9) i -7i ) -0 - i -i Write the epression in lowest terms. Assume that all variables represent positive real numbers. 88) Add or subtract as indicated. Write our answers in standard form. 9) (7 - i) + ( + i) + i 3 - i 3 + i -3 + i ) ( + i) - (- + i) Solve the equation. 89) = i - + 7i 9 - i 9 + i {3} Multipl ) ( + i)(3-7i) 3-3i + 8i Solve this equation. 90) + 3 = - 3 Solve the equation. {} {, 3} {, } {, 3} 9) 3 + = {} {9} {} {-} Write the number as a product of a real number and i. Simplif the radical epression i -i - 3i + 8 Use the square root propert to solve the given equation. 99) -k + 8 = 0 {, -} {3} {3, -3} {-.} 0) (p + 8) = , , ) -9 i 7-7i 7i ± 7 93) i 3-3 i 3

12 Find the imaginar solutions of the given equation. ) = i, 3 - i , , i -3 - i, 8 8 Use the quadratic formula to solve the given equation. (Solutions are real numbers.) ) 3n = -8n , , , , 3 3

13 Answer Ke Testname: MTH0PRACTICETESTFINAL ) A ) C 3) A ) A ) A ) A 7) C 8) D 9) D ) A ) B ) B 3) D ) A ) B ) C 7) D 8) C 9) D 0) D ) B ) D 3) B ) B ) C ) A 7) B 8) C 9) D 30) C 3) D 3) D 33) D 3) C 3) D 3) B 37) C 38) D 39) D 0) D ) B ) B 3) B ) C ) C ) C 7) B 8) B 9) A 0) C ) C ) B 3) C 3 ) B ) D ) B 7) C 8) D 9) B 0) A ) B ) A 3) A ) A ) D ) A 7) B 8) D 9) D 70) B 7) B 7) D 73) D 7) D 7) C 7) D 77) A 78) A 79) C 80) C 8) A 8) B 83) C 8) D 8) A 8) A 87) A 88) B 89) C 90) A 9) B 9) C 93) B 9) D 9) B 9) B 97) D 98) A 99) C 0) B ) A ) B