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Name ________________________ Period ______ Date ____________ Algebra II Unit 2 Model Curriculum Assessment 1 x 1. If 7 4 7, what is the value of x ? Explain your reasoning. 2. When the nth root of a positive number a is written as ax , what is the value of x ? Fill in the blanks in the partial solution below to explain your answer. n a ax _____ ax n a1 _____ 1 _____ _____ x 3. Rewrite the expression 9 5 27 as a power of 3. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 1 3 x 2 in exponential form. 4. Rewrite the expression 5. Which of the following is equivalent to a2 b 4 ? 1 a. ab3 b. a2b3 c. 4 ab3 d. 4 a2b3 6/18/2017 NJ DOE 3 Unit 2_Algebra 2 Page | 2 6. Which expression is equivalent to a. b. c. d. 7. 3x 2 2 x 1 , where x 1 ? x 1 6 3x 2x 1 6 3x 5 x 1 3x 1 6 3x 5 x 1 3x 5 2 3x 2 13x 4 4x 16 in simplest form, where x2 4 x 2 x 2, x 2, and x 4 ? Show your work. What is the quotient 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 3 8. Which expression is equivalent to x 4 ? 9. a. 1 x4 b. x 2 x 2 x 4 x 4 c. x 2 8x 4 x 4 x 4 d. x 2 8x 4 x 4 x 4 2x x2 4 2 , where x 4 and x 4 x 16 Rx x 4 x 3 3x 2 10x 2 , as Q x 2 2 x 3x 3 x 3x 3 where Q x is the quotient with degree 2 and R x is the remainder. Write the expression Show your work. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 4 10. Solve the equation below. Explain your reasoning for each step. 3 11. 2x 22 18 Solve the equation below. Show your work. 7x 15 x 1 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 5 12. x 5 x 0 x 5 All Real Numbers Except All Real Numbers x 5 or x 0 x 5 No Solution There are 4 equation cards labeled a–d below and 7 potential solution set cards above. Match each equation card to its corresponding solution set. Write the solution set in the box beside its corresponding equation. A solution set card can be used more than once. a. x x 2x 2 x 5 2x 10 x 2x x 5 2x 10 b. x x x 5 x 5 c. 1 5 x 5 x x 5 d. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 6 13. For each of the following statements, put a check mark in the circle to indicate whether the statement is never true, sometimes true, or always true for the operation. Never True Sometimes True Always True When solving equations for real solutions, extraneous solutions occur when a. squaring both sides of an equation b. multiplying both sides of an equation by an expression containing one or more variables c. multiplying both sides of an equation by a constant d. raising both sides of an equation m to the power, where m and n n are integers e. dividing both sides of an equation that has the variable x by x f. taking the square root of both sides of an equation 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 7 14. Solve the system of equations below by graphing on the coordinate plane provided. 1 x 3 2 1 1 y x 6 3 y Solution: _______________________ 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 8 15. Solve the system of equations below algebraically. 2 x 3y 8 4 x 2y 10 Solution: _______________________ 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 9 y 2x 5 16. y x 2 4x 10 Part A Solve the system of equations above algebraically. Show your work. Solution set: _______________________ Part B Graph both equations and indicate the solution on the graph. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 10 17. The function f x 82x 3 is equivalent to the function f x 2a bx , where a and b are integers. What are the values of a and b ? a _____ and b _____ 18. 0.1 in the form g x n b Rewrite the function g x 104 23 x x where n and b are constants. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 11 x , 19. Which of the following functions is equivalent to f x 3x 23x 2 ? a. f x 2 24 b. f x 2 6 c. f x 4 24 d. f x 4 6 6/18/2017 x 3 x2 x 3 x2 NJ DOE Unit 2_Algebra 2 Page | 12 20. Darah has 200 milliliters of a salt and water solution that is 12% salt. She begins to add a salt and water solution that is 5% salt to the 12% solution. The percent of salt in Darah’s combined solution when x milliliters of the 5% solution have been added can be modeled by 2, 400 5x C x . 200 x Two different tables of values for C x are given below. Use the tables to answer the questions that follow. x C x 50 100 150 200 250 300 350 400 450 500 10.6 9.67 9.0 8.5 8.11 7.8 7.55 7.33 7.15 7.0 x C x 500 1,000 5,000 10,000 50,000 100,000 1,000,000 7.0 6.17 5.27 5.14 5.03 5.01 5.001 Part A Is the function increasing or decreasing? What does this mean in the context of the problem? Part B What is the horizontal asymptote of the functions? Interpret the meaning of the asymptote in the context of the problem. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 13 21. At a diving competition, Holly jumps from a springboard that is 3 meters above the surface of the water at time t 0 seconds. She reaches a maximum height of 4.5 meters above the surface of the water after 0.5 seconds and enters the water 1.5 seconds after jumping. She then sinks to a minimum height of 1.5 meters below the surface of the water 1 second after entering the water and rises back to the surface of the water 2.5 seconds later. Sketch a possible graph of Holly’s height above the water, h, from the time she jumps until she rises to the surface of the water. Provide labels and scales for the axes. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 14 22. The figure above shows the graph of the profit function for a company. In the graph, y represents the profit, in thousands of dollars, that the company earns for selling x thousand items. Interpret the meaning of the two intercepts shown in the context of the problem. 6/18/2017 NJ DOE Unit 2_Algebra 2 Page | 15