advertisement

Name ______________________________________ ALG2/TRIG Regents Review #2 Directions: DUE DATE: Choose the best answer. Answer ALL questions. Show ALL work in column 2. If there is no mathematical work to be shown, write an explanation or definition to support your answer! This counts as a quiz grade!!! 1. What is the value of i99 - i3? 1. 1 2. 0 2. What is the sum of 1. 2. 3. 4. 3. –i and 4. i96 ? 5i 4i 2i 6i 3. The product of a + bi and its conjugate is 1. always a real number 2. always an imaginary number 3. can be either a real number or an imaginary number 4. always a negative number 4. Which statement must be true if a parabola represented by the equation y = ax2 + bx + c does not intersect the x-axis? 1. b2 - 4ac = 0 2. b2 - 4ac < 0 3. b2 - 4ac > 0, and b2 - 4ac is a perfect square. 4. b2 - 4ac > 0, and b2 - 4ac is not a perfect square. 5. If f(x) = x3 - 2x2, then f(i) is equivalent to 1. -2 + i 2. -2 – i 3. 2 + i 4. 2 – i 6. Use a graphical method to find a solution to the following system of equations in the interval -1 ≤ x ≤ 5: y = x2 – 4x + 2 y=x+2 The solution set to this system of equations in the interval -1 ≤ x ≤ 5 is 1. {} 3. {(0, 2), (5, 7)} 2. {(2, 0)} 4. {(2, 0), (7, 5)} 7. Express the product of 4 3i and 2 + i in simplest a + bi form. 1. 2. 3. 4. 2 + 11i 2 11i 11 + 2i 11 2i 8. The roots of the quadratic equation 4x2 = 2 + 7x are best described as 1. real, equal, and rational 2. real, unequal, and rational 3. real, unequal, and irrational 4. imaginary 9. Which quadratic equation has roots 2 + i and 2 i? 1. 2. 3. 4. x2 + 4x + 5 = 0 x2 4x 5 = 0 x2 + 4x 5 = 0 x2 4x + 5 = 0 10. Express 1. 2i 3. 2 i in simplest a + bi form. 2. i 2 4. 2 + i 11. Factor completely: 3x3y2 147x. 1. 2. 3. 4. 3x(x2y2 49) 3x(xy + 7)(xy 7) 3x3(y + 7)(y 7) 3x(xy 7)2 12. Express in simplest form. 13. What are the sum and product of the roots of the equation 6𝑥 2 − 4𝑥 − 12 = 0? 1. sum = −2 3 ; product = −2 2 2. sum = ; product = −2 3 3. sum = −2; product = 2 4. sum = −2; product = −2 3 3 14. For which equation does the sum of the roots equal 3/4 and the product of the roots equal -2? 1 4𝑥 2 − 8𝑥 + 3 = 0 2 4𝑥 2 + 8𝑥 + 3 = 0 3 4𝑥 2 − 3𝑥 − 8 = 0 4 4𝑥 2 + 3𝑥 − 2 = 0 15. Which equation is represented by the graph below? 1 (𝑥 − 3)2 + (𝑦 + 1)2 2 (𝑥 + 3)2 + (𝑦 − 1)2 3 (𝑥 − 1)2 + (𝑦 + 3)2 4 (𝑥 + 3)2 + (𝑦 − 1)2 =5 =5 = 13 = 13 16. What are the coordinates of the center of a circle whose equation is 𝑥 2 + 𝑦 2 − 16𝑥 + 6𝑦 + 53 = 0? 1 (−8, −3) 2 (−8, 3) 3 (8, −3) 4 (8, 3) 17. Factored completely, the expression 6𝑥 − 𝑥 3 − 𝑥 2 is equivalent to 1 x(x + 3)(x − 2) 2 x(x − 3)(x + 2) 3 −x(x − 3)(x + 2) 4 −x(x + 3)(x − 2) 18. When factored completely, the expression 3𝑥 3 − 5𝑥 2 − 48𝑥 + 80 is equivalent to 1 (x2 − 16)(3x − 5) 2 (x2 + 16)(3x − 5)(3x + 5) 3 (x + 4)(x − 4)(3x − 5) 4 (x + 4)(x − 4)(3x − 5)(3x − 5) 19. If 𝑥 2 + 2 = 6x is solved by completing the square, an intermediate step would be 1 (𝑥 2 (𝑥 3 (𝑥 4 (𝑥 + − − − 3)2 = 7 3)2 = 7 3)2 = 11 6)2 = 34 20. The roots of the equation 2𝑥 2 + 7x − 3 = 0 are 1 −12 and −3 2 12 and 3 3 4 −7 ±√73 4 7 ±√73 4 21. Solve the equation for x: 5 − 3(𝑥 − 6) = 2(𝑥 − 6) 22. Solve the Quadratic Inequality for x: 𝑥 2 − 2𝑥 − 15 ≥ 0