Name: Exam Date:MAT104 – College Algebra with Trigonometry I Practice Exam #2: Chapter 1Directions: 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. Find all real number solutions: 3 14 3 12x x- =2. Find all real number solutions: (1 2 ) (2 1)( 2)x x x x+ = - -3. Find all real number solutions:61 5xx=-. Check your result(s). checkMAT104 Practice Exam for Chapter 1 - Page 1 of 84. Find all real number solutions:5 833 3xx x++ =+ +. Check your result(s). check5. Solve the formula ( )5932C F= - for F. 6. The suggested list price of a new car is $18,000. The dealer’s cost is 85% of list. How much will you pay if the dealer is willing to accept $100 over cost for the car?7. Find all real number solution of 23 5 2 0x x+ - = by factoring.8. Find all real number solution of ( )21 3x + = by extraction of roots.9. Find all real number solution of 26 11x x- = by completing the square.MAT104 Practice Exam for Chapter 1 - Page 2 of 810. Find all real number solution of 21.3 1.5 2.8x x+ = by using the quadratic formula. Round your answer to three decimal places.11. Use the discriminant to determine the nature of the solutions of 23 1 5x x+ = in the real number system.12. The area for a patio is to be 270 square feet. If the width is to be three feet more than the length, what are the patio dimensions?13. An object is thrown from the top of a building 1280 feet tall with an initial velocity of 32 feet per second. The distance s (in feet) of the object from the ground after t seconds is21280 32 16s t t= - -a. What will the height of the object be after 4 seconds?b. When will the object strike the ground?14. Perform the operation in the complex number system: 2(1 ) 3(2 3 )i i+ - -MAT104 Practice Exam for Chapter 1 - Page 3 of 815. Perform the operation in the complex number system: 52 i-16. Perform the operation in the complex number system: 50i17. Perform the operation in the complex number system: 21i-18. Perform the operation in the complex number system: 3(2 3 )i+19. Solve in the operation in the complex number system: 281 0x + =MAT104 Practice Exam for Chapter 1 - Page 4 of 820. Solve in the operation in the complex number system: 22 5x x- =-21. Use the discriminant to determine the nature of the solutions of 22 1 2x x+ = in the complex number system.22. Find all real number solutions: 4 24x x=23. Find all real number solutions: 4 25 4 0x x- + =24. Find all real number solutions:2 3 3x x- + =. Check your result(s). checkMAT104 Practice Exam for Chapter 1 - Page 5 of 825. Find all real number solutions:42 3 2x + =. Check your result(s). check26. Solve 3 32 612x-� <. Express your answer in interval notation and graph the solution set.graph interval notation 27. Going into the final exam, which will count as two tests, Amy has test scores of 90, 86, 84 and 80. What score does Amy need on the final exam to earn at least a B, an average score of 80 or more?28. Find all real number solutions: 1 2 1 4x- + =MAT104 Practice Exam for Chapter 1 - Page 6 of 829. Solve 2 3 2 9x- + >. Express your answer in interval notation and graph the solution set.graph interval notation 30. Solve 1 2 8x- �-. Express your answer in interval notation and graph the solution set.graph interval notation Good luck on the Chapter 1 exam!Practice Exam #2 Answer Key1. 15x =16. 1-( )50 2Recall that remainder when 50 4i i= �s2. 13x =17. i- (Don’t forget to rationalize the denominator)MAT104 Practice Exam for Chapter 1 - Page 7 of 83. 6x = (Don’t forget the check )18. 46 9i- +4. no solution or � (Don’t forget the check as3x =-is extraneous )19. 9x i=�5. 9532F C= +20. 1 2x i= �6. You will pay the dealer $15,400 for the car. 21. There will be two complex number (not real) solutions as the discriminant of –4 is less than zero; the solutions will be complex conjugates.7. 132,x x=- =22. 0, 2x x= =�8. 1 3x =- �23. 1, 2x x=� =�9. 3 2 5x = �24. 2x = (Don’t forget the check as 6x =is extraneous )10. 2.154, 1x x�- =25. 132x =11. There will be two unequal real number solutions as the discriminant of 13 is greater than zero.26. 23 7x- < �-; graph:interval notation: (]23, 7- -12. The patio’s width is 18 feet and its length is15 feet.27. Amy needs an seventy or higher to earn at least a B.13. a. The height of the object 4 seconds after being thrown is 896 feet. b. The object will strike the ground 8 seconds after it is thrown.28. 1, 2x x=- =14. 4 11i- +29. 53 or 3x x<- >; graph:interval notation: ( )( )53, 3,-�-ȥ 15. 2 i+ (Remember to simplify.) 30. no solution or � MAT104 Practice Exam for Chapter 1 - Page 8 of