1st 9 Weeks Exam Algebra II PDF
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This is a high school algebra II exam covering topics such as quadratic equations, complex numbers, and solving equations by completing the square and by factoring. It includes example questions for practice.
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Name: _________________________________________ 1st 9 Weeks Exam Date:________________ Block: ___________________ Algebra II 1.Solve the quadratic equation by factoring: 2. Solve the quadratic equation by factoring: 2...
Name: _________________________________________ 1st 9 Weeks Exam Date:________________ Block: ___________________ Algebra II 1.Solve the quadratic equation by factoring: 2. Solve the quadratic equation by factoring: 2 2 𝑥 − 5𝑥 + 6 = 0 𝑥 + 10𝑥 + 24 = 0 A. 𝑥 = {2, 3} A. 𝑥 = {− 6, − 4} B. 𝑥 = {− 2, 3} B. 𝑥 = {− 2, − 12} C. 𝑥 = {1, 6} C. 𝑥 = {6, 4} D. 𝑥 = {3, − 6} D. 𝑥 = {3, − 8} 3. Simplify the expression below. 4. Simplify the expression below. − 100 − 2 − 16 − 9 + − 28 A. − 12𝑖 A. − 9 + 2𝑖 7 B. − 2𝑖 B. − 9 − 2𝑖 7 C. 12𝑖 C. 𝑖 7 D. 2𝑖 D. 5𝑖 3 5. Simplify the expression below. Give your answer 6. Simplify the expression below. Give your answer as a complex number in standard form. as a complex number in standard form. (7 + 𝑖) − (− 2 + 8𝑖) (4 − 5𝑖)(− 1 − 7𝑖) 7. Simplify the expression below. Give your answer 8. Simplify the expression below. Give your answer as a complex number in standard form. as a complex number in standard form. 2 −9+5𝑖 (− 7 + 3𝑖) + (− 2 + 8𝑖) 3−𝑖 9. Check all values that are equivalent to − 𝑖. 10. Which sets do not contain the value (2 + 6𝑖)(2 − 6𝑖) − 50 ? Check all that apply. 11. Which statement shows the associative property 12. Which of the following is the additive identity of of multiplication? 5 + 2𝑖? A. (− 4 + 17𝑖) · 1 = (− 4 + 17𝑖) A. 0 B. 3𝑖 + (− 1 + 9𝑖) = (− 1 + 9𝑖) + 3𝑖 B. 1 C. (− 5 + 3𝑖) · 6𝑖 =− 5 · 6𝑖 + 3𝑖 · 6𝑖 C. − (5 + 2𝑖) D. ((1 − 𝑖) · 8𝑖) ·− 2𝑖 = (1 − 𝑖) · (8𝑖 ·− 2𝑖) D. 5 − 2𝑖 13. Which of the following sets are closed under 14. What is the apparent solution set for the multiplication? Check all that apply. equation associated with the following graph? A. {-3, 1} B. {-1,3} C. {-3,1, 4} D. {-1,3,4} 15. Solve by factoring: 16. Solve by factoring: 2 2 𝑥 + 9𝑥 − 83 = 4𝑥 + 1 25𝑥 + 1 = 10 17. Solve by square roots: 18. Solve by square roots: 2 2 (2𝑥 + 3) = 36 2𝑥 + 11 = 131 19. Solve by square roots: 20. Solve by completing the square: 2 2 3(𝑥 + 1) =− 240 − 𝑥 + 16 = 6𝑥 + 1 21. Solve by completing the square: 22. Solve by completing the square: 2 2 𝑥 + 10𝑥 + 7 = 0 2𝑥 + 8𝑥 + 134 = 0 23. Solve by completing the square: 24. Which of the following statements is true? 2 𝑥 + 4𝑥 + 22 = 67 A. The product of any two complex numbers is always a real number. B. The square of an irrational number is always rational. C. The sum of a rational number and an irrational number is always irrational. D. The sum of a complex number and its conjugate is always equal to zero. 25. Which of the following sets is closed under subtraction? A. The set of natural numbers ℕ B. The set of rational numbers ℚ C. The set of positive real numbers ℝ D. The set of complex numbers ℂ
