# Algebra 2

### Parents, please note that these standards are listed in the order, and for the amount of time, that most Beyond Textbooks schools follow. These are guidelines, and your child's school may vary.

#### Benchmark 1:

1. Alg2.M.F.LE.A.02 (linear): I can create linear functions if provided either a graph, relationship description or input-output tables. - 15 Days
2. Alg2.M.A.APR.B.02a (quadratic): I can use a variety of techniques to factor and solve for the zeros of a polynomial. - 15 Days
3. Alg2.M.F.IF.C.07a (quadratic): I can graph quadratic functions and show/find intercepts and extrema. - 20 Days
4. Alg2.M.A.REI.B.04b (quadratic): I can determine the best method for solving a quadratic and explain whether the graph will have x-intercepts based off these solutions. - 20 Days

#### Benchmark 2:

1. Alg2.M.A.APR.B.03 (polynomial): I can identify zeroes of polynomials by factoring and use the zeroes to sketch the graph of a polynomial function. - 15 Days
2. Alg2.M.A.APR.B.02b (polynomial): I can use a variety of techniques to factor and solve for the zeros of a polynomial. - 15 Days
3. Alg2.M.A.REI.A.02 (rational):  I can solve a rational equation, remembering to check for extraneous solutions. I can solve a rational equation by graphing and justify each step. - 15 Days
4. Alg2.M.A.REI.A.02 (radical): I can solve rational equations, remembering to check for extraneous solutions. - 15 Days
5. Alg2.M.F.IF.C.07b (radical):  I can graph square root and cube root functions showing intercepts, maximums and minimums. - 15 Days
6. Alg2.M.F.IF.C.07d:  I can graph rational functions and showing the zeros, asymptotes, and end behavior. - 15 Days

#### Benchmark 3:

1. Alg2.M.F.LE.A.04: I can solve exponential functions by estimating graphically and calculating algebraically. - 30 Days
2. Alg2.M.F.BF.A.02: I can write recursive and explicit formulas for arithmetic and geometric sequences. - 30 Days
3. Alg2.M.F.IF.C.07e: I can graph exponential and logarithmic functions showing intercepts, maximums and minimums, and end behavior. - 25 Days
4. Alg2.M.F.LE.A.02 (exponential): I can create linear and exponential functions if provided either a graph, relationship description or input-output tables. - 30 Days
5. Alg2.M.A.REI.D.11: I can use technology to find and explain why x-coordinates are solutions to systems of equations. I can use technology to find a function that intersects another at a given point. - 10 Days

#### Benchmark 4:

1. Alg2.M.S.CP.A.05: I can use a multiplication rule to determine the probability of an event. - 10 Days
2. Alg2.M.S.CP.A.01:  I can use the addition rule to determine the probability of an event. - 10 Days
3. Alg2.M.F.IF.B.06: I can calculate and interpret the rate of change from functions and from real world data. - 15 Days
4. Alg2.M.S.ID.B.06a: I can draw or use a line of best fit to make predictions. - 15 Days
5. Alg2.M.S.ID.A.04: I can use the mean and standard deviation to fit to a normal distribution. - 15 Days
6. Alg2.M.F.TF.A.02: I understand how coordinates for the angles on the unit circle relate to sine and cosine ratios of a right triangle. - 10 Days
7. Alg2.M.F.IF.C.07e (trig): I can graph trigonometric functions showing period, midline and amplitude. - 10 Days

1. Alg2.M.F.IF.A.03: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n‐1) for n ≥ 1. (Month 1 & 2)
2. Alg2.M.F.LE.B.05: Interpret the parameters in a linear or exponential function in terms of a context. (Month 1, 2, 7, & 8)
3. Alg2.M.CED.A.01: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (Month 1, 2, 3, 4, 5, 7, & 8)
4. Alg2.M.F.BF.A.02: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (Month 1, 2, 4, & 5)
5. Alg2.M.F.BF.B.03: Identify the effect on the graph of replacing f (x ) by f (x ) + k , k f (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. (Month 1, 2, 3, 4, 5, 6, 7, 8, & 11)
6. Alg2.M.N.Q.A.02: Define appropriate quantities for the purpose of descriptive modeling. (Month 1 & 2)
7. Alg2.M.F.IF.C.07a: Graph linear and quadratic functions and show intercepts, maxima, and minina. (Month 1 & 2)
8. Alg2.M.F.IF.B.06: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (Month 2, 4, & 5)
9. Alg2.M.F.IF.C.08: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (Month 2, 3, & 7)
10. Alg2.M.F.IF.C.09: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (Month 2, 3, 8, & 11)
11. Alg2.M.F.BF.A.01a: 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. (Month 2 & 3)
12. Alg2.M.N.CN.A.01: Know there is a 2 complex number i such that i = −1, and every complex number has the form a + bi with a and b real. (Month 2 & 3)
13. Alg2.M.N.CN.C.07: Solve quadratic equations with real coefficients that have complex solutions. (Month 2 & 3)
14. Alg2.M.F.IF.B.04: 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. (Month 3, 4, & 5)
15. Alg2.M.F.IF.B.05: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person‐hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate. (Month 3 & 4)
16. Alg2.M.F.IF.C.07c: I can graph quadratic and polynomial functions showing intercepts, maximums and minimums, and end behavior. (Month 3, 4, & 5)
17. Alg2.M.F.BF.A.01b: Write a function that describes a relationship between two quantities. 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. (Month 3)
18. Alg2.M.APR.B.02: 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 ). (Month 3 & 4)
19. Alg2.M.A.REI.D.11: Explain why the x‐ coordinates of the points where the graphs of the equations y  = f (x ) and y  = g (x ) intersect are the solutions of the equation f (x ) = g (x ); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f (x ) and/or g (x ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (Month 3, 4, & 5)
20. Alg2.M.A.SSE.A.02: Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). (Month 3, 4, & 5)
21. Alg2.M.A.APR.D.06: 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. (Month 4 & 5)
22. Alg2.M.A.REI.A.01: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (Month 4 & 5)
23. Alg2.M.F.BF.B.04: Find inverse functions. a. Solve an equation of the form f (x ) = c  for a simple function f  that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x‐1) for x ≠ 1. (Month 5, 6, 7, & 8)
24. Alg2.M.N.RN.A.01: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. (Month 5 & 6)
25. Alg2.M.N.RN.A.02: Rewrite expressions involving radicals and rational exponents using the properties of exponents. (Month 5)
26. Alg2.M.A.SSE.B.03: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. (Month 5)
27. Alg2.M.F.IF.C.09b: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. (Month 7)
28. Alg2.M.A.SSE.B.04: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. (Month 7 & 8)
29. Alg2.M.A.REI.C.06: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (Month 8)
30. Alg2.M.A.REI.C.07: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. (Month 8)
31. Alg2.M.F.IF.C.08b: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. (Month 8)
32. Alg2.M.S.CP.A.02: Understand that two events A  and B  are independent if the probability of A  and B  occurring together is the product of their probabilities, and use this characterization to determine if they are independent. (Month 9)
33. Alg2.M.S.CP.A.03: Understand the conditional probability of A given B  as P (A  and B )/P (B ), and interpret independence of A and B  as saying that the conditional probability of A given B  is the same as the probability of A , and the conditional probability of B given A  is the same as the probability of B. (Month 9)
34. Alg2.M.S.CP.A.04: Construct and interpret two‐ way frequency tables of data when two categories are associated with each object being classified. Use the two‐ way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. (Month 9)
35. Alg2.M.S.CP.B.06: Find the conditional probability of A given B  as the fraction of B ’s outcomes that also belong to A , and interpret the answer in terms of the model. (Month 9)
36. Alg2.M.S.CP.B.07: Apply the Addition Rule, P (A  or B ) = P (A ) + P (B ) – P (A  and B ), and interpret the answer in terms of the model. (Month 9)
37. Alg2.M.S.IC.A.01: Understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population. (Month 10)
38. Alg2.M.S.IC.A.02: Decide if a specified model is consistent with results from a given data‐ generating process, e.g., using simulation. For example, a model says a spinning coin will fall heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? (Month 10)
39. Alg2.M.S.IC.B.03: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. (Month 10)
40. Alg2.M.S.IC.B.04: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. (Month 10)
41. Alg2.M.S.IC.B.06: Evaluate reports based on data. (Month 10)
42. Alg2.M.F.TF.A.01: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. (Month 10)
43. Alg2.M.G.SRT.C.08: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. (Month 10)

#### Yearly Standards:

• None
08:49, 2 Dec 2016

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