MATH 91 Final Stud Package Name Solve the sstem b the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to epress the solution set. 1) - = 1 1) 3-6 = 1 ) + = 11 16 + = ) Solve the problem. 3) One number is 3 less than a second number. Twice the second number is 1 more than 3 times the first. Find the two numbers. 3) ) A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and soft drinks for $30.33. The second group bought 7 slices of pizza and 6 soft drinks for $8.96. How much does one slice of pizza cost? ) Solve the sstem b the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to epress the solution set. ) + = 1 ) + = -3 6) 7 + 6 = 3 - = - 6) Solve the problem. 7) Devon purchased tickets to an air show for 8 adults and children. The total cost was $. The cost of a childʹs ticket was $ less than the cost of an adultʹs ticket. Find the price of an adultʹs ticket and a childʹs ticket. 7) 8) How much pure acid should be mied with gallons of a 0% acid solution in order to get an 80% acid solution? 8) 9) The owners of a cand store want to sell, for $6 per pound, a miture of chocolate-covered raisins, which usuall sells for $3 per pound, and chocolate-covered macadamia nuts, which usuall sells for $8 per pound. The have a 60-pound barrel of the raisins. How man pounds of the nuts should the mi with the barrel of raisins so that the hit their target value of $6 per pound for the miture? 9) ) Julie and Eric row their boat (at a constant speed) 63 miles downstream for 7 hours, helped b the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current. ) Solve the sstem. If there is no solution or if the sstemʹs equations are dependent, so state. + + z = 8 11) - + z = 3 + + z = 0 11) 1
1) + + z = - - - z = 1 3 + 3 + 3z =-1 1) Find the domain and range. 13) {(9,3), (9,-7), (,8), (-,7), (-6,-6)} 13) Decide whether the relation is a function. 1) {(-, ), (-1, ), (, 9), (, 7)} 1) Find the indicated function value. 1) Find f(-) when f() = 3 + +. 1) 16) f() - -1-3 3 0 1 3 7 31 Find f(3) 16) Use the graph to find the indicated function value. 17) = f(). Find f( - ). 17) 3 1 - - -3 - -1 1 3-1 - -3 - - Find the domain of the function. 1 18) f() = + 3 18) Find the indicated function value. 19) f() = -, g() = -3 - Find (f + g)(-). 19)
Find the requested value. 0) f() = -3-7, g() = + Find (f - g)(-3). 0) Find the composition. 1) If f() = 7 + and g() = 3, find (f g)(). 1) ) If f() = 6 + and g() = +, find (g f)(). ) Find the inverse of the one-to-one function. 3) f() = 8-7 3) Find the function value indicated for the function. If necessar, round to two decimal places. If the function value is not a real number and does not eist, state so. ) Evaluate p() = - + 11 for p(-) ) Find the domain of the square root function. Graph of the function. ) f() = - ) Use radical notation to rewrite the epression. Simplif, if possible. 6) (-8)1/3 6) 7) (-6)/3 7) 8) 31/ + 161/ 8) Rewrite the epression with a positive rational eponent. Simplif, if possible. 9) 0-3/ 9) Simplif b factoring. 30) 600 30) 31) 3-7a11b 31) Multipl and simplif. Assume that all variables in a radicand represent positive real numbers. 3) 3) Add or subtract as indicated. You will need to simplif terms to identif like radicals. 33) 3 a + 3 6a 33) 3) - 18-8 - 3 00 3) 3
Multipl and simplif. Assume that all variables represent positive real numbers. 3) ( - )(6 - ) 3) 36) (9 7 - ) 36) Rationalize the denominator and simplif. 37) 3 37) Rationalize the denominator. 7 + 38) 7-38) Solve the equation. 39) - + 6 = + 6 39) 0) + 3 - + 1 = 1 0) Find each product. Write the result in the form a + bi. 1) 3i( - 6i) 1) Divide and simplif to the form a + bi. ) 6 + i 8-3i ) Find each product. Write the result in the form a + bi. 3) (9 + i)(7 - i) 3) Solve the equation b the square root propert. If possible, simplif radicals or rationalize denominators. Epress imaginar solutions in the form a + bi. ) 7 - = 0 ) ) ( - ) = -81 ) Complete the square for the binomial. Then factor the resulting perfect square trinomial. 6) + 9 6) 7) + 3 7) Solve the quadratic equation b completing the square. 8) + 1 + 17 = 0 8)
Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplif radicals and rationalize denominators. 9) V = s h for s 9) 3 Find the distance between the pair of points. Give an eact answer. 0) (, 3) and (-, -6) 0) Use the quadratic formula to solve the equation. 1) + 7 + 7 = 0 1) ) = -8-1 ) Solve the problem. 3) The length of a rectangular storage room is feet longer than its width. If the area of the room is 7 square feet, find its dimensions. 3) ) The area of a rectangular wall in a classroom is 198 square feet. Its length is feet shorter than three times its width. Find the length and width of the wall of the classroom. ) ) A ball is thrown downward with an initial velocit of 1 meters per second from a cliff that is 90 meters high. The height of the ball is given b the quadratic equation h = -.9t - 1t + 10 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 60 meters from the ground. Round our answer to the nearest tenth of a second. ) The graph of a quadratic function is given. Find the functionʹs equation. 6) 8 6 6) - -8-6 - - - 6 8 - -6-8 -
7) 8 6 7) - -8-6 - - - 6 8 - -6-8 - Sketch the graph of the quadratic function. Identif the verte, intercepts, and the equation for the ais of smmetr. 8) f() = + + 1 8) - - - - Determine whether the given quadratic function has a minimum value or maimum value. Then find the minimum or maimum value and determine where it occurs. 9) f() = - + - 8 9) Solve the equation b making an appropriate substitution. 60) - 13 + 36 = 0 60) 61) ( - 1) - 7( - 1) + = 0 61) 6) - - -1 + 3 = 0 6) 6
Graph the function b making a table of coordinates. 63) f() = 6 63) -6 - - 6 - - -6 Write the equation in its equivalent eponential form. 6) log 3 = 6) Write the equation in its equivalent logarithmic form. 6) 13 = 6) Evaluate the epression without using a calculator. 66) log 7 7 66) 67) log 1 67) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 68) logb(z8) 68) 69) log b z6 69) Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic epressions. 70) 8 ln - 1 ln 70) 71) ln a - 9 ln b 71) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 7) log 6 3 7) Solve the equation b epressing each side as a power of the same base and then equating eponents. 73) 3 = 1 81 73) 7
7) - = 8 7) 7) 3(1 + ) = 7 7) Solve the logarithmic equation. Give an eact answer. 76) log 3 + log 3 = 1 76) 77) log 3 ( + ) - log 3 = 77) 78) ln + ln( - 1) = 0 78) 79) log( + ) - log( - ) = log 79) Solve the problem. 80) The formula A = 11e0.031t models the population of a particular cit, in thousands, t ears after 011. When will the population of the cit reach 10 thousand? 80) Solve. 81) The value of a particular investment follows a pattern of eponential growth. You invested mone in a mone market account. The value of our investment t ears after our initial investment is given b the eponential growth model A = 300e0.09t. When will the account be worth $6683? 81) Write the standard form of the equation of the circle with the given center and radius. 8) Center (-6, -), r = 1 8) Give the center and radius of the circle described b the equation and graph the equation. 83) ( - 3) + ( - 1) = 83) - - - - 8
Find the standard form of the equation of the ellipse. 8) 8 6 8) - -8-6 - - - 6 8 - -6-8 - Find the vertices of the hperbola with the given equation. 8) 1-81 = 1 8) Determine whether the sstem is a nonlinear sstem or a linear sstem. - = 86) = + 11 86) Solve the sstem b the substitution method. = + 87) = 8 87) Solve the sstem b the addition method. 88) 3 + = 9 3 - = 9 88) Write the first four terms of the sequence whose general term is given. 89) an = n - 1 89) 90) an = (-)n 90) 91) an = n (n - 1)! 91) Find the indicated sum. 9) (i - ) 9) i = 93) i 93) i = 1 9
Find the common difference for the arithmetic sequence. 9) 8, 11, 1, 17,... 9) Write the first five terms of the arithmetic sequence with the given first term, a1, and common difference, d. 9) a1 = ; d = 9) Find the common ratio for the geometric sequence. 96) 1, -3, 9, -7, 81,... 96) Write the first four terms of the geometric sequence with the given first term, a1, and common ratio, r. 97) a1 = ; r = 97) Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation. 98) + - 6-8 - 11 = 0 98) - - - - Sketch the ellipse for the equation. 99) ( - 1) + ( + 1) = 1 9 99) - - - -
Use vertices and asmptotes to graph the hperbola. 0) 9 - = 36 0) - - - - 11
Answer Ke Testname: MATH 91 SAMPLE TEST NONMULTIPLE 1) {(-1, -3)} ) infinitel man solutions; {(, ) + = 11} or {(, ) 16 + = } 3) -1 and -1 ) $.86 per slice of pizza ) no solution; 6) {(-, 8)} 7) adultʹs ticket: $; childʹs ticket: $17 8) 7. gal 9) 90 pounds ) 1 mph 11) {(-,, )} 1) no solution or 13) domain = {-6, -, 9, }; range = {-6, 7, -7, 8, 3} 1) not a function 1) - 3 16) 7 17) 1. 18) (-, -3) or (-3, ) 19) -13 0) -3 1) 63 + 1 ) 6 + 9 3) f-1() = + 7 8 ) -3 ) domain of f: [, ) - - - - 6) - 7) 16 8) 1 9) 00 30) 6 31) -3a3b3 3 ab 3) 6 1
Answer Ke Testname: MATH 91 SAMPLE TEST NONMULTIPLE 33) 6 3 a 3) -9 3) 30-11 + 36) 71-36 7 37) 3 38) 9 + 1 39) {} 0) {3, -1} 1) 18 + 1i ) 36 73 + 0 73 i 3) 83-17i ) ± 3 7 ) { ± 9i} 6) 81 ; + 9 + 81 = + 9 7) 9 ; + 3 + 9 = + 3 8) {-6 ± 19} 9) s = 3Vh h 0) 130 units 1) ) -7 ± 1 - ± 3 3) ft b 1 ft ) width = 9 ft; length = ft ).6 sec 6) f() = ( + 3) + 3 7) f() = - + 1 13
Answer Ke Testname: MATH 91 SAMPLE TEST NONMULTIPLE 8) verte: (-3, ) -intercepts: none -intercept: (0, 1) ais of smmetr: = -3 - - - - 9) Maimum is - 7 at = 1. 60) {-,, -3, 3} 61) {3, 6} 1 6) 3, 1 63) 6-6 - - 6 - - -6 6) = 3 6) log 13 = 66) 1 67) 1 3 68) log b + 8 log b z 69) log b + log b - 6 log b z 70) ln 8 71) ln a b9 7) 0.6131 1
Answer Ke Testname: MATH 91 SAMPLE TEST NONMULTIPLE 73) {-} 7) {-3} 7) {1} 3 76) 77) 1 6 78) 79) {13} 80) 018 81) 9 ears after the initial investment 8) ( + 6) + ( + ) = 1 83) center (3, 1), r = - - - - 8) 9 + = 1 8) (-1, 0), (1, 0) 86) nonlinear sstem 87) {(, )} 88) {( 3, 0), (- 3, 0)} 89) 3, 7, 11, 1 90) -, 16, -6, 6 91) 1, 16, 81, 18 3 9) 0 93) 30 9) 3 9), 8, 1, 16, 0 96) -3 97),, 0, 0,... 1
Answer Ke Testname: MATH 91 SAMPLE TEST NONMULTIPLE 98) ( - 3) + ( - ) = 36 center (3, ), r = 6 - - - - 99) - - - - 0) - - - - 16