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MST Standard 3 Math: Algebra 2 and Trigonometry
Through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability, students will:
  • understand the concepts of and become proficient with the skills of mathematics;
  • communicate and reason mathematically;
  • become problem solvers by using appropriate tools and strategies;
Algebra
Students will represent and analyze algebraically a wide variety of problem solving situations.
Equations and Inequalities
  A2.A.3

Solve systems of equations involving one linear equation and one quadratic equation algebraically  Note: This includes rational equations that result in linear equations with extraneous roots.

 
  A2.A.4

Solve quadratic inequalities in one and two variables, algebraically and graphically

 
  A2.A.5

Use direct and inverse variation to solve for unknown values

  A2.A.6

Solve an application which results in an exponential function

  A2.A.1

Solve absolute value equations and inequalities involving linear expressions in one variable

 
  A2.A.2

Use the discriminant to determine the nature of the roots of a quadratic equation

 
       
Algebra
Students will perform algebraic procedures accurately.
Variables and Expressions
  A2.A.18

Evaluate logarithmic expressions in any base

  A2.A.19

Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms

  A2.A.17

Simplify complex fractional expressions

 
  A2.A.16

Perform arithmetic operations with rational expressions and rename to lowest terms

 
  A2.A.10

Rewrite algebraic expressions with fractional exponents as radical expressions

 
  A2.A.11

Rewrite algebraic expressions in radical form as expressions with fractional exponents

 
  A2.A.12

Evaluate exponential expressions, including those with base

  A2.A.13

Simplify radical expressions

 
  A2.A.14

Perform addition, subtraction, multiplication, and division of radical expressions

 
  A2.A.15

Rationalize denominators involving algebraic radical expressions

 
  A2.A.7

Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials

  A2.A.8

Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents

 
  A2.A.9

Rewrite algebraic expressions that contain negative exponents using only positive exponents

 
       
Algebra
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Patterns, Relations, and Functions
  A2.A.46

Perform transformations with functions and relations:  f (x + a), f (x)+ a), f (-x), - f (x), af (x)

  A2.A.45

Determine the inverse of a function and use composition to justify the result

 
  A2.A.44

Define the inverse of a function

  A2.A.43

Determine if a function is one-to-one, onto, or both

 
  A2.A.41

Use functional notation to evaluate functions for given values in the domain

 
  A2.A.42

Find the composition of functions

  A2.A.38

Determine when a relation is a function

  A2.A.39

Determine the domain and range of a function from its equation

  A2.A.40

Write functions in functional notation

 
  A2.A.37

Define a relation and function

  A2.A.36

Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion

 
  A2.A.35

Determine the sum of the first n terms of an arithmetic or geometric series

  A2.A.34

Represent the sum of a series, using sigma notation

 
  A2.A.32

Determine a specified term of an arithmetic or geometric sequence

  A2.A.33

Specify terms of a sequence, given its recursive definition

  A2.A.31

Determine the common ratio in a geometric sequence

  A2.A.30

Determine the common difference in an arithmetic sequence

  A2.A.29

Identify an arithmetic or geometric sequence and find the formula for its nth term

 
       
Algebra
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Coordinate Geometry
  A2.A.48

Write the equation of a circle, given its center and a point on the circle

 
  A2.A.49

Write the equation of a circle from its graph

 
  A2.A.50

Approximate the solution to polynomial equations of higher degree by inspecting the graph

  A2.A.53

Graph exponential functions of the form  y = bx for positive values of b, including b = e

  A2.A.54

Graph logarithmic functions, using the inverse of the related exponential function

  A2.A.51

Determine the domain and range of a function from its graph

  A2.A.52

Identify relations and functions, using graphs

 
  A2.A.47

Determine the center-radius form for the equation of a circle in standard form

 
       
Algebra
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Trigonometric Functions
  A2.A.63

Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function

 
  A2.A.64

Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent

  A2.A.65

Sketch the graph of the inverses of the sine, cosine, and tangent functions

 
  A2.A.66

Determine the trigonometric functions of any angle, using technology

 
  A2.A.67

Justify the Pythagorean identities

  A2.A.68

Solve trigonometric equations for all values of the variable from 0º to 360º

 
  A2.A.69

Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function

  A2.A.70

Sketch and recognize one cycle of a function of the form y = A sin Bx or y = A cos Bx

  A2.A.71

Sketch and recognize the graphs of the functions y = sec(x),  y = csc(x),  y = tan(x),  and y = cot(x)

  A2.A.72

Write the trigonometric function that is represented by a given periodic graph

  A2.A.77

Apply the double-angle and half-angle formulas for trigonometric functions

  A2.A.76

Apply the angle sum and difference formulas for trigonometric functions

 
  A2.A.75

Determine the solution(s) from the SSA situation (ambiguous case)

  A2.A.74

Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle

  A2.A.55

Express and apply the six trigonometric functions as ratios of the sides of a right triangle

  A2.A.56

Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and270º angles

 
  A2.A.57

Sketch and use the reference angle for angles in standard position

 
  A2.A.58

Know and apply the co-function and reciprocal relationships between trigonometric ratios

  A2.A.59

Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles

  A2.A.61

Determine the length of an arc of a circle, given its radius and the measure of its central angle

  A2.A.60

Sketch the unit circle and represent angles in standard position

 
  A2.A.62

Find the value of trigonometric functions, if given a point on the terminal side of angle θ

 
  A2.A.73

Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines

       
Algebra
Students will perform algebraic procedures accurately.
Equations and Inequalities
  A2.A.28

Solve a logarithmic equation by rewriting as an exponential equation

  A2.A.25

Solve quadratic equations, using the quadratic formula

 
  A2.A.26

Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula

 
  A2.A.23

Solve rational equations and inequalities

  A2.A.27

Solve exponential equations with and without common bases

  A2.A.24

Know and apply the technique of completing the square

  A2.A.22

Solve radical equations

 
  A2.A.21

Determine the quadratic equation, given the sum and product of its roots

 
  A2.A.20

Determine the sum and product of the roots of a quadratic equation by examining its coefficients

 
       
Communication
Students will organize and consolidate their mathematical thinking through communication.
  A2.CM.1

Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem

 
  A2.CM.2

Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams

       
Communication
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
  A2.CM.3

Present organized mathematical ideas with the use of  appropriate standard notations, including the use ofsymbols and other representations when sharing an idea in verbal and written form

  A2.CM.4

Explain relationships among different representations of a problem

  A2.CM.5

Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid

 
  A2.CM.6

Support or reject arguments or questions raised by others about the correctness of mathematical work

 
       
Communication
Students will analyze and evaluate the mathematical thinking and strategies of others.
  A2.CM.7

Read and listen for logical understanding of mathematical thinking shared by other students

 
  A2.CM.8

Reflect on strategies of others in relation to one's own strategy

  A2.CM.9

Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

 
       
Communication
Students will use the language of mathematics to express mathematical ideas precisely.
  A2.CM.10

Use correct mathematical language in developing mathematical questions that elicit, extend, or challengeother students' conjectures

 
  A2.CM.11

Represent word problems using standard mathematical notation

 
  A2.CM.12

Understand and use appropriate language, representations, and terminology when describingobjects, relationships, mathematical solutions, and rationale

  A2.CM.13

Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

       
Connections
Students will recognize and use connections among mathematical ideas.
  A2.CN.2

Understand the corresponding procedures for similar problems or mathematical concepts

  A2.CN.1

Understand and make connections among multiple representations of the same mathematical idea

       
Connections
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
  A2.CN.5

Understand how quantitative models connect to various physical models and representations

  A2.CN.4

Understand how concepts, procedures, and mathematical  results in one area of mathematics can be used to solve problems in other areas of mathematics

 
  A2.CN.3

Model situations mathematically, using representations to draw conclusions and formulate new situations

       
Connections
Students will recognize and apply mathematics in contexts outside of mathematics.
  A2.CN.8

Develop an appreciation for the historical development of  mathematics

 
  A2.CN.7

Recognize and apply mathematical ideas to problem situations that develop outside of mathematics

  A2.CN.6

Recognize and apply mathematics to situations in the outside world

       
Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
  A2.M.1

Define radian measure

 
  A2.M.2

Convert between radian and degree measures

       
Number Sense and Operations
Students will understand meanings of operations and procedures, and how they relate to one another.
Operations
  A2.N.5

Rationalize a denominator containing a radical expression

 
  A2.N.6

Write square roots of negative numbers in terms of i

  A2.N.7

Simplify powers of i

 
  A2.N.8

Determine the conjugate of a complex number

  A2.N.9

Perform arithmetic operations on complex numbers and write the answer in the form a + bi    Note: This includes simplifying expressions with complex denominators.

  A2.N.10

Know and apply sigma notation

 
  A2.N.3

Perform arithmetic operations with polynomial expressions containing rational coefficients

 
  A2.N.1

Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (whenthe answers are rational numbers)

 
  A2.N.2

Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containingirrational numbers in radical form

 
  A2.N.4

Perform arithmetic operations on irrational expressions

 
       
Problem Solving
Students will build new mathematical knowledge through problem solving.
  A2.PS.2

Recognize and understand equivalent representations of a problem situation or a mathematical concept

  A2.PS.1

Use a variety of problem solving strategies to understand new mathematical content

       
Problem Solving
Students will solve problems that arise in mathematics and in other contexts.
  A2.PS.3

Observe and explain patterns to formulate generalizations and conjectures

  A2.PS.4

Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically)

       
Problem Solving
Students will apply and adapt a variety of appropriate strategies to solve problems.
  A2.PS.7

Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving

  A2.PS.5

Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic)

  A2.PS.6

Use a variety of strategies to extend solution methods to other problems

       
Problem Solving
Students will monitor and reflect on the process of mathematical problem solving.
  A2.PS.10

Evaluate the relative efficiency of different representations and solution methods of a problem

  A2.PS.9

Interpret solutions within the given constraints of a problem

  A2.PS.8

Determine information required to solve the problem, choose methods for obtaining the information, and define parameters for acceptable solutions

       
Reasoning and Proof
Students will recognize reasoning and proof as fundamental aspects of mathematics.
  A2.RP.1

Support mathematical ideas using a variety of strategies

       
Reasoning and Proof
Students will make and investigate mathematical conjectures.
  A2.RP.2

Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion

  A2.RP.3

Evaluate conjectures and recognize when an estimate or  approximation is more appropriate than an exact answer

  A2.RP.4

Recognize when an approximation is more appropriate than an exact answer

 
       
Reasoning and Proof
Students will develop and evaluate mathematical arguments and proofs.
  A2.RP.5

Develop, verify, and explain an argument, using appropriate mathematical ideas and language

 
  A2.RP.6

Construct logical arguments that verify claims or counterexamples that refute claims

 
  A2.RP.7

Present correct mathematical arguments in a variety of forms

 
  A2.RP.8

Evaluate written arguments for validity

 
       
Reasoning and Proof
Students will select and use various types of reasoning and methods of proof.
  A2.RP.9

Support an argument by using a systematic approach to test more than one case

  A2.RP.10

Devise ways to verify results, using counterexamples and informal indirect proof

 
  A2.RP.11

Extend specific results to more general cases

  A2.RP.12

Apply inductive reasoning in making and supporting mathematical conjectures

       
Representation
Students will create and use representations to organize, record, and communicate mathematical ideas.
  A2.R.3

Use representation as a tool for exploring and understanding mathematical ideas

  A2.R.2

Recognize, compare, and use an array of representational forms

  A2.R.1

Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts

       
Representation
Students will select, apply, and translate among mathematical representations to solve problems.
  A2.R.4

Select appropriate representations to solve problem situations

 
  A2.R.5

Investigate relationships among different representations and their impact on a given problem

       
Representation
Students will use representations to model and interpret physical, social, and mathematical phenomena.
  A2.R.6

Use mathematics to show and understand physical phenomena (e.g., investigate sound waves using the sine             and cosine functions)

  A2.R.7

Use mathematics to show and understand social phenomena (e.g., interpret the results of an opinion poll)

 
  A2.R.8

Use mathematics to show and understand mathematical phenomena (e.g., use random number generator to simulate a coin toss)

       
Statistics and Probability
Students will collect, organize, display, and analyze data.
Collection of Data
  A2.S.2

Determine factors which may affect the outcome of a survey

  A2.S.1

Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment)

       
Statistics and Probability
Students will collect, organize, display, and analyze data.
Organization and Display of Data
  A2.S.5

Know and apply the characteristics of the normal distribution

  A2.S.3

Calculate measures of central tendency with group frequency distributions

  A2.S.4

Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations

       
Statistics and Probability
Students will make predictions that are based upon data analysis.
Predictions from Data
  A2.S.6

Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate

  A2.S.7

Determine the function for the regression model, using appropriate technology, and use the regression functionto interpolate and extrapolate from the data

  A2.S.8

Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship  

       
Statistics and Probability
Students will understand and apply concepts of probability.
Probability
  A2.S.9

Differentiate between situations requiring permutations and those requiring combinations

  A2.S.10

Calculate the number of possible permutations (n Pr) of n items taken r at a time

  A2.S.16

Use the normal distribution as an approximation for binomial probabilities

 
  A2.S.14

Calculate empirical probabilities

  A2.S.15

Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most

  A2.S.13

Calculate theoretical probabilities, including geometric applications

  A2.S.12

Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event)

  A2.S.11

Calculate the number of possible combinations (n C r) of n items taken r at a time

       
 
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