# Review Sheet 1.pdf

## Mathematics 112 with De Witt at University of Wisconsin - Madison *

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Review Sheet 1 Math 112 Fall 2008 1. Simplify parenleftbigg a3b−4c2 a5b2c−4 parenrightbigg2 2. Simplify 3√108 + 3√−81 + radicalBig 3√9 3. Rewrite the expression using only rational exponents: 5 radicalBigg√ x 3√y 3√z2 4. Factor 6x3 + 13x2 −5x 5. Simplify 5 2x + 2 − 3 x2 + x + 2 x + 1 6. Solve for x 1 2 − 1 x = 1 x − 1 3 7. Find the equation of the line through the point (1,2) and perpendicular to the line through the points (−1,3) and (2,−7). 8. Determine the center and radius of the circle given by the equation 4x2 −4x + 4y2 + 8y −59 = 0 9. Determine the symmetries of |x + y| = 2 10. Solve the following: A)2y2 −5y −2 = 0 B) x6 −10x4 + 24x2 = 0 11. The difference of two positive numbers is one-third of their sum. The sum of the squares of the two numbers is 180. Find the two numbers. 1 2 12. Solve the following and write the answers in interval notation: A) x−14 − 2x+35 ≤ x B) 1x ≥ 1x+1 13. Solve the following and give the solution in number line and interval notation: vextendsinglevextendsingle vextendsinglevextendsinglex + 1 2 − x−1 3 vextendsinglevextendsingle vextendsinglevextendsingle < 1 14. Solve the following and give the solution in number line and interval notation: 2x x + 5 + x−1 x−5 ≤ 1 5 15. Solve the following: 4x3 + 8x2 + 5x = 0 16. Find the value of k such that the equation below has exactly one real root: kx2 + kx + 1 = 0 17. Find the equation have roots r1 = 13(4−√5) and r2 = 13(4 +√5) 18. Solve the following: 4|x−2| = 3x−4 19. Solve the following: 8t−4 −17t−2 + 2 = 0 20. Solve the following: √3 + 2x +√−1 + 4x = 1 21. Find three consecutive integers such that twice the first plus half of the second is seven more than twice the third. 22. Solve (2y + 3)4 = 5 23. Solve (x2 −1)4 −81 = 0 24. Solve x(4/3) + 3x(2/3)−28 = 0 3 25. Simplify the following: parenleftbiga + 1 b parenrightbigaparenleftbiga− 1 b parenrightbigb parenleftbigb + 1 a parenrightbigaparenleftbigb− 1 a parenrightbigb 26. Find the x and y intercepts of xy −12y = x2 −2x + 1 27. Find the equation of the line passing through the point (−1,2) and parallel to the line passing through the points (−1,3) and (7,−4). 28. Determine the symmetries of xy = x2 −4 29. Find the center and radius of 3x2 + 3y2 + 5x−4y = 1 30. Simplify the following: parenleftbigg x3y2z6w−2 x−1y4z3w−1 parenrightbigg−2 31. Simplify the following: 4√24−8√54 + 2√6 32. Factor the following: 4x3 + 8x2 −5x 33. Simplify the following: x(x + y)−1 −y(x−y)−1 34. Give the answer in both interval notation and graphical number line form: |x−4| > 4 35. Give the center and radius of the circle which has (1,−3) and (6,4) as the endpoints of a diameter. 36. Solve the following: 6x−4/3 + x−2/3 −2 = 0 37. Solve the following and give the answer in interval notation: 2x−1 x + 1 ≥ 3x + 2 x−2

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