2014Algebra2 WinterBreakPractice AnswerKey This practice is a review of topics covered from August 2014 to December 2014. Topics include: x Equations and Inequalities x Linear Systems x Functions, Equations, and Graphs x Graphing Quadratic Functions and Equations x Polynomials & Polynomial Functions x Quadratic Functions and Equations Determine the best answer for each question. Demonstrate your understanding by showing all your work. Use additional paper as needed. Answer Key 1. MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. DOK 3 Let be the number of bags of cookies sold and let be the number of pies sold. It is possible for the students to make at least $125 selling no more than 30 items, but only if they do not sell more than 8 cookie bags. 2. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. DOK 2 Part A: $44.75 Part B: $13.50; $19.75; $26.00; $32.25; $38.50 Part C: Part D: Part E: 13 medium pizzas Part F: about 590 in.2 Part G: about $.08 per square inch 3. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales DOK 2 a=c–9 9a + 4c = 43 4. MAFS.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables DOK 1 Answer D 5. MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. DOK 2 As approaches negative infinity, both functions approach positive infinity. As approaches positive infinity, the function approaches negative infinity, but the function approaches positive infinity. 6. MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational, absolute, and exponential functions. DOK 2 Let represent the distance in miles from the lake to the fire. Use the fact that distance divided by rate equals time to write an inequality for the total time, 90 minutes, or 1.5 hours. The fire is at most 220 miles from the lake. 7. MAFS.912.F-BF.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. DOK 2 Part A: Part B: Part C: The domain of consists of all real numbers. The domain of consists of all real numbers except x = 0. 8. MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them DOK 3 Answer A 9. MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. DOK 1 MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Part A: Sunshine Plumbing: c = 80h + 100; National Plumbing: c = 60h + 140 Part B: Part C: National Plumbing is less expensive than Sunshine Plumbing when more than 2 hours of work are completed. The graph of the lines intersect when h = 2, which means that the cost of using either plumber is the same when 2 hours of work is completed. When more than 2 hours of work is completed, the graph representing Sunshine Plumbing is higher than the graph representing National Plumbing. Since the graph for Sunshine Plumbing is higher, it means that it costs more. 10. MAFS.912.A-APR1.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. DOK 1 11. MAFS.912.A-APR.2.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). DOK 1 -23 12. MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. DOK 2 A. -4 and -3 B. y 5 4 3 2 1 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 1 2 3 4 5 x 13. MAFS.912.A-APR.4.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. DOK 2 Part A: 2x + 3 Part B: x + Part C: Stephen is correct. Even though 6x2 + 5x – 6 cannot be evenly divided by x + 1, the quotient can be expressed with a remainder. The quotient is 6x – 1 – . 14. MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. DOK 2 ; ; 15. MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a) Factor a quadratic expression to reveal the zeros of the function it defines b) Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. DOK 2 150,000 units 16. MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. DOK 2 150,000 units Part A: Part B: Part C: Because implies , h. = g2. 17. MAFS.912.n-CN.1.1 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real. DOK 2 -20 18. MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.For example, represent inequalities describing nutritional and cost constraints on combinations of different foods DOK 2 (3,0) (9,6) 19. MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. DOK 2 ࢟ ൏ ሺ࢞ ሻ െ ࢟ ሺ࢞ െ ሻ 20. MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 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