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