ED 337 Paul Garrett Selected Response Assessment 10 th Grade Mathematics Examination Algebra II Clear Purpose: The purpose of this selected response is to ensure an understanding of expressions, manipulation of polynomials, comprehension of exponents and logarithms, as well as memorization of common formulas and their applications. This will allow the instructor to properly assess the students understanding of complex algebraic equations and their use in real, practical applications. In order to properly deduce student s comprehension the assessment includes several different methods including: true/false, multiple-choice, short answer, matching, and fill-in-the-blank. Each question must be answered fully and all work must be written down in full detail in order for proper assessment. Content Standards & Learning Targets: The following standards are those set down for this unit that the teacher expects from the students along with a short I can statement the students should read while assessing their own understanding of the concepts A1.1.1 - Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables. A1.1.4 - Add, subtract, multiply, and simplify polynomials and rational expressions. A1.1.5 - Divide a polynomial by a monomial. A1.1.6 - Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms, including the inverse relationship between exponents and logarithms. A1.2.2 - Associate a given equation with a function whose zeros are the solutions of the equation. A1.2.5 - Solve polynomial equations and equations involving rational expressions and justify steps in the solution. A1.2.7 - Solve exponential and logarithmic equations and justify steps in the solution. A1.2.8 - Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution. A1.2.9 - Know common formulas and apply appropriately in contextual situations.
Many of the questions test more than one skill. This is unavoidable as much of mathematics is intertwined together. The number of points possible is the points possible for those particular subjects but the total is the total number of points on the assessment. Target Question Number(s) Number of Points Possible I can examine an equation by graphing it in proper parameters I can verbally describe an equation using its giving variables I can evaluate complex equations given the values of certain or all variables I can manipulate polynomials using subtraction, multiplication, and rationalization I can divide a polynomial of variables by a monomial I can properly use properties of exponents and logarithms I can determine the zeroes of an equation by rationalization and factoring I can solve exponential and logarithmic equations with justification and clear written dialogue I can solve a given equation with multiple variables for a designated variable I understand the common formulas of Algebra and how to use them properly and to my advantage 1a, 1b, 11 13 2, 3, 4, 5, 6, 15 22 19 2 9, 10, 32, 33, 34, 36 17 10 3 7, 23, 25 7 12, 13, 14, 15, 16, 17, 18 7 20, 21, 23, 24, 28, 30, 31 14 8 3 21, 14, 15, 16, 17, 18, 22, 24, 26, 27, 28, 29, 35 Total: N/A 87 pts (+5 bonus points) 21
Teacher Directions: The test is not timed and allows the proper amount of time for completion to the extent of the teacher s discretion. Prior to handing out the test read aloud the following section: The following assessment has been designed to determine your understanding and comprehension of the fundamentals of Algebra II. This test is not timed and you have ample time to complete it. Graphing calculators are permitted as long as they meet state requirements for state examination (TI-83 Plus, TI-84 Plus, TI-84 Plus Silver Edition, TI- Nspire with Touchpad, and the TI-Nspire CX are all permitted on this test). The test is comprised of six different types of questions of no particular order: fill-in-the-blank, multiple-choice, matching, true/false, short answer, and a final portion that is optional. The final portion is there for students who would be willing to try and contains advanced material. YOU WILL NOT BE GRADED ON THIS FINAL BONUS SECTION. If you have any questions please raise your hand quietly and I will get to you as soon as possible. Please do not leave your seat for any reason. When you have finished the test please raise your hand and I will collect it from you; you have then do your homework from other classes or read a book. Please do not pull out material from this class while tests are still being taken. Do you have any questions before we begin? Good luck and lets begin! Hand out the exam and make sure to monitor the students for the remainder of the time. Answer any questions they may have and be attentive. Answer Key: 1) Table 0 3 1 3 2 9 3 15 4 21 5 27 6 33 7 39 8 45 9 51 10 57 2) The sum of 36 multiplied by y cubed, 12 multiplied by y squared, 12 multiplied by y and negative 4. 3) Graph should appear as a very sharp increase 4) x = r + 2 5) A 6) B 7) B 8) D 9) B 10) A 11) C 12) C 13) F 14) D 15) B 16) G 17) E 18) A 19) True 20) False 21) False 22) True 23) False 24) False 25) Logarithm 26) Constants 27) Irrational Number 28) Exponential Decay 29) Coefficients 30) Exponential Growth 31) Real Numbers 32) Polynomial 33) Variable 34) Quadratic Equation 35) Rational Number 36) FOIL Method 37) x=2, y=5, z=3
Algebra II Assessment Polynomials and Complex Numbers Name Date Short Answer Answer each question fully and SHOW ALL WORK. Partial answers will not be accepted. 1. a) Create a table and evaluate 3-6x at the integral [0, 10] (5 pts) b) Sketch a graph of the table you ve just created using whole numbers of x on the integral. Make sure your graph is clear and the values of x and y are visible. (5 pts) 2. Describe 36y^3 + 12y^2 + 12y 4 verbally. (5 pts) 3. Describe the shape of the graph of the equation in question 2 (5 pts)
4. Solve for x: (x+2)(r)=x^2 + 2x -4-2x (5 pts) Multiple Choice After carefully reading the question circle the answer you believe answers the question best. 5. Which of the following equations matches this statement, the quantity of x squared plus x divided by the quantity x squared plus three multiplied by x minus 10 (3 pts) a. (x^2 + x) / (x^2 + 3x -10) b. (x^2 + x + x^2) / (3x -10) c. (x^2 + x -10) / (x^2 + 3x) d. (x^2) / (x^2 + 3x -10) + x 6. There are two numbers with the following properties, (3 pts) a. The second number is 3 more than the first number b. The product of the two numbers is 9 more than their sum Which of the follwing represent possible values of these two numbers? (3 pts) a. -6, -3 b. -4, -1 c. -1, 4 d. -3, 6 7. Which of the following sentences is true about the graphs of y=(x-5)^2 and y=3(x+5)^2 + 1 (3 pts) a. Their vertices are maximums b. The graphs have the same shape with different vertices c. The graphs have different shapes with different vertices d. One graph has a vertex that is a maximum, while the other graph has a vertex that is a minimum 8. (3 pts) log6 40 = a. log10 6 + log10 40 b. log10 6 log10 40 c. (log10 6)(log10 40) d. (log10 40)/(log10 6)
9. What is the simplest form of (5x^3y + [20x^2]y^2 + 20xy^3)/5xy? (3 pts) a. (x+2)^2 b. (x+2y)^2 c. x^2 + y^2 d. x^2 + 2y^2 10. Which product is equivalent to (4x^2 16)/(2-x)? (3 pts) a. 4(x-2) b. 4(x+2) c. -4(x-2) d. -4(x+2) 11. (3 pts)
Matching (1 pt each) Write the correct letter in the space below to match the equation to the x coordinates provided when y=0 (you can only use each answer once) True or False (2 pts each) Write T for True if the statement is true or F for False if the statement is false on the lines below. Justify your answer with a counterexample if false. 19. The inequality x+1 < 0 has no solution 20. 31.5((1.004)^20) < 31.6((1.003)^25) 21. X^-3 and -3x are like terms
22. The discriminate of the equation ax^2 + bx + c is b^2 4ac 23. a^(loga (x)) = a 24. F(x) = -2x^2 + 8x 4 is a one to one function
Fill in the Blank (2 pts each) Match the following vocabulary to the sentences below Variable Coefficients Constants Real Numbers Word Box Rational Numbers Irrational Numbers Logarithm Quadratic Equation FOIL Method Polynomial Exponential Decay Exponential Growth 25. The base b of a number x is the power to which b must be raised in order to equal x 26. are the terms in the algebraic expression that contain only numbers; they re the terms without variables. 27. cannot be expressed as a quotient of two integers. 28. An is a model for decreasing size of a quantity for which the rate is directly proportional to the amount present. 29. are the number part of the terms with variables. 30. An is a model for growth of a quantity for which the rate is directly proportional to the amount present. 31. In algebra we work with the set of, which we can model using a number line and describe real-world quantities. 32. A is the sum or difference of terms that have variables raised to positive integer powers and which have coefficients that may be real or complex. 33. In algebraic expressions, letters represent. 34. is an equation in which the highest power of an unknown quantity is a square. 35. A technique for distributing two binomials is called and stands for first, outer, inner, and last. BONUS SECTION (5 pts) 36. Solve by substitution and elimination: x + y + z = 10 2x + y + z = 2 -x +2y z = 5
Your done with your assessment! Congratulations! After determining which questions (if any!) you missed, check on this table, circle the questions you missed, and determine what areas of algebra you may not understand quite as well. Each question may fall into multiple categories. Target Question Number(s) Teacher s Comments I can examine an equation by graphing it in proper parameters I can verbally describe an equation using its giving variables I can evaluate complex equations given the values of certain or all variables I can manipulate polynomials using subtraction, multiplication, and rationalization I can divide a polynomial of variables by a monomial I can properly use properties of exponents and logarithms I can determine the zeroes of an equation by rationalization and factoring I can solve exponential and logarithmic equations with justification and clear written dialogue I can solve a given equation with multiple variables for a designated variable I understand the common formulas of Algebra and how to use them properly and to my advantage 1a, 1b, 11 2, 3, 4, 5, 6, 15 19 9, 10, 32, 33, 34, 36 10 7, 23, 25 12, 13, 14, 15, 16, 17, 18 20, 21, 23, 24, 28, 30, 31 8 21, 14, 15, 16, 17, 18, 22, 24, 26, 27, 28, 29, 35
Which area do you believe you should work on the most? Which portion of this assessment did you find the most difficult? Which portion did you find the easiest? Do you believe there is anything I as a teacher could do anything different? Good luck in your future endeavors! Congratulations on finishing your assessment!