MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 MAT 0 Fall 00 - Practice Test Dr. Schnackenberg MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the epression is rational. ) 6 ) No Yes Use the verbal representation of a rational function to find the symbolic representation. ) Add to and then divide the result by the quantity plus 0. ) Evaluate f() at the given value of by hand. ) f() = + 4 ; = - ) - - Solve the equation. 4) + = - 9 = - 9 No solution = - 4 = ) ) 4 - = + 4 ) =, -4 = = -, 4 = - 9 Solve the problem. 6) In the following formula, y is the minimum number of hours of studying required to attain a test 6) score of : y = 0.. How many hours of study are needed to score? hr 00. hr.6 hr 6.0 hr Simplify. ) - - )

2 Simplify the epression. 4 + ) ) Find the reciprocal. 9) + ( + ) ( + ) + 9) Simplify the epression. 0) k + k + 0 k + 9k + 0 k + 4k k - k - 0) k - 4 k k - 4 k + 4k k - 4 k k + 9k + 0 ) z + z + 0 z + z + z + z z + z + 4 ) z + 6 z + 6 z z z + z + z + 6 z + z Find the least common multiple. ) +, + ) + + ( + ) + Simplify. ) m m m - (m + ) m - 0 m - ) 4) ) ( + )( + 4) ( + )(4 + 4) + 4 0( + )( + 4) + 49 ( + )(4 + 4)

3 Solve the problem. ) The formula ) a = v - v t - t gives an object's average acceleration a when its velocity changes from v at time t to v at time t. Solve for t. t = a - t v - v t = v - v + t a t = v - v + at a t = v - v a - t Solve the equation. 6) - 9 = - 6) + = - = No solution = Solve the rational equation symbolically, numerically, or graphically. ) = = = = 6 = 0 ) Solve the formula for the specified letter. ) P = A for r ) + rt r = P - At r = A - P Pt r = P - A + t r = P - ta Solve. 9) Martha can rake the leaves in her yard in 4 hours. Her younger brother can do the job in 6 hours. 9) How long will it take them to do the job if they work together? hr 6 hr hr hr Divide and simplify. 6 0) 0)

4 Simplify the epression. r - - ) ) r - + r - r - r r - r r + r r Simplify the epression, using only positive eponents in your answer. ) -4 + y y- y4 + 4 y4 + 4y + y + y y y ) Solve the proportion. ) = 4 ) Write a proportion that models the situation described. Then, solve the proportion for. 4) is to, as is to 4) = ; = 6 = ; = = ; = 4 = ; = 6 Solve the problem. ) Suppose that y is directly proportional to and that y = 6 when = 6. Find the constant of ) proportionality k. Then, find y when =. k = ; y = 04 k = 6; y = k = 6; y = 6 k = - 6; y = - 6) Suppose that y is inversely proportional to and that y = when =. Find the constant of 6) proportionality k. Then, find y when =. k = 4; y = 6 k = 96; y = k = 4; y = k = ; y = 6 ) Suppose that z varies jointly with and y and that z = 00 when = 0 and y =. Find the ) constant of proportionality k. Then, find z when = and y = 6. k = 0.6; z = 0. k = 6; z = 0 k = 94,400; z = 000 k = ; z = 44 4

5 Determine whether the data represent direct variation, inverse variation, or neither. ) 4 y Inverse Direct Neither ) Solve the problem. 9) The intensity I of light varies inversely as the square of the distance D from the source. If the 9) intensity of illumination on a screen ft from a light is foot-candles, find the intensity on a screen ft from the light. foot-candles foot-candles 9 foot-candle 9 foot-candle If possible, evaluate the epression by hand. If not, approimate the answer to the nearest hundredth. 0) 96 0), ) -0 ) ) ( - 0)0 ) -( - 0)4 60( - 0)4 ( - 0)4 ( - 0)4 Write the epression using radical notation. ) 6/4 ) 64 Simplify the epression involving rational eponents. 4) 6/4 4) 6, ,4 6,6 If possible, evaluate the epression by hand. If not, approimate the answer to the nearest hundredth. ) () -/ ) - - Simplify the epression. Assume that all variables are positive. 6 -/ 6) y4 y y y y 6)

6 ) t z0 ) t z z t tz tz ) z/4(z/4 - z-/4) ) z/ - z z/ + z z - z/ z + z/ 9) ( + ) 9) + ( + ) Not a real number + Simplify the epression. If any variables are present, assume that they are positive. 40) 0 40) ) 64 z z 4) 4 Not a real number 4) 4) ) 04 4y y 4) y y 6 y y Use properties of polynomials to simplify the epression. 44) ) Solve the equation. 4) = 4) 9 6 Not possible 6

7 Simplify the radical epression by factoring out the largest perfect nth power. 46) 4 46) Simplify the radical epression by factoring out the largest perfect nth power. Assume that all variables are positive. 4) -64ab 4) 4 ab 4ab ab 4ab ab -4ab ab Simplify the epression. If any variables eist, assume that they are positive and write your answer in radical notation. 4) 4 4) 0 0, , ,000 49) 4 49) Rationalize the denominator. 0 0) 0) Simplify the epression. If any variables eist, assume that they are positive. ) ) 6 6 ) 4 m9p6 - mp 4 mp ) 9mp 4 mp mp 4 mp Cannot be simplified ) - ) 6-0 Multiply, then simplify the product. If variables are present, assume they are positive. 4) ( + 6)( + ) 4)

8 Rationalize the denominator. ) 6 - ) Evaluate the function at the given value of the variable. 6) f() = + + at = 4 6) 4 Find the domain of f. Write your answer in interval notation. ) f() = 6 + ) -, -, -, -, Solve the equation. ) = ) ± - 9) (6 - ) = 600 9), 0,, -, Solve the equation symbolically. 60) a - 6 = a ) 6) + = ) - -, -, No solution 6) = - 6) No solution - 0 Solve the formula for the indicated variable. S 6) r = for S 6) 4 S = 4 r S = 6 r S = 4 r S = r 4 Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. 64) a = 0, c = 6 64) b = b = b = 4 b =

9 Use the distance formula to find the distance between the two points. Unless specified otherwise, give your answer in eact form. 6) (, ) (-4, -) 6) Find if the distance between the given points is d. Assume that is positive. 66) (, 4), (-, ), d = 66) 6 Solve the problem. 6) The period, P, of a pendulum in seconds is given by the formula P = L, where L is the length 6) of the pendulum. Find P when the value of L is inches. Round your answer to the nearest hundredth..9 seconds 4. seconds. seconds.9 seconds 6) A formula for calculating the distance, d, that can be seen from an airplane to the horizon is 6) d =., where is the altitude of the plane in feet. Find d when the altitude is, feet. Round your answer to the nearest hundredth..6 feet 6.6 feet,. feet 6.6 feet 9