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Name: ____________________________ Math 990 Preparation for College Mathematics Fall 2012 Test 1 Form A Directions: Work the following problems neatly and completely and leave all your answers in simplest form. You may not use scratch paper. You must show all your work to get full credit. You may not use books, notes, cell phones, graphing calculator, or any other resource other than a scientific calculator when completing this test. Good luck!! Each problem is worth 5 points. 1. Solve the equation 4 x 9 11 2 x 2. Solve the equation. 15 x 4(3 x 4) 9 3. Solve the equation. 5x 3 x 2 4 3 4. Solve the equation. 0.56 x 6 0.2 x 12 5. Solve the equation for the indicated variable. C a D for a n 6. Solve the inequality and write the solution set in interval notation. 4 x 3 3x 11 7. Solve the inequality and write the solution set in interval notation. 3x 15 8. How many mL of a 10% acid solution must be mixed with 300 mL of a 50% acid solution to make a 40% solution. 9. Give the degree of the polynomial. a. 5 x 6 3 x 3 b. 9 p 4 s 5 7 p 2 s 10. Perform the indicated operations and then simplify. 8 x 2 4 x 3 3x 2 5 x 5 2 x 2 9 x 1 11. Divide the monomials. 48 x 6 y 3 4x3 y 12. Raise the monomial to the indicated power. ( 3 x 4 y 2 ) 3 13. Perform the indicated operation and then simplify. 3x 22 x 7 14. Perform the indicated operation and then simplify. ( x 3) 2 15. Perform the indicated operation and then simplify. (3x 5 y ) 2 16. Perform the indicated operation and then simplify. ( x 2)( x 3 2 x 2 5) 17. Perform the indicated operation and then simplify. ( x 4)( x 4) 18. Factor by grouping. 6 x 2 12 x x 2 19. Factor. 20 mn 2 28m 2 n 20. Factor. 4x 2 9 y 2 Name: ____________________________ Math 990 Preparation for College Mathematics Fall 2012 Test 2 Form A Directions: Work the following problems neatly and completely and leave all your answers in simplest form. You may not use scratch paper. You must show all your work to get full credit. You may not use books, notes, cell phones, graphing calculator, or any other resource other than a scientific calculator when completing this test. Good luck!! 1. (6 points each) Factor completely: (a) x 2 4 x 3 (b) 4n 2 12 n 9 (c) 3 x 2 7 x 6 2. (6 points) Solve the equation: a 2 5a 24 3. (6 points each) Perform the indicated operations and write your answers in lowest terms. 3x 4 y 3 x 4 (a) x 4 2 xy 2 (b) (c) (d) x 2 2x x 2 18 9 5 2 3x y 3 4 5x 3 y 2 2x 5 2 x 3 x x 12 4. (6 points) Simplify the complex fraction and write your answer in lowest terms: 1 1 y2 1 1 y 5. (6 points) Divide: 40 x 3 y 2 25 x 2 y 12 x 4x 2 6. (6 points) Divide using long division: x 3 7 x 2 x 1 7. (6 points each) Solve the rational equations: 1 4 1 2 (a) x2 x 4 x2 (b) a3 a a 1 a 2 8. (6 points) Solve the equation for the variable y: x6 3 y 1 4 Set up an algebraic equation for and solve each of the following problems: 9. (6 points) Julie can paint a fence by herself in 12 hours. With Betsy’s help, it takes only 5 hours to finish the job. How long would it take Betsy to do the job by herself? 10. (6 points) The total value of a house and a lot is $168,000. If the ratio of the value of the house to the value of the lot is 7 to 1, find the value of the house. 11. (4 points) The product of two consecutive integers is 56. Find the integers. Name: Math 990 Preparation for College Mathematics Fall 2012 Test 3 Form C Directions: Work the following problems neatly and completely and leave all your answers in simplest form. You may not use scratch paper. You must show all your work to get full credit. You may not use books, notes, cell phones, graphing calculator, or any resource other than a scientific calculator when completing this test. Each part of each problem is worth 5 points. Good luck!! 1. Simplify each expression below. Express your answers without using zero or negative integers as exponents. 2 3 −2 (a) − (b) 23 2−2 (c) x−3 y −4 x2 y −1 (d) 3x2 y −4 4x−3 y −1 2. Express the following radicals in simplest form. r (a) (b) √ 3 7 12 54 3. Simplify the following expression: √ √ √ 2 18 − 2 + 3 50 4. Express the following radical in simplest radical form (Assume that all variables represent positive real numbers). p 20x7 y 6 5. Find the following product. Express your answer in simplest radical form (Assume that all variables represent positive real numbers). √ √ 2 5−7 3 5+2 6. Rationalize the denominator and simplify (Assume that all variables represent positive real numbers). √ 3 x−5 7. Solve each of the following radical equations: √ (a) 3 2x − 1 = −3 √ (b) 4x − 3 − 2 = 3 8. Convert the following expression to radical form and simplify. 3 16 4 9. Simplify the following expression. Express your answer using positive exponents only. 1 24x 3 4x 1 4 10. Use scientific notation and the properties of exponents to simplify the following expression.Write your final answer in scientific notation. (0.0000009) (200) 0.003 11. Simplify and write your answer in standard form: (6 − 2i) (7 − i). 12. Simplify and write your answer in standard form: −2 − 5i . −3 + 4i 13. Solve: x2 = −63. 14. Use the factoring method to solve the quadratic equation x2 − 9x = −14. 15. Solve: t2 − 8t − 5 = 0. BONUS QUESTION (Up to 5 points): Given the complex number −3 + 4i, find the following: Real part: Imaginary part: Complex conjugate: Name:_________________________________ Math 990 Preparation for College Mathematics Fall 2012 Test 4 Form B Directions: Work the following problems neatly and completely and leave all your answers in simplest form. You may not use scratch paper. You must show all your work to get full credit. You may not use books, notes, cell phones, graphing calculator, or any resource other than a scientific calculator when completing this test. Good luck!! 1. (9 pts) Graph and label the following points on the same graph: A(−4, 2), B(3, −4), C(4, 1), D(0, 4), E(−1, −4), F (2, 0). For each point state the quadrant or axis where it is located. 5 x -5 O 5 Point A B C D E F Quadrant/Axis -5 2. (7 pts) Find x and y intercepts and graph the following equation 5x + 2y = 10. 5 x -5 O 5 -5 x-intercept:_________ y-intercept:_________ 1 3. (7 pts) Graph the following equations by finding x and y intercepts and, if necessary use additional points y = 2x. 5 x O -5 5 -5 x-intercept:_________ y-intercept:_________ 4. (6 pts) Graph the following linear equations. State whether is the line is horizontal, vertical or neither (a) x = 3 (b) y = −2 5 5 x -5 O 5 x O -5 -5 5 -5 a. b. 5. (6 pts) Given points (−3, 8) and (5, −).. (a) Find the midpoint of the line segment connecting given points. (b) Find the distance between the given points. 2 6. (7 pts) Graph the inequality x + 3y ≤ 6 5 x -5 O 5 -5 7. (7 pts) Graph the inequality x − 2y > 4 5 x -5 O 5 -5 8. (7 pts) (a) Graph the line determined with the points (−3, 3) and (−1, −1). 5 x -5 O 5 -5 (b) Find the slope of the line passing through the given points. 3 9. (6 pts) Find the equation of the line given the point (−5, 2) and the slope m = 2. 10. (7 pts) Graph the line that passes through the given point (1, −2) and has the slope m = 13 . 5 x -5 O 5 -5 11. (6 pts) Find the equation of the line which passes through the points (2, −3) and (−1, 3). 12. (6 pts) Find the equation of the line which has slope m = −3 and y-intercept b = 2. 4 13. (7 pts) (a) Rewrite the equation of the line 3x − 6y = 16 in slope-intercept form. (b) Find the slope (c) Find y−intercept. 14. (6 pts) Find the equation of the line parallel to the line 2x + y = 4 and passing through the point (−2, 3). 15. (6 pts) Find the equation of the line perpendicular to the line 3x − 6y = 8 and passing through the point (2, 4). 5