Name: Exam Date:MAT104 – College Algebra with Trigonometry I Practice Exam #1: Review ChapterDirections: The purpose of this packet is to provide you with the general scope and level of difficulty of the class exam. Complete each of the problems in this packet and check your answers with those provided at the end of the packet. You are encouraged to work in groups, see me for help during my office hours or seek help at our Tutoring Center. Remember that all answers should be fully simplified and in proper form. 1. List the numbers in the set { }210 , 0.65 , 7 , 3+ , 55p-that are:real numbers:irrational numbers:rational numbers:integersnatural numbers:2. Evaluate the expression ( )2 8 3 4 2 3� - + -� �� �3. Evaluate2 3x y- - for 5x =- and 7y =4. Evaluate 13135x y-for 5x =- and 27y =MAT104 Practice Exam for Chapter R - Page 1 of 95. Determine the domain of 15 8xx+-. Place your answer in interval and set notation.6. Determine the domain of 2 5x+ -. Place your answer in interval and set notation.For #7-9, express your answers so that all exponents are positive. Whenever an exponentis 0 or negative, assume that the base is not 0.7. Simplify: 0 3 42a ba b.8. Simplify: 22x yxy-.9. Simplify: 2323xy--� �� �� �.10. Write an inequality using an absolute value to describe the statement: x is more than 3 units from 5.MAT104 Practice Exam for Chapter R - Page 2 of 911. The weekly production cost C of manufacturing x calculators is given by the formula23000 61000xC x= + -. What is the cost of producing 2000 calculators?12. Find the side of a right triangle whose hypotenuse is 85 cm. and whose other leg is 36 cm.13. A statue with a circular base of radius 5 feet is enclosed by a circular pond whose width is2 feet. What is the exact area of the pond?14. Find the volume of a cylinder with a radius of 5 meters and a height of 6 meters. Round your answer to three decimal places.15. Find the surface area of a sphere with a radius of 7 feet. Round your answer to three decimal places.16. Identify the leading coefficient and the degree of the polynomial 5 44 3 12x x x- + - -.MAT104 Practice Exam for Chapter R - Page 3 of 92 f5 fleading coefficient:degree:17. Perform the operation: ( ) ( )3 2 3 28 3 4 4 7 2 3x x x x x x+ - + - - - +18. Perform the operation: ( )25 2x +19. Perform the operation: ( 1)( 3)( 5)x x x+ + -20. a. Divide using long division ( ) ( )3 2 24 2 1x x x- + - � -. b. Indicate if 21x -is a factor of the polynomial.21. a. Divide using synthetic division ( )( )51 1x x+ � +. b. Indicate if 1x +is a factor of the polynomial.MAT104 Practice Exam for Chapter R - Page 4 of 922. Factor completely over the integers: 2 218 12 6a b ab ab- + -.23. Factor completely over the integers: 24 12 9x x+ +.24. Factor completely over the integers: 280 5x -.25. Factor completely over the integers: 327 8x -.26. Factor completely over the integers: 3 22 3 4 6x x x+ + +.MAT104 Practice Exam for Chapter R - Page 5 of 927. Factor completely over the integers: 29 1x +.28. Simplify : 225 14 24x x xx x- - -�-29. Perform the operation and simplify: 2 23 4 2 34 4 4x xx x x+ -+- + +30. Perform the operation and simplify: 2215 612xx xxx-- ++-31. Perform the operation and simplify: 431 24xx++MAT104 Practice Exam for Chapter R - Page 6 of 932. Simplify 5 8 2 32-33. Simplify ( )25 2-For #34-36 assume that the exponents are positive and that x and y are positive.34. Simplify 32 510x xyy35. Simplify 3 7316x y-36. Simplify ( )32 123 325xy x-37. Rationalize the denominator: 45MAT104 Practice Exam for Chapter R - Page 7 of 938. Rationalize the denominator: 310239. Rationalize the denominator: 4 3 22 3 1++40. Factor the expression: ( ) ( )4 13 32 23 4 4 4 2x x x x+ + � + �Good luck on the Review Chapter exam!Practice Exam #1 Answer KeyMAT104 Practice Exam for Chapter R - Page 8 of 91. real numbers:{ }210 , 0.65 , 7 , 3+ , 55p- irrational numbers: { }27 , 3+p rational numbers: { }10 , 0.65 , 55- integers: { }10 , 55- natural numbers: { }5520. a. 4 1x- + with a remainder of 4 1x- - b. It is not a factor as there is a remainder.21. a. 4 3 21x x x x- + - + b. It is a factor as there is no remainder.2. – 2322. 6 (3 2 1)ab a b- - +3. 1123. ( )22 3x +4. – 2124. 5(4 1)(4 1)x x+ -5. interval notation:( ) ( )8 85 5, ,-�ȥ set notation: { }85x x �25. ( )( )23 2 9 6 4x x x- + +26. ( )( )22 2 3x x+ +6. interval notation:)5,��� set notation: { }5x x �27. prime (i.e. not factorable)28. 7xx- 7. 3 52a b29. 225 3 14( 2) ( 2)x xx x+ ++ - 8. 31x y30. 13xx-- 9. 6 49x y31. 4 ( 4)3( 8)x xx++ 10.5 3x - > (i.e. the distance from x to 5 is greater than 3) 32. 2 233. 9 4 5-11. The weekly production cost of producing 2,000 calculators is $11,000.34. xy 12. 77 cm35. 232 2xy y-13. The area of the pond is 24p ft2.36. 2125xy14. 471.239 m315. 615.752 ft2 37. 4 55 16. leading coefficient is -1 and degree is 517. 3 23 15 1x x x- + - +38. 35 418. 225 20 4x x+ +39. 219. 3 217 15x x x- - -40. ( ) ( )12 234 11 12x x+ +MAT104 Practice Exam for Chapter R - Page 9 of