Organization: Pearson Education
Product Name: Envision Integrated Mathematics III
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Curriculum Standards:

Analyze functions that include absolute value expressions. - HSM.A1.5.1
Graph and apply piecewise-defined functions. - HSM.A1.5.2
Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and justify results. Include problems that involve algebraic expressions, composite figures, geometric probability, and real-world applications. - G.GGMD.3
Use the change of base formula. - MAFS.912.F-BF.2.a
Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems. (e.g., Find the equation of a line parallel or perpendicular to a given line that passes through a given point.) Instructional Note: Relate work on parallel lines to work in High School Algebra I involving systems of equations having no solution or infinitely many solutions. - CAG.M.GHS.30
Express linear equations in slope-intercept, point-slope, and standard forms and convert between these forms. Given sufficient information (slope and y-intercept, slope and one-point on the line, two points on the line, x- and y-intercept, or a set of data points), write the equation of a line. - A1.A.4.3
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. - LER.M.A1HS.13
Graph and apply step functions. - HSM.A1.5.3
Graph and analyze transformations of the absolute value function. - HSM.A1.5.4
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. - MAFS.912.F-IF.3.9
Rewrite simple rational expressions in different forms; write ??(????)/??????(????????) in the form ??????????(????????????) + ??????????????(????????????????)/??????????????????(????????????????????), where ??????????????????????(????????????????????????), ??????????????????????????(????????????????????????????), ??????????????????????????????(????????????????????????????????), and ??????????????????????????????????(????????????????????????????????????) are polynomials with the degree of ??????????????????????????????????????(????????????????????????????????????????) less than the degree of ??????????????????????????????????????????(????????????????????????????????????????????), using inspection, long division, or, for the more complicated examples, a computer algebra system. - MAFS.912.A-APR.4.6
(HONORS ONLY) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. - MAFS.912.A-APR.4.7
Use coordinates to prove simple geometric theorems algebraically. (e.g., Prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, v3) lies on the circle centered at the origin and containing the point (0, 2). - CAG.M.GHS.29
Add, subtract, and multiply polynomials. - HSM.A2.3.2
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - MAFS.K12.MP.3.1.a
Prove and use polynomial identities. - HSM.A2.3.3
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - MAFS.912.F-BF.1.2
Predict the behavior of polynomial functions. - HSM.A2.3.1
Use roots of a polynomial equation to find other roots. - HSM.A2.3.6
Identify symmetry in and transform polynomial functions. - HSM.A2.3.7
Divide polynomials. - HSM.A2.3.4
Model and solve problems using the zeros of a polynomial function. - HSM.A2.3.5
Find and graph the inverse of a function, if it exists, in real-world and mathematical situations. Know that the domain of a function f is the range of the inverse function f-_, and the range of the function f is the domain of the inverse function f-_. - A2.F.2.3
Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another. - A2.F.2.4
Add, subtract, multiply, and divide functions using function notation and recognize domain restrictions. - A2.F.2.1
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Instructional Note: Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k² times the area of the first. Similarly, volumes of solid figures scale by k³ under a similarity transformation with scale factor k. - ETD.M.GHS.26
Combine functions by composition and recognize that g(x) = f-_(x), the inverse function of f(x), if and only if f(g(x))= g(f(x)) = x. - A2.F.2.2
vertical and horizontal asymptotes; - F.AII.7.i
end behavior; - F.AII.7.h
composition of functions algebraically and graphically. - F.AII.7.k
determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line; - EI.A.6.a
inverse of a function; and - F.AII.7.j
write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line; and - EI.A.6.b
intercepts; - F.AII.7.e
Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to calculate trigonometric ratios. - MAFS.912.F-TF.3.8
graph linear equations in two variables. - EI.A.6.c
zeros; - F.AII.7.d
connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs; - F.AII.7.g
values of a function for elements in its domain; - F.AII.7.f
domain, range, and continuity; - F.AII.7.a
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. - CAG.M.GHS.31
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. This standard provides practice with the distance formula and its connection with the Pythagorean theorem. - CAG.M.GHS.32
extrema; - F.AII.7.c
Derive the equation of a parabola given a focus and directrix. Instructional Note: The directrix should be parallel to a coordinate axis. - CAG.M.GHS.33
intervals in which a function is increasing or decreasing; - F.AII.7.b
Use graphs to find approximate solutions to systems of equations. - HSM.A1.4.1
Solve an equation of the form ??????????????????????????????????????????????(????????????????????????????????????????????????) = ?????????????????????????????????????????????????? for a simple function ???????????????????????????????????????????????????? that has an inverse and write an expression for the inverse. Example: For example, ??????????????????????????????????????????????????????(????????????????????????????????????????????????????????) =2 ??????????????????????????????????????????????????????????³ or ????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????) = (????????????????????????????????????????????????????????????????+1)/(??????????????????????????????????????????????????????????????????–1) for ???????????????????????????????????????????????????????????????????? ? 1. - MAFS.912.F-BF.2.4.a
Solve systems of linear equations using the substitution method. - HSM.A1.4.2
Verify by composition that one function is the inverse of another. - MAFS.912.F-BF.2.4.b
Solve systems of linear equations using the elimination method. - HSM.A1.4.3
Read values of an inverse function from a graph or a table, given that the function has an inverse. - MAFS.912.F-BF.2.4.c
Produce an invertible function from a non-invertible function by restricting the domain. - MAFS.912.F-BF.2.4.d
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: For example, if the function ??????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????) gives the number of person-hours it takes to assemble ?????????????????????????????????????????????????????????????????????????? engines in a factory, then the positive integers would be an appropriate domain for the function. - MAFS.912.F-IF.2.5
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. - MAFS.912.F-IF.2.6
Find the zeros of quadratic functions. - HSM.A2.2.3
Solve problems with complex numbers. - HSM.A2.2.4
Identify key features of quadratic functions. - HSM.A2.2.1
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. - MAFS.912.F-IF.2.4
Write and graph quadratic functions in standard form. - HSM.A2.2.2
Solve linear-quadratic systems. - HSM.A2.2.7
Solve quadratic equations by completing the square. - HSM.A2.2.5
Solve quadratic equations using the Quadratic Formula. - HSM.A2.2.6
Graph exponential and logarithmic functions. Identify asymptotes and x- and y-intercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically. - A2.F.1.4
Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease. - A2.F.1.5
Recognize the graphs of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x + c), f(x) + c, f(cx), and cf(x), where c is a positive or negative real-valued constant] algebraically and graphically, using various methods and tools that may include graphing calculators or other appropriate technology. - A2.F.1.2
Graph a quadratic function. Identify the x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology. - A2.F.1.3
Graph piecewise functions with no more than three branches (including linear, quadratic, or exponential branches) and analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant. - A2.F.1.8
Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. - A2.ASE.1
Graph a rational function and identify the x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology. (Excluding slant or oblique asymptotes and holes.) - A2.F.1.6
Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. - A2.ASE.2
Graph a radical function (square root and cube root only) and identify the x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology. - A2.F.1.7
solve multistep linear inequalities in one variable algebraically and represent the solution graphically; - EI.A.5.a
solve practical problems involving inequalities; and - EI.A.5.c
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. Instructional Note: Consider extending this standard to infinite geometric series in curricular implementations of this course description. Example:: For example, calculate mortgage payments. - PRR.M.A2HS.8
Use the structure of an expression to identify ways to rewrite it. Instructional Note: Extend to polynomial and rational expressions. Example:: 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). - PRR.M.A2HS.7
Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.) - A1.ACE.2
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. Instructional Note: Extend beyond the quadratic polynomials found in Algebra I. - PRR.M.A2HS.9
Extend polynomial identities to the complex numbers. Instructional Note: Limit to polynomials with real coefficients. Example:: For example, rewrite x² + 4 as (x + 2i)(x – 2i). - PRR.M.A2HS.4
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. - MAFS.912.G-SRT.2.5
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Instructional Note: Limit to polynomials with real coefficients. - PRR.M.A2HS.5
values of a function for elements in its domain; and - F.A.7.e
connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. - F.A.7.f
Factor a quadratic trinomial. - HSM.A1.7.5
Factor a quadratic trinomial when a ? 1. - HSM.A1.7.6
determining whether a relation is a function; - F.A.7.a
Factor special trinomials. - HSM.A1.7.7
domain and range; - F.A.7.b
Combine like terms to simplify polynomials. - HSM.A1.7.1
Multiply two polynomials. - HSM.A1.7.2
Represent relationships in various contexts with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line. - A1.A.2.2
Use patterns to multiply binomials. - HSM.A1.7.3
Factor a polynomial. - HSM.A1.7.4
Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function. - 9.2.1.6
Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods. - 9.2.1.7
evaluate algebraic expressions for given replacement values of the variables. - EO.A.1.b
Make qualitative statements about the rate of change of a function, based on its graph or table of values. - 9.2.1.8
Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations. - 9.2.1.9
The student will perform operations on complex numbers and express the results in simplest form using patterns of the powers of i. - EO.AII.2
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If ???????????????????????????????????????????????????????????????????????????? is a function and ?????????????????????????????????????????????????????????????????????????????? is an element of its domain, then ????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????) denotes the output of ???????????????????????????????????????????????????????????????????????????????????? corresponding to the input ??????????????????????????????????????????????????????????????????????????????????????. The graph of ???????????????????????????????????????????????????????????????????????????????????????? is the graph of the equation ?????????????????????????????????????????????????????????????????????????????????????????? = ????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????). - MAFS.912.F-IF.1.1
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. - MAFS.912.F-IF.1.2
Relate roots and rational exponents and use them to simplify expressions and solve equations. - HSM.A2.5.1
represent verbal quantitative situations algebraically; and - EO.A.1.a
Solve radical equations and inequalities. - HSM.A2.5.4
Perform operations on functions to answer real-world questions. - HSM.A2.5.5
Use properties of exponents and radicals to simplify radical expressions. - HSM.A2.5.2
Graph and transform radical functions. - HSM.A2.5.3
Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain. - 9.2.1.1
Distinguish between functions and other relations defined symbolically, graphically or in tabular form. - 9.2.1.2
Find the domain of a function defined symbolically, graphically or in a real-world context. - 9.2.1.3
Obtain information and draw conclusions from graphs of functions and other relations. - 9.2.1.4
Represent the inverse of a relation using tables, graphs, and equations. - HSM.A2.5.6
Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f (x) = ax2 + bx + c, in the form f(x) = a(x – h)2 + k , or in factored form. - 9.2.1.5
Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.) - A1.FLQE.5
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. - CCSS.Math.Content.HSG-GMD.A.3
Know and apply the Remainder Theorem: For a polynomial ????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????) and a number ????????????????????????????????????????????????????????????????????????????????????????????????????, the remainder on division by ?????????????????????????????????????????????????????????????????????????????????????????????????????? – ???????????????????????????????????????????????????????????????????????????????????????????????????????? is ??????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????), so ??????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????) = 0 if and only if (?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? – ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) is a factor of ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????). - MAFS.912.A-APR.2.2
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. - MAFS.912.A-APR.2.3
The student will solve problems involving equations of circles. - PC.G.12
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. - MAFS.912.G-SRT.3.8
Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph. (Limit to polynomials with degrees 3 or less.) - A2.AAPR.3
Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations. - A2.AAPR.1
Use properties of exponents to solve equations with rational exponents. - HSM.A1.6.1
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Instructional Note: Extend to simple rational and radical equations. - PRR.M.A2HS.16
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. Instructional Note: Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Instructional Note: Include combinations of linear, polynomial, rational, radical, absolute value, and exponential functions. - PRR.M.A2HS.17
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Instructional Note: Relate this standard to the relationship between zeros of quadratic functions and their factored forms. - PRR.M.A2HS.18
Prove polynomial identities and use them to describe numerical relationships. Instructional Note: This cluster has many possibilities for optional enrichment, such as relating the example in M.A2HS.10 to the solution of the system u² + v² = 1, v = t(u+1), relating the Pascal triangle property of binomial coefficients to (x + y)n+¹ = (x + y)(x + y)n, deriving explicit formulas for the coefficients, or proving the binomial theorem by induction. Example:: For example, the polynomial identity (x² + y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples. - PRR.M.A2HS.12
Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. Instructional Note: This cluster has many possibilities for optional enrichment, such as relating the example in M.A2HS.10 to the solution of the system u² + v² = 1, v = t(u+1), relating the Pascal triangle property of binomial coefficients to (x + y)n+¹ = (x + y)(x + y)n, deriving explicit formulas for the coefficients, or proving the binomial theorem by induction. - PRR.M.A2HS.13
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. Instructional Note: The limitations on rational functions apply to the rational expressions. - PRR.M.A2HS.14
Interpret the parameters in a linear or exponential function in terms of a context. Instructional Note: Limit exponential functions to those of the form f(x) = b? + k. - LER.M.A1HS.32
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Instructional Note: This standard requires the general division algorithm for polynomials. - PRR.M.A2HS.15
Describe and graph exponential functions. - HSM.A1.6.2
Use exponential functions to model situations and make predictions. - HSM.A1.6.3
Identify and describe geometric sequences. - HSM.A1.6.4
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). - PRR.M.A2HS.10
Perform, analyze, and use transformations of exponential functions. - HSM.A1.6.5
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. - PRR.M.A2HS.11
Determine the maximum or minimum value of a quadratic function by completing the square. - A2.ASE.3b
add, subtract, multiply, divide, and simplify rational algebraic expressions; - EO.AII.1.a
add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents; and - EO.AII.1.b
Use inverse variation and graph translations of the reciprocal function. - HSM.A2.4.1
factor polynomials completely in one or two variables. - EO.AII.1.c
Graph rational functions. - HSM.A2.4.2
Prove polynomial identities and use them to describe numerical relationships. Example: For example, the polynomial identity (??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)² = (??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² – ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????²)² + (2??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)² can be used to generate Pythagorean triples. - MAFS.912.A-APR.3.4
(HONORS ONLY) Know and apply the Binomial Theorem for the expansion of (?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)n in powers of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and y for a positive integer ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, where ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? are any numbers, with coefficients determined for example by Pascal’s Triangle. - MAFS.912.A-APR.3.5
Understand that the standard equation of a circle is derived from the definition of a circle and the distance formula. - G.GGPE.1
Solve rational equations and identify extraneous solutions. - HSM.A2.4.5
Find the product and the quotient of rational expressions. - HSM.A2.4.3
Find the sum or difference of rational expressions. - HSM.A2.4.4
Solve systems of linear equations using the substitution method. - A1.AREI.6
Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation. - A1.AREI.5
Use the properties of exponents to transform expressions for exponential functions. - A2.ASE.3c
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - A1.AREI.3
Use coordinates to prove simple geometric theorems algebraically. - G.GGPE.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. Instructional Note: Focus on linear and exponential functions. - LER.M.A1HS.21
Analyze slopes of lines to determine whether lines are parallel, perpendicular, or neither. Write the equation of a line passing through a given point that is parallel or perpendicular to a given line. Solve geometric and real-world problems involving lines and slope. - G.GGPE.5
Given two points, find the point on the line segment between the two points that divides the segment into a given ratio. - G.GGPE.6
Use the distance and midpoint formulas to determine distance and midpoint in a coordinate plane, as well as areas of triangles and rectangles, when given coordinates. - G.GGPE.7
Recognize that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear functions and exponential functions having integral domains. - LER.M.A1HS.18
Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context. Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear functions and exponential functions having integral domains. - LER.M.A1HS.19
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Instructional Note: Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to standards in Geometry which require students to prove the slope criteria for parallel lines. - LER.M.A1HS.14
use knowledge of transformations to convert between equations and the corresponding graphs of functions. - F.AII.6.b
recognize the general shape of function families; and - F.AII.6.a
Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????+?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? for real numbers ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - A2.AREI.4b
Write and solve equations with a variable on both sides to solve problems. - HSM.A1.1.3
Find the probability of an event given that another event has occurred. - HSM.G.12.2
Rewrite and use literal equations to solve problems. - HSM.A1.1.4
Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. Example: For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? - MAFS.912.S-IC.1.2
Use permutations and combinations to find the number of outcomes in a probability experiment. - HSM.G.12.3
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. - MAFS.912.G-CO.1.1
Solve and graph inequalities. - HSM.A1.1.5
Write and solve compound inequalities. - HSM.A1.1.6
Use probability to make decisions. - HSM.G.12.6
Understand statistics as a process for making inferences about population parameters based on a random sample from that population. - MAFS.912.S-IC.1.1
Create and solve linear equations with one variable. - HSM.A1.1.2
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. Example: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. - MAFS.912.A-CED.1.3
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - MAFS.912.A-SSE.2.3.b
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - MAFS.912.A-CED.1.2
Factor a quadratic expression to reveal the zeros of the function it defines. - MAFS.912.A-SSE.2.3.a
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: For example, rearrange Ohm’s law D.?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? = ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? to highlight resistance ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - MAFS.912.A-CED.1.4
Use the properties of exponents to transform expressions for exponential functions. Example: For example the expression 1.15 to the ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power can be rewritten as ((1.15 to the 1/12 power) to the 12?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power) is approximately equal to (1.012 to the 12???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. - MAFS.912.A-SSE.2.3.c
Write and solve absolute-value equations and inequalities - HSM.A1.1.7
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. - MAFS.912.A-CED.1.1
Use relationships among events to find probabilities. - HSM.G.12.1
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Limit to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. - RQ.M.A1HS.6
The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions. - S.A.9
Solve one-variable rational equations and check for extraneous solutions. - A2.A.1.3
Solve polynomial equations with real roots using various methods and tools that may include factoring, polynomial division, synthetic division, graphing calculators or other appropriate technology. - A2.A.1.4
Solve square root equations with one variable and check for extraneous solutions. - A2.A.1.5
Solve common and natural logarithmic equations using the properties of logarithms. - A2.A.1.6
Represent real-world or mathematical problems using quadratic equations and solve using various methods (including graphing calculator or other appropriate technology), factoring, completing the square, and the quadratic formula. Find non-real roots when they exist. - A2.A.1.1
Represent real-world or mathematical problems using exponential equations, such as compound interest, depreciation, and population growth, and solve these equations graphically (including graphing calculator or other appropriate technology) or algebraically. - A2.A.1.2
Fit a linear function for a scatter plot that suggests a linear association. - MAFS.912.S-ID.2.6.c
Use dilation and rigid motion to establish triangle similarity theorems. - HSM.G.7.3
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Extend work on linear and exponential equations in the Relationships between Quantities and Reasoning with Equations unit to quadratic equations. - EE.M.A1HS.46
Determine whether figures are similar. - HSM.G.7.2
Find the lengths of segments using proportional relationships in triangles resulting from parallel lines. - HSM.G.7.5
Use similarity and the geometric mean to solve problems involving right triangles. - HSM.G.7.4
Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions. - MAFS.912.G-CO.2.8
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Instructional Note: Include systems consisting of one linear and one quadratic equation. Include systems that lead to work with fractions. Example:: For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3. Example:: For example, finding the intersections between x² + y² = 1 and y = (x+1)/2 leads to the point (3/5, 4/5) on the unit circle, corresponding to the Pythagorean triple 3² + 4² = 5². - EE.M.A1HS.49
Dilate figures and identify characteristics of dilations. - HSM.G.7.1
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. - A2.FLQE.1b
Solve real-world and mathematical problems that can be modeled using arithmetic or finite geometric sequences or series given the nth terms and sum formulas. Graphing calculators or other appropriate technology may be used. - A2.A.1.7
Represent real-world or mathematical problems using systems of linear equations with a maximum of three variables and solve using various methods that may include substitution, elimination, and graphing (may include graphing calculators or other appropriate technology). - A2.A.1.8
Solve systems of equations containing one linear equation and one quadratic equation using tools that may include graphing calculators or other appropriate technology. - A2.A.1.9
Use the volumes of right and oblique pyramids and cones to solve problems. - HSM.G.11.3
Calculate the volume of a sphere and solve problems involving the volumes of spheres. - HSM.G.11.4
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. - MAFS.912.S-IC.2.4
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. - MAFS.912.S-IC.2.3
Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original context. - A1.A.1.3
Identify space figures and their relationships with polygons to solve problems. - HSM.G.11.1
Use the properties of prisms and cylinders to calculate their volumes. - HSM.G.11.2
Use knowledge of solving equations with rational values to represent and solve mathematical and real-world problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context. - A1.A.1.1
Add, subtract, multiply, divide, and simplify polynomial and rational expressions. - A2.A.2.2
Recognize that a quadratic function has different equivalent representations [f(x) = ax_ + bx + c, f(x)= a(x _ h)_ + k, and f(x) = (x _ h)(x _ k)]. Identify and use the representation that is most appropriate to solve real-world and mathematical problems. - A2.A.2.3
Rewrite expressions involving radicals and rational exponents using the properties of exponents. - A2.A.2.4
Factor polynomial expressions including but not limited to trinomials, differences of squares, sum and difference of cubes, and factoring by grouping using a variety of tools and strategies. - A2.A.2.1
The student will use surface area and volume of three-dimensional objects to solve practical problems. - TDF.G.13
Interpret parts of an expression, such as terms, factors, and coefficients. - PRR.M.A2HS.6.a
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. - MAFS.912.A-APR.1.1
Use trigonometry to solve problems. - HSM.G.8.5
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Note: Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. - CPC.M.GHS.9
Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.) - HSF-LE.B.5
Use trigonometric ratios to find lengths and angle measures of right triangles. - HSM.G.8.2
Prove the Pythagorean Theorem using similarity and establish the relationships in special right triangles. - HSM.G.8.1
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Instructional Note: Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems. - CPC.M.GHS.8
Use the Law of Cosines to solve problems. - HSM.G.8.4
Use the Law of Sines to solve problems. - HSM.G.8.3
Evaluate reports based on data. - MAFS.912.S-IC.2.6
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. - MAFS.912.S-IC.2.5
Determine whether a function is a relation. - HSM.A1.3.1
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. - MAFS.912.G-SRT.1.1.a
Identify, evaluate, and graph linear functions. - HSM.A1.3.2
Identify and describe arithmetic sequences. - HSM.A1.3.4
Interpret the parameters in a linear or exponential function in terms of a context. - MAFS.912.F-LE.2.5
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. - CPC.M.GHS.1
The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic and exponential functions. - S.AII.9
Use a scatter plot to describe the relationship between two data sets. - HSM.A1.3.5
Find the line of best fit for a data set and evaluate its goodness of fit. - HSM.A1.3.6
The dilation of a line segment is longer or shorter in the ratio given by the scale factor. - MAFS.912.G-SRT.1.1.b
Interpret key features of linear, quadratic, and absolute value functions given an equation or a graph. - HSM.A2.1.1
Interpret arithmetic sequences and series. - HSM.A2.1.4
Use graphs and tables to approximate solutions to algebraic equations and inequalities. - HSM.A2.1.5
Apply transformations to graph functions and write equations. - HSM.A2.1.2
Graph and interpret piecewise-defined functions. - HSM.A2.1.3
Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables. - A2.FLQE.2
Use a variety of tools to solve systems of linear equations and inequalities. - HSM.A2.1.6
Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval. - A2.FLQE.1
Solve systems of equations using matrices. - HSM.A2.1.7
The student will verify and use properties of quadrilaterals to solve problems, including practical problems. - PC.G.9
Interpret the parameters in a linear or exponential function in terms of the context. - A2.FLQE.5
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. - CWC.M.GHS.35
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - MAFS.912.A-REI.2.3
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - A2.FBF.2
Describe the effect of the transformations ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)+????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????+??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), and combinations of such transformations on the graph of ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????=??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) for any real number ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. Find the value of ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? given the graphs and write the equation of a transformed parent function given its graph. - A2.FBF.3
Use the equations and graphs of parabolas to solve problems. - HSM.G.9.4
Use the coordinate plane to analyze geometric figures. - HSM.G.9.1
Use the equations and graphs of circles to solve problems. - HSM.G.9.3
Prove geometric theorems using algebra and the coordinate plane. - HSM.G.9.2
Write and graph linear equations using point-slope form. - HSM.A1.2.2
Interpret expressions for exponential functions by using the properties of exponents. - A2.FIF.8b
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). - MAFS.912.F-LE.1.2
Use coordinates to prove simple geometric theorems algebraically. (e.g., Prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, v3) lies on the circle centered at the origin and containing the point (0, 2).) Instructional Note: Include simple proofs involving circles. - CWC.M.GHS.40
Write and graph linear equations using standard form. - HSM.A1.2.3
Write equations of parallel lines and perpendicular lines. - HSM.A1.2.4
For exponential models, express as a logarithm the solution to ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? to the ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? power = ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? where ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, and ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? are numbers and the base ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? is 2, 10, or ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????; evaluate the logarithm using technology. - MAFS.912.F-LE.1.4
Write and graph linear equations using slope-intercept form. - HSM.A1.2.1
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. Example: For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. - MAFS.912.N-RN.1.1
Rewrite expressions involving radicals and rational exponents using the properties of exponents. - MAFS.912.N-RN.1.2
Identify the effect on the graph of replacing ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) by ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) + ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? + ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) for specific values of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? (both positive and negative); find the value of ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 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. - MAFS.912.F-BF.2.3
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Understand that such systems may have zero, one, two, or infinitely many solutions. (Limit to linear equations and quadratic functions.) - A2.AREI.7
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Instructional Note: Emphasize the similarity of all circles. Reason that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course. - CWC.M.GHS.38
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. - CWC.M.GHS.39
Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise. - A2.AREI.2
the Pythagorean Theorem and its converse; - T.G.8.a
properties of special right triangles; and - T.G.8.b
Understand the conditional probability of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? given ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? as ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)/????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????), and interpret independence of ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? as saying that the conditional probability of ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? given ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? is the same as the probability of ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????, and the conditional probability of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? given ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? is the same as the probability of ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????. - MAFS.912.S-CP.1.3
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. - MAFS.912.A-REI.3.5
Define angle, perpendicular line, parallel line, line segment, ray, circle, and skew in terms of the undefined notions of point, line, and plane. Use geometric figures to represent and describe real-world objects. - G.GCO.1
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: For example, find the points of intersection between the line ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? = –3?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and the circle ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² = 3. - MAFS.912.A-REI.3.7
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. - MAFS.912.A-REI.3.6
Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence c - G.GCO.7
Prove, and apply in mathematical and real-world contexts, theorems about the relationships within and among triangles, including the following: a) measures of interior angles of a triangle sum to 180°; b) base angles of isosceles triangles are congruent; c) the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; d) the medians of a triangle meet at a point. - G.GCO.9
Solve an equation of the form ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)=????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) graphically by identifying the ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????-coordinate(s) of the point(s) of intersection of the graphs of ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????=????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????) and ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????=??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????). - A2.AREI.11
Prove, and apply in mathematical and real-world contexts, theorems about lines and angles, including the following: a vertical angles are congruent; b) when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles are supplementary; c) any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment; d) perpendicular lines form four right angles. - G.GCO.8
Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. - MAFS.912.G-CO.3.10
Understand that two events ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? are independent if the probability of ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? and ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? occurring together is the product of their probabilities, and use this characterization to determine if they are independent. - MAFS.912.S-CP.1.2
Identify the dependent and independent variables as well as the domain and range given a function, equation, or graph. Identify restrictions on the domain and range in real-world contexts. - A1.F.1.2
(HONORS ONLY) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. - MAFS.912.N-CN.3.9
(HONORS ONLY) Extend polynomial identities to the complex numbers. Example: For example, rewrite ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????² + 4 as (???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? + 2??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????)(???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? – 2??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????). - MAFS.912.N-CN.3.8
Evaluate reports based on data. Instructional Note: In earlier grades, students are introduced to different ways of collecting data and use graphical displays and summary statistics to make comparisons. These ideas are revisited with a focus on how the way in which data is collected determines the scope and nature of the conclusions that can be drawn from that data. The concept of statistical significance is developed informally through simulation as meaning a result that is unlikely to have occurred solely as a result of random selection in sampling or random assignment in an experiment. - ICD.M.A2HS.43
Use probabilities to make fair decisions (e.g., drawing by lots or using a random number generator). Instructional Note: Extend to more complex probability models. Include situations such as those involvi