Algebra 2 TE: 3rd Quarter Exam Review Packet 1. Factor each expression completely. x2 - 8x – 33 c. (x + 11) 2 d. (x - 11) (x – 3) 2. Factor each expression completely. 9x2y + 18xy2 a. CBF b. 9x2y (1 + 2y) c. 9xy (x + 2y) d. 18xy (y + 2) 3. Factor each expression completely. 3x2 + 10x + 8 a. (x + 2) (x + 2) b. (3x + 4) (x + 2) c. (3x + 4) (3x – 2) d. 3x(x+2) + 4(x+2) 4. Factor each expression completely. x2 + 5x - 15 a. (x + 15) (x – 1) b. (x + 3) (x – 5) c. (x + 5) (x – 15) a. (x – 11) (x + 3) b. (x + 11) (x – 3) 5. Solve by factoring.4x2 + 17x – 42 = 0 2 a. b. –6, 4 6, 3 6. Solve by factoring. 4x2 + 27x – 40 = 0 a. –8, 4 b. 5 4 , 1 2 c. c. –6, 8, 1 2 d. CBF 7 d. 7 4 4 d. –8, , 5 4 2 3 Solve the equation by finding square roots. 7. 2x2 = 18 a. 3 b. √18 ± 2 c. −√9, √18 d. ± 3 8. 3x2 = 33 a. 11 b. √33 ± 3 c. ±√11 d. −√11, √33 9. The function y = -16t2 + 404 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second. a. 10.05 seconds c. 5.02 seconds b. 7.11 seconds d. 0.25 seconds 10. Simplify √−75 using the imaginary number i. a. 5√−3 b. 𝑖√75 c. −5√3 d. 5𝑖√3 11. Simplify √−32 using the imaginary number i. a. 4𝑖√2 b. 4√−2 c. 𝑖√32 d. −4√2 Write the number in the form a + bi. 12. √−9 + 8 a. 9 + 8i b. 8 + i√9 c. 8 + 3i d. 3 + 8i 13. 1 − √−175 a. −1 − 5𝑖√7 b. 1 − 5𝑖√7 c. −1 + 𝑖√175 d. 1 + 5𝑖√7 Simplify the expression. 14. (-6 – 2i) + (2 – i) a. -8 + i b. -4 – 3i c. -7i d. 4 + 3i 15. (3 + 5i) – (6 – i) a. 3i b. 3 – 6i c. 9 + 4i d. -3 + 6i 16. (-5i)(3i) a. 15 17. (5 – 6i)(4 + 5i) a. -10 + i b. 20 – 30i b. –15 c. 15i c. 50 + i d. 20 + i 18. Solve the equation by square roots, 9x2 + 25 = 0 a. ± 5 𝑖 c. ± 3 𝑖 5 3 b. ± 5 d. ± 25 𝑖 3 9 d. –15i 19. Solve the equation by factoring, x2 + 6x + 9 = 49 a. 10, –4 c. 4, –10 b. 4, –4 d. 10, –10 Use the Quadratic Formula to solve the equation. 20. –x2 + 5x – 4= 0 21. 3x2 + 5x + 7 = 0 22. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 300 square yards. The situation is modeled by the equation h2 + 5h = 300. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. a. 610 yards c. 15 yards b. 17.5 yards d. 30 yards 23. Classify –4x4 – 3x2 by degree and by number of terms. a. quintic binomial c. quintic trinomial b. quartic binomial d. quartic trinomial 24. Classify –5x5 – 8x4 – 2x3 by degree and by number of terms. a. cubic binomial c. quartic trinomial b. quintic trinomial d. quadratic binomial 25. Zach wrote the formula w(w – 1)(2w + 3) for the volume of a rectangular prism he is designing, with width w, which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree and by number of terms. 26. Write 2x2(3x2 – 5x3) in standard form. Then classify it by degree and number of terms. a. –10x5 – 15x4; quartic binomial c. –10x5 + 6x4; quintic binomial b. 5x5 + 6x4; quintic trinomial d. 5x – 3x4; quintic binomial 27. Write the expression (x + 6)(x – 3) as a polynomial in standard form. a. x2 + 9x – 9 c. x2 + 9x – 18 b. x2 – 9x + 3 d. x2 + 3x – 18 28. Write the expression (x + 5)(x – 3) as a polynomial in standard form. a. x2 + 2x – 15 c. x2 – 8x + 2 b. x2 + 8x – 15 d. x2 + 8x – 8 29. Write 2x3 + 8x2 – 24x in factored form. a. 2x(x – 2)(x – 6) c. 6x(x – 2)(x + 2) b. –2x(x + 2)(x + 6) d. 2x(x + 6)(x – 2) 30. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of y= x3 + 16x2 – 10x – 30. If necessary, round to the nearest hundredth.