Revised: 10/28/13 1 BOROUGH OF MANHATTAN COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS Practice Problems for the MAT 056 Departmental Final Form Q The actual final exam will have 20 questions. Please do not assume that the content or difficulty level of these practice questions are exactly the same as the actual examination. We suggest you study the range of topics described on the syllabus as well as the types of problems on this sample test. 1. Simplify: 2. Solve for p: prsprS 2 3. Solve the following equation: 4. Solve for a) b) c) 5. Solve the following absolute value inequality and graph your solution set: a) 14522 x b) Write solution in interval notation. 6. Solve the following equation be sure to check the solutions: 7. Solve for : 8. Write down a quadratic equation that has roots: { } 9. Find the and intercepts of the line2045  yx, then graph the line. 10. What is the equation of the line that passes through the point (1 , 1) and is perpendicular to the line632  yx? 11. What is the equation of the line that passes through the point  1,4  and is parallel to the line545  yx? 12. What is the slope of the line expressed by the equation x2y8 1 13. Subtract the following complex numbers. Then, write the answer in standard form: )2()43( ii  (Hint: leave answer inbia  form) 14. Multiply the complex numbers and then write the answer in standard form: (4+2i)(5–3i) 15. Simplify. Express the following as a single fraction in simplified form: a) abab11 b) yxxyyx2211 c) 1 1x  21 –3x  2 16. Solve for x. Express the answer in simplified radical form if possible: a) 0611152 xx b) 17. Simplify the following. Express your answer using only positive exponents. a) 252433qpqp b) 321232)2()6(yxyx 18. Solve the inequality – (a+1)–4 < 2a –8. Graph solution on the number line. 19. Solve the system of equations –6x – 10y  203x  5y  25Revised: 10/28/13 2 25 20. Michael has $1.85 in dimes and Nickels. He has a total of 25 coins. How many of each does he have? 21. Simplify the following completely: a) 5432 b) 234)16(y 22. Solve for x: a) 3x 10  x b) 23. Express 23 – 1as an equivalent fraction with a rational denominator in simplified form. 24. Rationalize the denominator in the expression: a) 3232 b) 32x 25. Find the quotient. Express your answer in a + bi form: ii5252 26. Find the sum or difference and simplify your answer completely: a) 121xxx b) 965222 xxxx c. 15211 xxx 27. Divide and simplify your answer completely: 1252384163722222xxxxxxx 28. Write the expression “zyxbbblog2log41log5 ” as a single logarithm. 29. Find the exact value of150tan 30. Find the length of side c in a triangle labeled ABC, if a = 6 cm, b =10 cm and C = 60. 31. A student stands at ground level, 600 feet away from a building. When she looks up to the top of the building, she finds that the angle of elevation in 60. What is the height of the building? Express your answer in the simplest radical form. 32. Solve)31(log27y by writing it in exponential form first. 33. Solve the following logarithmic equation: 34. If 53sin and  terminates in quadrant II, findtan. 35. Given that sin(25) 0.4266, cos(25) 0.9063, and tan(25) 0.4663, find the length of the side labeled x in the triangle below: 16cm xRevised: 10/28/13 3 y ANSWER KEY for MAT 056 Practice Final Exam Form Q 1. 2. 3. 4a. x = 4b. no solution 4c. x = 5a. ; intervals ] [ -6 1 5b. 2 ; interval (-1,2) ( ) -1 2 6. x 7. x = , 5 8. Any multiple of: 9. x-intercept is y-intercept is 10. 11. 12. 13. 14. 15. a. b. c. 16. a. b. 17. a. b. 18. [ 1 19. no solution 20. 12 dimes and 13 nickels 21. a. 16 b. 22. a. b. i.e. 6 does not check) 23. 24. a. b. 25. 26. a. b. c. 27. 28. 29. 30. 31. ft. 32. 33. 34.