<p> Summer Mathematics Prep Chesterfield County Public Schools Entering Trig/Analysis or Trig/Advanced Algebra Department of Mathematics</p><p>Summer Mathematics Prep documents provide self-directed student review, practice, and preparation for high school mathematics courses. Students are encouraged to first attempt these review problems on their own. Checking accuracy against the solution document can help students identify their own strengths and areas of challenge. Students can utilize instructional online resources to address areas of challenge. All of these resources can be found at http://mychesterfieldschools.com/about/instruction/other-academic-programs/summer-programs/.</p><p>Pythagorean Theorem</p><p>1. In , AC = 32 and BC = 24. What is the length of ?</p><p>2. A guy wire stretches from a point on the ground 16 feet away from a vertical pole to the top of the 12- foot pole. How many feet long is the guy wire?</p><p>3. If a 25-foot ladder is placed against a wall so that it reaches a height of 24 feet, how far away from the base of the wall are the feet of the ladder?</p><p>4. In quadrilateral ABCD, AD = 8, DC = 6 and BC = 20. Find AB.</p><p>5. A square has perimeter of 24 units. What is the length of the diagonal of the square?</p><p>Chesterfield County Public Schools Page 1 of 5 Department of Mathematics May 2012 Special Right Triangles</p><p>6. If is a special right triangle with m C = 30, m D = 60, and ED = 3 inches, how long is the hypotenuse?</p><p>7. In , DF = . What is the length of ?</p><p>8. In , SR = 4. Find the length of .</p><p>9. In , ST = . Find SR.</p><p>10. In , RT = . Find SR.</p><p>11. In , XZ = . Find the length of .</p><p>Basic Trig Functions</p><p>12. Given AB = 7 and AC = 11, what is the ?</p><p>13. Given AC = 23 and BC = 12, what is the sin A ?</p><p>14. Given AB = 3 and BC = 4, what is the cos C ?</p><p>Exponents 15. Simplify: 17. Simplify:</p><p>Chesterfield County Public Schools Page 2 of 5 Department of Mathematics May 2012 16. Simplify: 18. Simplify: </p><p>Factor Completely</p><p>19.</p><p>20.</p><p>21.</p><p>22.</p><p>23.</p><p>24. </p><p>25.</p><p>26. </p><p>27. </p><p>28.</p><p>29.</p><p>30. </p><p>Complex Numbers</p><p>31. Simplify: </p><p>32. Simplify: </p><p>33. Simplify: </p><p>34. Simplify: </p><p>Chesterfield County Public Schools Page 3 of 5 Department of Mathematics May 2012 Solving Equations (Solving techniques may include using the Quadratic Formula, Factoring, Taking the Square Root, Squaring both sides, Using a Common Denominator, and/or Cross Multiplying)</p><p>35. Solve: </p><p>36. Solve: </p><p>37. Solve: </p><p>38. Solve: </p><p>39. Solve: </p><p>40. Solve: </p><p>41. Solve: </p><p>42. Solve: </p><p>43. Solve: </p><p>44. Solve: </p><p>45. Solve: </p><p>Non-Linear Graphing Sketch the graph by hand and state the parent function.</p><p>46.</p><p>47. </p><p>48.</p><p>49. </p><p>50. Sketch the graph with asymptote(s): </p><p>Domain and Range State the domain and range of the function and name the parent function.</p><p>Chesterfield County Public Schools Page 4 of 5 Department of Mathematics May 2012 51. </p><p>52.</p><p>53.</p><p>Simplifying Rational Expressions</p><p>54. Simplify: </p><p>55. Multiply: </p><p>56. Simplify: 57. Simplify: </p><p>58. Divide: </p><p>59. Simplify:</p><p>60. Simplify: </p><p>61. Simplify: </p><p>Chesterfield County Public Schools Page 5 of 5 Department of Mathematics May 2012</p>