# Algebra 2

## Algebra 2 Standards

##### Quarter 1 Standards:
1. Alg2.M.A.APR.B.02 (polynomial): The Highly Proficient student can determine if (x-a) is a factor of a given polynomial and explain why.

2. Alg2.M.A.APR.B.02 (quadratic): The Highly Proficient student can determine if (x-a) is a factor of a given quadratic and explain why.

3. Alg2.M.A.APR.B.03 (polynomial): The Highly Proficient student can identify zeros of polynomials by factoring, use the zeros to sketch a graph, and identify and use zeros from a graph to construct the function.

4. Alg2.M.A.APR.C.04: Prove polynomial identities and use them to describe numerical relationships.

5. Alg2.M.A.REI.B.04 (quadratic): The Highly Proficient student can determine the best method for solving a quadratic and explain whether the graph will have x-intercepts based off these solutions.

6. Alg2.M.CED.A.01: The Highly Proficient student can create equations and inequalities in one variable and use them to solve problems. Include problem-solving opportunities utilizing real-world context. Focus on equations and inequalities arising from linear, quadratic, rational, and exponential functions.

7. Alg2.M.F.IF.C.07 (quadratic): The Highly Proficient student can graph quadratic functions and show intercepts, maximums and minimums, multiplicity of zeros, domain and range, and increasing and decreasing intervals.

8. Alg2.M.F.IF.C.08: The Highly Proficient student can 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 and classify those functions as exponential growth or decay.

9. Alg2.M.F.IF.C.09: The Highly Proficient student can compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions.). Functions include linear, quadratic, exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root and piecewise-defined functions.

10. Alg2.M.F.LE.B.05: The Highly Proficient student can interpret the parameters in an exponential function with rational exponents utilizing real-world context.

11. Alg2.M.N.CN.A.01: The Highly Proficient student can apply the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Write complex numbers in the form (a+bi ) with a and b real.

12. Alg2.M.N.CN.C.07: The Highly Proficient student can solve quadratic equations with real coefficients that have complex solutions.

##### Quarter 2 Standards:
1. Alg2.M.A.APR.D.06: The Highly Proficient student can rewrite 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.

2. Alg2.M.A.REI.A.02 (radical): The Highly Proficient student can solve radical equations, explain extraneous solutions, and can justify steps by applying and naming properties.

3. Alg2.M.A.REI.A.02 (rational): The Highly Proficient student can solve rational equations, explain extraneous solutions, and can justify steps by applying and naming properties.

4. Alg2.M.A.REI.D.11: The Highly Proficient student can 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 problems in real-world context. Extend from linear, quadratic, and exponential functions to cases where f(x) and/or g(x) are polynomial, rational, exponential, and logarithmic functions.

5. Alg2.M.A.SSE.A.02: The Highly Proficient student can use structure to identify ways to rewrite polynomial and rational expressions. Focus on polynomial operations and factoring patterns.

6. Alg2.M.F.BF.B.04: The Highly Proficient student can restrict the domain of a function in order to find its inverse and interpret the meaning of and relationship between a function and its inverse in real-world context.

7. Alg2.M.F.IF.B.04: For a function that models a relationship between two quantities, the Highly Proficient student can 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. Include problem-solving opportunities utilizing a real-world context. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Functions include linear, quadratic and exponential, polynomial, logarithmic, rational, sine, cosine, tangent, square root, cube root, and piecewise-defined functions.

8. Alg2.M.F.IF.C.07 (exponential & log): The Highly Proficient student can graph exponential and logarithmic functions showing intercepts, maximums and minimums, end behavior, domain and range, and increasing and decreasing intervals.

9. Alg2.M.F.IF.C.07 (radical): The Highly Proficient student can graph square root and cube root functions showing intercepts, maximums and minimums, and increasing and decreasing intervals.

10. Alg2.M.F.IF.C.07 (rational): The Highly Proficient student can graph rational functions and show the zeros, asymptotes, and end behavior.

11. Alg2.M.F.LE.A.04: The Highly Proficient student can convert an exponential equation to a logarithmic equation and can use logarithms to solve for variables in a contextual situation.

12. Alg2.M.N.RN.A.01: The Highly Proficient student can explain how the definition 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.

13. Alg2.M.N.RN.A.02: The Highly Proficient student can rewrite expressions involving radicals and rational exponents using the properties of exponents.

##### Quarter 3 Standards:
1. Alg2.M.A.REI.C.07: The Highly Proficient student can solve a 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.

2. Alg2.M.A.SSE.B.03: The Highly Proficient student can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Include problem-solving opportunities utilizing real-world context and focus on expressions with rational exponents. c. Use the properties of exponents to transform expressions for exponential functions.

3. Alg2.M.A.SSE.B.04: The Highly Proficient student can 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.

4. Alg2.M.F.IF.C.07 (trig): The Highly Proficient student can use transformations to graph trigonometric functions showing period, midline and amplitude.

5. Alg2.M.F.TF.A.02: The Highly Proficient student can understand that any point on any circle can be identified using trigonometry functions.

6. Alg2.M.F.TF.B.05: The Highly Proficient student can create and interpret sine, cosine and tangent functions that model periodic phenomena with specified amplitude, frequency, and midline.

7. Alg2.M.F.TF.C.08: The Highly Proficient student can use the Pythagorean identity sin2(θ) + cos2(θ) = 1 and the quadrant of the angle θ to find sin(θ), cos(θ), or tan(θ) given sin(θ) or cos(θ).

8. Alg2.M.S.CP.A.03: The Highly Proficient student can 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.

9. Alg2.M.S.CP.A.04: The Highly Proficient student can 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.

10. Alg2.M.S.CP.A.05: The Highly Proficient student can explain conditional probability and independence and use them to interpret real-world probabilities.

11. Alg2.M.S.CP.B.06: The Highly Proficient student can use Bayes Rule to 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.

12. Alg2.M.S.CP.B.07: The Highly Proficient student can apply the addition rule to different representations of probability models and interpret answers in real-world context.

13. Alg2.M.S.CP.B.08: The Highly Proficient student can apply the multiplication rule to different representations of probability models and interpret answers in real-world context.

##### Quarter 4 Standards:
1. Alg2.M.A.S.ID.C.10: The Highly Proficient student can interpret parameters of exponential models.

2. Alg2.M.F.BF.A.01: The Highly Proficient student can use context to build a function to model the relationship between two quantities using an explicit expression, a recursive process, or through a combination or composition of two functions.

3. Alg2.M.F.BF.A.02: The Highly Proficient student can write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

4. Alg2.M.F.BF.B.03: The Highly Proficient student can identify the effects of transformations applied to a parent function, can find the transformation value given the graph of the transformed function, can graph a transformed function, and can recognize even and odd functions in transformation form.

5. Alg2.M.F.IF.B.06: The Highly Proficient student can calculate and interpret the rate of change from functions and from real-world data.

6. Alg2.M.F.TF.A.01: The Highly Proficient student can understand radian measure of an angle as the length of the arc on any circle subtended by the angle, measured in units of the circle's radius.

7. Alg2.M.S.IC.A.01: The Highly Proficient student can understand statistics as a process for making inferences about population parameters based on a random sample from that population.

8. Alg2.M.S.IC.A.02: The Highly Proficient student can explain whether a specified model is consistent with results from a given data-generating process.

9. Alg2.M.S.IC.B.03: The Highly Proficient student can recognize the purposes of and differences between designed experiments, sample surveys and observational studies.

10. Alg2.M.S.IC.B.04: The Highly Proficient student can use data from a sample survey to estimate a population mean or proportion; recognize that estimates are unlikely to be correct and the estimates will be more precise with larger sample sizes.

11. Alg2.M.S.ID.A.04: The Highly Proficient student can use the mean and standard deviation to fit to a normal distribution and recognizes that there are data sets for which this is not appropriate. The Highly Proficient student can use a calculator or a table to estimate areas under the normal curve.

12. Alg2.M.S.ID.B.06: The Highly Proficient student can represent data of two quantitative variables on a scatter plot, and describe how the quantities are related. Extend to polynomial and exponential models. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions, or choose a function, suggested by the context.

##### Yearly Standards (taught throughout the school year):
1. Alg2.M.A.REI.A.01: Explain each step in solving an 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. Extend from quadratic equations to rational and radical equations.

2. Alg2.M.N.Q.A.01: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays, include utilizing real-world context.

3. Alg2.M.N.Q.A.02: Define appropriate quantities for the purpose of descriptive modeling. Include problem-solving opportunities utilizing real-world context.

4. Alg2.M.N.Q.A.03: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities utilizing real-world context.

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