Name:________________________ Per:______ Chapter 8 Test Review 1. If y varies directly with x cubed, and y = 3 when x = 2, find y when x = 4. k =________ new equation:____________________ y =________ 2. If y varies inversely with x, and x = 2 when y =12, find y when x = 8. k =________ new equation:____________________ y =________ 3. a. _____________ a. Is the relationship between the values in the table direct variation, b. _____________ inverse variation, or neither? b. Write an equation to model the variation. 4. a. _____________ a. Is the relationship between the values in the table direct variation, b. _____________ inverse variation, or neither? b. Write an equation to model the variation. For problems 5 – 10, a) find the restrictions, and b) simplify. 6 x3 3xy 5. y2 2 2u 6 u3 u 6. 2 u 2u 3 u 2 u 2 x 2 25 7. 10 x 50 x y 1 5 3 15 7 35 x y 1 36 3 12 6 6 8. u2 9 u 3 u 2 u2 4 9. 4x3 y 2 z 5 10. 20 x 3 y 7 z 6 x 48 x 2 5 x 24 3x 2 8 x 3 11. Why is it necessary to find restrictions when simplifying rational expressions? 12. Write your own expression that would simplify to x2 9 x3 5x For problems 13 – 16, circle the choice that CANNOT be a factor of the given polynomial. 13. x2 – 9x + 20 a. x - 4 b. x + 5 c. x - 5 14. 8x3y – 50xy3 a. 2xy2 b. 2x + 5y c. 2x – 5y 15. x3 – 4x2y – 21xy2 a. x – 7y b. x c. x – 3y 16. 15x4 – 27x3y – 6x2y2 a. 3x2 b. x – 2y c. 6x2 17. 8y3 - 27 a. 2y - 3 b. 4y2 – 6y + 9 c. 4y2 + 6y + 9 Answers: 1.a. 3 3 b. y = x3 c. 24 8 8 4. a. inverse b. xy = 36 OR y = 7. a. x ≠ -5 b. x5 10 2.a. 24 b. xy = 24 OR y = 36 4x 2 5. a. x ≠ 0, y ≠ 0 b. x y3 8. a. u ≠ -2, -3 b. (u – 3)(u – 2) 1 6 10. a. x ≠ -3, , 3, 8 b. 3 3x 1 xy 3 y will vary, but an example is 5 xy 24 c. 3 x 3. a. direct b. y = 5x 6. a. u ≠ -3, -1, 1, 2 b. 9. a. x ≠ 0, y ≠ 0, z ≠ 0 b. 2u u2 z4 5y 5 11. So that no denominator may have the value of 0 12. Answers 13. b 14. a 15. c 16. c 17. b