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1 Fall 018 Preview Exam Math 110 This is only provided to you are a resource to help you practice and prepare for an upcoming exam. It is not a contract of inclusion and/or exclusion. You are still responsible for all material coveredin class. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the Add or subtract. Write the answer in lowest terms. 1) 7 r + 9 r - r - 1 r( - r) 1r - r(r - ) 1r - r( - r) r - 1 r(r - ) ) m m m m - m - 10m m + m - m - 10m m - m - m - 10m m - m - m - m m - m - m - 10m Solve the problem. ) Find an expression that represents the perimeter of the rectangle. Give the simplified form. 1k + 1 k k + 10k + 19 (k + 7) 7k + 10k + 19 (k + 7) 7k + 10k + 17 (k + 7) ) Find an expression that represents the area of the rectangle. Give the simplified form. 10p - p - "... the great enemy of the truth is very often not the lie deliberate, contrived, and dishonest but the myth persistent, persuasive, and unrealistic.... We enjoy the comfort of opinion without the discomfort of thought." ~~ John F. Kennedy,19 1

2 Simplify the complex fraction. 17 ) ) 8 y y + y + 8y (y + ) y 8y(y + ) y (y + ) 7) r r r r + r r - r r r - r Provide an appropriate response. 8) Which of the following complex fractions is equivalent to ? Solve the equation. 9) 9x + x = ) m + m + m + - m + m + 9 = m - m + m + {} {} {-} {-0}

3 Solve the formula for the specified variable. 11) 1 a + 1 b = 1 c for c c = a + b c = a + b ab c = ab a + b c = ab(a + b) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the Provide an appropriate response. 1) Without multiplying by the least common denominator and solving, explain why the rational equation x x - = has no solution. (Hint: Examine both numerators and denominators carefully.) x - MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the Solve the problem. 1) The difference of the reciprocals of two consecutive integers is 1. Find the integers. 7 and 8 or -7 and -8 8 and 9 or -8 and -9 8 and 9 or -8 and -9 and 7 or - and -7 1) The numerator of a fraction is times the denominator. If 1 is subtracted from the numerator, and added to the denominator, the resulting fraction is equal to. What was the original fraction (not written in lowest 7 terms)? ) A quantity, of it, 1 of it, and 1 7 of it, added together, equals 1. What is the quantity? ) A jet plane traveling at a constant speed goes 100 mi with the wind, then turns around and travels for 1000 mi against the wind. If the speed of the wind is 0 mph and the total flight took hr, find the speed of the plane. 0 mph mph 0 mph mph

4 Find the square root. 17) Not a real number Identify the given number as "Rational", "Irrational", or "Not a real number". If the number is rational, give its exact value. If the number is irrational, give a decimal approximation to the nearest thousandth. 18) 10 Irrational, Not a real number Rational, 11.8 Irrational, 11.8 Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator. 19) (-18) Find the root. 0) 1 Not a real number Simplify the expression. 1) Simplify the radical. Assume that all variables represent nonnegative real numbers. ) c 1 d 8 c d 8 c d c 1 d 8 c d Simplify the radical. ) ) k k k9 k k

5 Simplify and add or subtract wherever possible. ) ) ) Perform the indicated operations and express the result in simplest form. 8) ( - (-)) + (-17-7) Rationalize the denominator. Assume that all variables represent positive real numbers. 9) p p p p p 1 p p 0) a 1a a a 9 Provide the proper response. 1) Which one of the following would be an appropriate choice for multiplying the numerator and the denominator of in order to rationalize the denominator? SHORT ANSWER. Write the word or phrase that best completes each statement or answers the ) Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression 7 is to multiply both the numerator and denominator of by 100.

6 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the Simplify the expression. ) (10 + )(7 + 7 ) Simplify the radical expression. Assume that all variables represent nonnegative real numbers. ) ( 7t + r) 9t + 7tr + r 9t + 7tr + r 7t + 7tr + r 7t + 7tr + r Rationalize the denominator. Write the quotient in lowest terms. ) k - ( k - ) k + ( k + ) k + ( k + ) k - ( k + ) k - SHORT ANSWER. Write the word or phrase that best completes each statement or answers the Provide an appropriate response. ) Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression is to multiply both the numerator and denominator by +. - MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the Solve the equation. 7) x = -10 {0} {100} {-100} 8) x = 9x ) x x = {-} { 1, -} {0} {, -} Solve the problem. 0) A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 1 feet and the height from the ground to the front doors is feet, how long is the ramp? 1. ft 0. ft.7 ft.0 ft

7 If necessary, write the equation in the standard form ax + bx + c = 0. Then identify the values of a, b, and c. Do not actually solve the equation. 1) -x - x + 1 = 0 a = 1, b =, c = - a =, b =, c = 1 a = -, b = -, c = 1 a =, b = -, c = 1 ) (x- ) = a = -, b = -8, c = 18 a = 1, b =, c = 1 a = -1, b = 8, c = -1 a = 1, b = -8, c = 1 ) (x- )(x - 9) = 0 a = 1, b = -1, c = a = 1, b = -1, c = - a = 1, b = 0, c = a = 0, b = 1, c = ) (7x + )(9x - ) = x(x + ) a =, b = 11, c = - a =, b = 0, c = a =, b = 10, c = - a = -, b =, c = - Use the quadratic formula to solve the equation. Simplify any radicals. ) p - 1p + 9 = 0 {7} {0, 7} {± 7} {0, 1} ) 1k + k + 1 = 0 {± 1} {0, 1} ± ) a + 1a - 1 = 0 {1,-1} {± 7} {0,-1} {-1, 1} 8) m - m = 0 -, 0 ±, 0 9) x = 7 - x {-1 ± 11} {- ± 11} {- ± 11} { + 11} 0) y + 19y + 1 = 0,- - 1, - 1, -, - 7

8 1) x - x + 7 = 9x + 8 ± 1-1 ± 1-8 ± 1 1 ± 1 ) x - x + = 0 1 ± 7 1 ± 7 {1 ± 7 } Solve the equation. Express radicals in simplest form. ) x 10 + x + 10 = 0 {-10 + } {- ± } { ± } { + } ) y + 1 = 7 y - 1, - 1 1, 1, 1, 1 ) 1 x + 1 x - 1 = 0 -, {-1} -1 ± 17 ) 1 m = - 1 m + 1 -, -1 -, 1 7) 0.1x - 0.x = 0.9 {1 + 10} {- 10} {1 ± 10} { ± 10} 8) 0.1x - 0.x = 0. {1 ± } {- } { ± } {1 + } 9) 0.m + 0.m + 0. = 0 - ± - ± 1 - ± - ± 0) 0.m + 1.m = 0 - ± 8-1 ± - ± - ± 8

9 Answer Key Testname: PREVIEWEM110F18 1) B ) B ) B ) A ) A ) B 7) C 8) B 9) A 10) C 11) C 1) Since the denominators are the same, the numerators must be the same. Then x = ; but this value of x makes the denominators 0, so the equation has no solution. 1) A 1) C 1) D 1) C 17) D 18) D 19) D 0) B 1) B ) B ) C ) A ) B ) B 7) D 8) B 9) C 0) B 1) A ) False. The correct answer is to multiply numerator and denominator by 10 in order to make the denominator the cube root of a perfect cube. ) B ) C ) D ) True. Multiply numerator and denominator by the conjugate of the denominator, +, so that, by using the product of the sum and difference of two numbers, the "middle term" of the product is zero. 7) A 8) B 9

10 Answer Key Testname: PREVIEWEM110F18 9) A 0) A 1) C ) D ) A ) C ) A ) D 7) A 8) D 9) C 0) D 1) D ) D ) B ) C ) D ) D 7) C 8) A 9) C 0) C 10