Alg2.M.A.APR.B.02a (quadratic): The Highly Proficient student can determine if (x-a) is a factor of a given polynomial and explain why.
Alg2.M.A.REI.B.04b (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.
Alg2.M.CED.A.01: The Highly Proficient student can 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.
Alg2.M.F.BF.A.01a: The Highly Proficient student can 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.
Alg2.M.F.BF.B.03: The Highly Proficient student can 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.
Alg2.M.F.LE.A.02 (linear): The Highly Proficient student can create exponential functions or sequences if provided either a graph, relationship description, or input-output tables.
Alg2.M.F.LE.B.05: The Highly Proficient student can interpret the parameters in a linear or exponential function in terms of a context.
Alg2.M.F.IF.A.03: The Highly Proficient student can 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.
Alg2.M.F.IF.C.07a (quadratic): The Highly Proficient student can graph quadratic functions showing intercepts, maximums and minimums, multiplicity of zeros, domain and range, and increasing and decreasing intervals.
Alg2.M.F.IF.C.07a: The Highly Proficient student can graph linear and quadratic functions and show intercepts, maxima, and minina.
Alg2.M.N.CN.A.01: The Highly Proficient student can 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.
Alg2.M.N.CN.C.07: The Highly Proficient student can solve quadratic equations with real coefficients that have complex solutions.
Alg2.M.N.Q.A.02: Define appropriate quantities for the purpose of descriptive modeling.
Alg2.M.APR.B.02: The Highly Proficient student can 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 ).
Alg2.M.A.APR.B.02b (polynomial): The Highly Proficient student can determine if (x-a) is a factor of a given polynomial and explain why.
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.
Alg2.M.A.APR.D.06: The Highly Proficient student can 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.
Alg2.M.A.REI.A.01: The Highly Proficient student can 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.
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.
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.
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 cases where f (x ) and/or g (x ) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Alg2.M.A.SSE.A.02: The Highly Proficient student can 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).
Alg2.M.F.BF.A.01b: The Highly Proficient student can 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.
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Alg2.M.F.IF.B.06: The Highly Proficient student can 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.
Alg2.M.F.IF.C.07c: The Highly Proficient student can graph quadratic and polynomial functions showing intercepts, maximums and minimums, and end behavior.
Alg2.M.F.IF.C.07b (radical): The Highly Proficient student can graph square root and cube root functions showing intercepts, maximums and minimums, and increasing and decreasing intervals.
Alg2.M.F.IF.C.07d: The Highly Proficient student can graph rational functions and show the zeros, asymptotes, and end behavior.
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.
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). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Alg2.M.A.REI.C.06: The Highly Proficient student can solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Alg2.M.A.REI.C.07: The Highly Proficient student can 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.
Alg2.M.A.REI.D.11: The Highly Proficient student can find the intersection of two functions set equal to each other and explain why the x-coordinate is the solution.
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. 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%.
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.
Alg2.M.F.BF.A.02: The Highly Proficient student can write recursive and explicit formulas for arithmetic and geometric sequences.
Alg2.M.F.BF.B.04: The Highly Proficient student can 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.
Alg2.M.F.LE.A.02 (exponential): The Highly Proficient student can create exponential functions or sequences if provided either a graph, relationship description, or input-output tables.
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.
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.
Alg2.M.F.IF.C.07e: 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. The Highly Proficient student can use transformations to graph trigonometric functions showing period, midline and amplitude.
Alg2.M.F.IF.C.08b: 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. 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.
Alg2.M.F.IF.C.09b: 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). 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.
Alg2.M.N.RN.A.01: The Highly Proficient student can 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.
Alg2.M.N.RN.A.02: The Highly Proficient student can rewrite expressions involving radicals and rational exponents using the properties of exponents.
Alg2.M.F.IF.C.07e (trig): 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. The Highly Proficient student can use transformations to graph trigonometric functions showing period, midline and amplitude.
Alg2.M.F.TF.A.02: The Highly Proficient student can understand that any point on any circle can be identified using trigonometry functions.
Alg2.M.F.TF.A.01: The Highly Proficient student can understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Alg2.M.S.CP.A.01: The Highly Proficient student can describe and make sense of probability events using appropriate set language, such as union, intersection and complement.
Alg2.M.S.CP.A.02: The Highly Proficient student can 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.
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.
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. 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.
Alg2.M.S.CP.A.05: The Highly Proficient student can explain conditional probability and independence and use them to interpret real-world probabilities.
Alg2.M.S.CP.B.06: The Highly Proficient student can 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.
Alg2.M.S.CP.B.07: The Highly Proficient student can 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.
Alg2.M.S.IC.A.01: The Highly Proficient student can understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population.
Alg2.M.S.IC.A.02: The Highly Proficient student can 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?
Alg2.M.S.IC.B.03: The Highly Proficient student can recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Alg2.M.S.IC.B.04: The Highly Proficient student can 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.
Alg2.M.S.IC.B.06: The Highly Proficient student can evaluate reports based on data.
Alg2.M.S.ID.A.04: The Highly Proficient student can use the mean and standard deviation to fit to a normal distribution.
Alg2.M.S.ID.B.06a: The Highly Proficient student can find and use the best function for data in a scatterplot, including linear and non-linear functions.
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