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Potomac Falls High School Algebra II Quarter 2 Review 2015 – 2016 This review covers the major topics in the material that will be tested on the quarter two cumulative test. It is not necessarily all inclusive and additional study and problem solving practice may be required to fully prepare for the semester exam. This test is designed to evaluate your knowledge of the material presented in the second quarter and your ability to apply that knowledge. In order to complete this test in the allotted time, you must work quickly and efficiently. If you get stuck on a problem, move on to another problem and go back later. Avoid spending an excessive amount of time on a single problem at the expense of the rest of the test. Name:___________________ Algebra 2 Quarter 2 Assessment Review Name:_______________ For Numbers 1 – 5: Classify each number into all appropriate number systems. 1. 1 2 2. –2i 3. -2 4. 0.501021… 5. 2 + 3i For Numbers 6 – 15: Simplify using exact numbers – no decimals. 6. 200 10. 3 2i 7. 2 13. 6 2i 3 5i 12 3 8. 10 12 11. 4 3i 2 5i 14. 3 2i 4i 9. i 8 12. 7 3i 2 i 15. 4i 2i Solve each of the following. Leave all answers in exact form. (Factor, Square Roots, Quadratic Formula, Completing the Square, or Graphing) 16. x 3 81 17. 4 x 2 9 0 18. 3x 2 10 x 8 19. x 2 5 x 6 0 21. x 2 6 x 17 0 22. 2 2 2 x 2 30 3 20. 14 x 2 3x 2 23. x 2 8x 9 Factor each of the following. 24. 81x 2 36 y 2 25. 12 x3 10 x 2 12 x 26. 4 x 2 3x 10 27. 2 x3 7 x 2 8x 28 28. x3 125 29. x 2 8 x 9 Solve the system. 30. x 2 y 2 36 2x y 2 31. y 2x2 7 x 6 y 2 x 3 32. List all possible real roots for the function f ( x) 4 x3 7 x 2 4 x 3 33. Find all factors of the polynomial function f ( x) x3 3x 2 10 x 24 . 34. What is the quotient of 2 x3 3x 2 4 x 1 x 3 ? 35. What is the quotient when 5 x 4 10 x3 16 x 2 31x 7 is divided by 5 x 2 1 ? 36. State the end behavior for the function g ( x) 4 x7 6 x 4 3x 2 2 x 10 37. Write the equation of the function graphed. 38. Find all zeros for the function f ( x) x3 3x 2 7 x 5 . 39. Find the remainder for x3 8 x 2 7 x 3 40. A diver jumps off a platform 25 feet up from the water level with an initial velocity of 20 feet per second. Answer the following and round all answers to three decimal places. a) What is the maximum height the diver reaches during her flight? b) When will the diver enter the water? Explain how you determined your answer. 41. Consider the data in the chart. Find the equation of the curve of best fit for the data. x y -9 -222 -6 -100 -4 -43 -3 -23 a) y 3.97 x 92.34 1 10 3 -4 5 -37 7 -90 9 -163 12 -311 b) y 2.49 x 2 3.24 x 9.26 c) y 1.36 x3 2.49 x 2 3.23x 9.28 Explain how you determined the curve of best fit. 42. Find all values of b that make the trinomial factorable: x 2 bx 42 43. Find the discriminant and state the type and number of solutions: 3x 2 10 x 5 0 44. What would you add to both sides of the following equation to complete the square? 𝑥 2 − 10𝑥 = 7 45. Find p(-3) when p(x) = 3 x3 6 x 2 x 1. 46. Are you prepared?