MATH 60 Review Problems for Final Exam


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1 MATH 60 Review Problems for Final Eam Scientific Calculators Onl  Graphing Calculators Not Allowed NO CLASS NOTES PERMITTED Evaluate the epression for the given values. m 1) m + 3 for m = 3 2) m 2  n2 m  n for m =, n = ; Find the value(s) of the variable for which the rational epression is undefined. 4 3) r  9 4) Simplif the epression ) + 6) 6  m m  6 Simplif the rational epression k2 7) k24k  21 Find the product and simplif. z3 8) 20z 3z2 9) ) ( )
2 Solve the problem. 11) A square shaped pasture has a side of length meters meters Epress the perimeter of the pasture as a rational epression. Subtract the rational epressions and simplif, if possible ) Perform the indicated operation and simplif the result, if possible. 13) Find the LCD of the given rational epressions. 1 14) r2 + 18r + 81, 1 r2 + 9r 1) 6 8, 3 2 Write an equivalent rational epression with the given denominator. 16) 8 m with denominator 4m 3 17) with denominator Identif the LCD and then write each as an equivalent rational epression with that denominator. 3 18) 74 ; ) p p22 ; 4 p + Perform the indicated operation. Simplif if possible. 20) )
3 Simplif the comple rational epression. 3p ) p ) Solve the equation and state the solution set. 24)  = ) 2 t = t t  12 Solve the equation for the indicated variable. A 26) P = for t 1 + rt Solve. 27) On an architect's blueprint, 1 inch corresponds to 6 feet. If an eterior wall is 4 feet long, find how long the blueprint measurement should be. Write answer as a mied number if necessar. List the intercepts of the graph. 28)
4 Solve the problem. 29) The graph below shows the height, in feet, of a ball thrown straight up with an initial speed of 96 feet per second from an initial height of 112 feet after t seconds. 20 (3, 26) (0, 112) At what time is the height a maimum? What is the maimum height? Identif the domain and range of the relation. 30) {(4, 13), (3, 6), (0, 3), (3, 6), (, 22)} Use the graph of the relation to identif the domain and range. 31) = Identif the domain and the range of the relation from the graph. 32) Determine whether the equation is a function. 33) = ) = 2 4
5 Determine wheter the graph is that of a function. 3) Graph the function. 36) h() = ) g() =
6 The graph of a function f is given. Use the graph to answer the question. 38) For what numbers is f() = 0?   Find the domain of the function. 1 39) h() = Solve the problem. 40) David recentl switched to a long distance phone compan which charges a monthl fee of $8.4 plus $0.04 per minute. A linear function that epresses the monthl bill B as a function of minutes used m is B(m) = 0.04m What are the independent and dependent variables? Solve the compound inequalit. 41) Solve the compound inequalit. Epress the solution using interval notation. Graph the solution set. 42) 8 < 24 and + 8 > 6 Solve the inequalit. Graph the solution set, and state the solution set in interval notation. 43) + 6 > 18 44) < 3 Simplif the radical. 4) 4 t4 6
7 Rewrite the epression with a positive rational eponent. Simplif, if possible. 46) 3 47) 9 ( + )2 48) (1623/2) 1/2 Simplif the radical epression. Assume that all variables represent positive real numbers. 49) 8 24 Simplif b factoring out the given factor. 0) 2k4 + k8; k8 Use the product rule to multipl. Assume all variables represent positive real numbers. 1) Use the product rule to simplif the epression. Assume that the variables can be an real number. 2) 20k7q8 Simplif the epression. 3) Use the quotient rule to divide and simplif. 4) Multipl, and then simplif if possible. Assume all variables represent positive real numbers. ) ( ) 2 Rationalize the denominator. Assume that all variables represent positive real numbers. 6) 98 Rationalize the denominator and simplif. Assume that all variables represent positive real numbers )  1 Complete the square for the binomial. Then factor the resulting perfect square trinomial. 8) 27
8 Solve the equation. 9) = 0 60) = 0 Determine the discriminant of the quadratic equation. Use the value of the discriminant to determine whether the quadratic equation has two rational solutions, two irrational solutions, one repeated real solution, or two comple solutions that are not real. 61) = 0 62) = 36 Solve the problem. 63) The length of a rectangular storage room is 6 feet longer than its width. If the area of the room is 91 square feet, find its dimensions. Eplain how to obtain the graph of the given quadratic function from the graph of = 2. 64) f() = (  8)27 Sketch the graph of the quadratic function. Identif the verte and ais of smmetr. 6) f() = Eplain how to obtain the graph of the given quadratic function from the graph of = 2. 66) f() = 4(  9)2 Epress the function in the form f() = a(  h)2 + k and indicate the verte. 67) f() =
9 Graph the quadratic function. 68) f() = Solve the inequalit. Graph the solution set and write the solution set in seṯ builder notation. 69) (  7)( + 3) > ) ) ) Find the distance d(p1, P2) between the points P1and P2. 73) P1 = (4, 4); P2 = (1, 16) Find the midpoint of the line segment formed b joining the points P1 and P2. 74) P1 = (3, 9); P2 = (3, 7) 9
10 Find the center and radius of the circle whose graph is shown. Write the standard form of the equation of the circle. 7) 8 6 (3, 3) 4 (2, 3) Write the standard form of the equation of the circle whose radius is r and whose center is (h, k). 76) r =9; (h, k) = (0, 7) 77) r = ; (h, k) = (1, 0) Find the standard form of the equation of the circle. 78) Center at (3, ) and containing the point (7, 1). 79) Center at (2, 6) and tangent to the ais. Graph the circle whose radius is r and whose center is (h, k). 80) r = 2; (h, k) = (4, ) Find the center (h, k) and the radius r of the circle. 81) = 0
11 Solve the sstem of linear equations. 82)  7 = = 1 83) = 42 = 21 6 Solve. 84)  z = = z = 18 8)  + z = z = z = 2 Determine if the sstem is dependent, inconsistent or has a unique solution. If it has a solution, state the solution. 86) 2  = = ) + = 4  = 12 11
12 Answer Ke Testname: SOLNSAMPLENEW 1) 1 2 ; undefined; 3 2 2) 0; undefined; 8 7 3) r = 9 4) 0, 8, 2 ) 9 6) 1 7)  k + 7 k + 3 8) ) 4 ) ) 12) meters ) ) r(r + 9)2 1) ) 32m 2 4m ) ) 19) 1 34 ; p (p + )(p  ) ; 4p  20 (p + )(p  ) 20) ) 22) ) ( + 4)(  4) ) {17} 2) {4, 6} 26) t = A  P Pr 27) 9 in. 28) (0, 4), (4, 0) 29) 3 seconds; 26 feet 30) domain: {4, 3, 0, 3, } range: {13, 6, 3, 22} 31) domain: { is a real number} range: { 1 < } 32) Domain: (, ) Range: [4, ) 33) function 34) not a function 3) function 36) 37) ) 3, 3., 39) { } ) The independent variable is m; the dependent variable is B 41) [6, 4] 42) (2, 3)
13 Answer Ke Testname: SOLNSAMPLENEW 43) (, 24) (12, ) 44) (3, 3) ) f() = 7( + 1)22 verte: (1, 2) 68) 4) t 46) 1/ ) ( + )2/9 48) 43/4 49) 3 0) k8(2k4 + 1) 1) ) 2k3q4 k 3) ) 3 3 ) ) 7 2 7) + 1 8) = (  )2 9) {,  8} 60) {  4i,  + 4i} 61) Two irrational solutions 62) Two irrational solutions 63) 7 feet b 13 feet 64) Take the graph of = 2 and shift it 8 units to the right and 7 units down. 6) verte (0, 1) ais of smmetr: = ) { <3 or > 7} ) { 1 4} ) { 3 or 1} ) ) 13 74) 0, ) r = ; (h, k) = (3, 3); ( + 3)2 + (  3)2 = 2 76) 2 + (  7)2 = 81 77) ( + 1)2 + 2 = 0 78) ( + 3)2 + ( + )2 = 2 79) ( + 2)2 + (  6)2 = ) Take the graph of = 2 and shift it 9 units to the right and verticall stretch it b a factor of 4 13
14 Answer Ke Testname: SOLNSAMPLENEW 80) ) (h, k) = (2, 4); r = 2 82) (, 0) 83) (6, 8) 84) (2, 7, 9) 8) (4, 1, ) 86) Inconsistent: no solutions 87) Unique solution: (8, 4) 14
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