References to ‘Middle School’ convey that select Washington State College Readiness Mathematics Standards (CRS) are more aligned with Washington State Middle School-level (MS) standards (especially those in the geometry and probability sections). There are also some CRS that exceed the knowledge and skill expectations of the high school standards and fit in the realm of pre-calculus as noted as well. Some of these standards match the blue, italicized extra expectations found in the CRS.

Component 8.1Recognize functional relationships presented in words, tables, graphs, and symbols.

Evidence of Learning

College Readiness Standards Wash. State K–12 Math Standards

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Alignment Code Legend:

  • 0 = No match for CRS item
  • 1 = Approximate match; wording or grain size differences
  • 2 = Clear match
8.1a
Recognize whether a relationship given in a symbolic, graphical, or tabular form is a function.
2
A1.3.A
Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.
8.1b
Determine the domain and range of a function.
2
A1.3.A
Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.
8.1c
Understand and interpret function notation, particularly as it relates to graphic displays of data.
2
A1.3.C
Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x)= b.
2
A2.5.B
Plot points, sketch, and describe the graphs of functions of the form , and solve related equations.
2
A2.5.C

Plot points, sketch, and describe the graphs of functions of the form ,, and , and solve related equations. (2)

2
A2.5.D
Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
8.1d
Demonstrate an understanding of parametric equations.

Precalculus

Component 8.2Represent basic functions (linear, quadratic, exponential, and reciprocal) and piecewise-defined
functions (varying over subintervals of the domain) using and translating among words, tables,
graphs, and symbols.

Evidence of Learning

College Readiness Standards Wash. State K–12 Math Standards

Extra Expectations: Most of the College Readiness Standards reflected here represent the basic expectations for the variety of entry-level college math (and other disciplines requiring quantitative reasoning) in Washington two- and four-year public institutions. Students needing to take higher level math courses when they enter college, especially pre-calculus and calculus courses, will need additional skills and knowledge to be prepared for those courses. These extra expectations are embedded throughout the content standards (standards 4 through 8) and are indicated by blue italicized text to distinguish them from the basic expectations.

Alignment Code Legend:

  • 0 = No match for CRS item
  • 1 = Approximate match; wording or grain size differences
  • 2 = Clear match
8.2a
Evaluate functions to generate a graph.
2
A1.7.A
Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
2
A1.5.B
Sketch the graph of a quadratic function, describe the effects changes in the parameters have on the graph, and interpret the x- intercepts as solutions to a quadratic equation. Parameters considered most useful are:
  • a and c in f(x)= ax²+ c
  • a, h, and k in f(x)= a(x – h)² + k, and
  • a, r, and s in f(x)= a(x – r)(x –s) 
2
A2.5.B
Plot points, sketch, and describe the graphs of functions of the form , and solve related equations.
2
A2.5.C
Plot points, sketch, and describe the graphs of functions of the form ,, and , and solve related equations.
2
A2.5.D
Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³+ d as an example of higher order polynomials and solve related equations.
8.2b
Describe relationships between the algebraic features of a function and the features of its graph and/or its tabular representation.
2
A1.7.A
Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
2
A1.5.B
Sketch the graph of a quadratic function, describe the effects changes in the parameters have on the graph, and interpret the x- intercepts as solutions to a quadratic equation. Parameters considered most useful are:
  • a and c in f(x)= ax²+ c
  • a, h, and k in f(x)= a(x – h)² + k, and
  • a, r, and s in f(x)= a(x – r)(x –s) 
2
A1.3.B
Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.
2
A1.4.E
Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.
1
A2.3.A
Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.
8.2c
Use simple transformations (horizontal and vertical shifts, reflections about axes, shrinks and stretches) to create the graphs of new functions using linear, quadratic, and/ or absolute value functions, cubic, quartic, exponential, logarithmic, square root, cube root, absolute value, piecewise, and rational functions of the type f(x)=1/(x-a).
2
A1.7.A
Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
2
A1.5.B
Sketch the graph of a quadratic function, describe the effects changes in the parameters have on the graph, and interpret the x- intercepts as solutions to a quadratic equation. Parameters considered most useful are:
  • a and c in f(x)= ax²+ c
  • a, h, and k in f(x)= a(x – h)² + k, and
  • a, r, and s in f(x)= a(x – r)(x –s) 
2
A1.8
Core Processes: Reasoning, problem solving, and communication (This is in everything)
2
A2.5.A
Construct new functions using the transformations f(x – h), f(x)+ k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).
8.2d
Algebraically construct new functions using addition and subtraction (e.g., profit function), multiplication, division, and composition.
2
A2.5.A
Construct new functions using the transformations f(x – h), f(x)+ k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s). 
8.2e
Given an algebraic representation of a rational function, find the intercepts, asymptotes (horizontal, vertical, and slant), and holes (discontinuities), then sketch the graph.
8.2f
Given a graph or graphical features, including degrees, intercepts, asymptotes, and/or holes (discontinuities), generate an algebraic representation of a polynomial or rational function.
8.2g
Sketch the graph of a polynomial given the degree, zeros, max/min values, and/or initial conditions.
8.2h
Graphically/numerically construct new functions using addition, subtraction and composition.
8.2i
Identify the components of composite functions (e.g., given f • g • h , find suitable functions f, g, and h) and determine the domain and range.

Component 8.3Analyze and interpret features of a function.

Evidence of Learning

College Readiness Standards Wash. State K–12 Math Standards

Footer information goes here

Alignment Code Legend:

  • 0 = No match for CRS item
  • 1 = Approximate match; wording or grain size differences
  • 2 = Clear match
8.3a
Describe patterns in the function’s rate of change, identifying intervals of increase, decrease, constancy, and, if possible, relate them to the function’s description in words or graphically (using graphic calculator).
2
A1.4.C
Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.
2
A2.5.D
Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
2
A2.5.B
Plot points, sketch, and describe the graphs of functions of the form , and solve related equations.
2
A2.5.C
Plot points, sketch, and describe the graphs of functions of the form ,, and , and solve related equations.
8.3b
Identify y-intercepts and zeros using symbols, graphs, and tables.
2
A2.5.D
Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
2
A2.5.B
Plot points, sketch, and describe the graphs of functions of the form , and solve related equations.
2
A2.5.C
Plot points, sketch, and describe the graphs of functions of the form ,, and , and solve related equations.
8.3c
Identify extrema and trends using graphs and tables.
2
A2.5.D
Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
2
A2.5.B
Plot points, sketch, and describe the graphs of functions of the form , and solve related equations.
2
A2.5.C
Plot points, sketch, and describe the graphs of functions of the form ,, and , and solve related equations.
8.3d
Recognize and sketch, without the use of technology, the graphs of the following families of functions: linear, quadratic, cubic, quartic, exponential, logarithmic, square root, cube root, absolute value, and rational functions of the type f(x)=1/(x-a), using the symmetry of odd and even functions when appropriate.
2
A1.7.A
Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
2
A1.5.B
Sketch the graph of a quadratic function, describe the effects changes in the parameters have on the graph, and interpret the x- intercepts as solutions to a quadratic equation. Parameters considered most useful are:
  • a and c in f(x)= ax²+ c
  • a, h, and k in f(x)= a(x – h)² + k, and
  • a, r, and s in f(x)= a(x – r)(x –s) 
2
A2.5.B
Plot points, sketch, and describe the graphs of functions of the form , and solve related equations.
2
A2.5.C
Plot points, sketch, and describe the graphs of functions of the form ,, and , and solve related equations.
2
A2.5.D
Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
2
A2.4.B
Graph an exponential function of the form f(x) = abx and its inverse logarithmic function.

Precalculus
8.3e
Understand the relationship between the degree of a polynomial and the number of roots; interpret the multiplicity of roots graphically.
2
A2.3.B
Determine the number and nature of the roots of a quadratic function.

Precalculus

Component 8.4 Model situations and relationships using a variety of basic functions (linear, quadratic, logarithmic, exponential, and reciprocal) and piecewise-defined functions.

Evidence of Learning

College Readiness Standards Wash. State K–12 Math Standards

Footer information goes here

Alignment Code Legend:

  • 0 = No match for CRS item
  • 1 = Approximate match; wording or grain size differences
  • 2 = Clear match
8.4a
Choose a function suitable for modeling a real world situation presented using words or data.
2
A1.1.A AND A2.1.A
Select and justify functions and equations to model and solve problems.
2
A2.6.E
Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.
8.4b
Determine and interpret the meaning of rates of change, intercepts, zeros, extrema, and trends.
2
A1.1.A AND A2.1.A
Select and justify functions and equations to model and solve problems.
2
A2.3.B
Determine the number and nature of the roots of a quadratic function.
8.4c
Abstract mathematical models from word problems and interpret solutions in the context of these source problems.
2
A1.1.A AND A2.1.A
Select and justify functions and equations to model and solve problems.
2
A1.1.B
Solve problems that can be represented by linear functions, equations, and inequalities.
2
A1.1.D
Solve problems that can be represented by quadratic functions and equations.
2
A1.1.E
Solve problems that can be represented by exponential functions and equations.
2
A1.6.D
Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.
8.4d
Identify and justify whether a result obtained from a function model has real world significance.
2
A1.8.C
Evaluate a solution for reasonableness , verify its accuracy, and interpret the solution in the context of the original problem.
2
A2.8.C
Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.

Component 8.5 (Extra Expectations)Recognize, analyze, and interpret inverse functions.

Evidence of Learning

College Readiness Standards Wash. State K–12 Math Standards

Footer information goes here

Alignment Code Legend:

  • 0 = No match for CRS item
  • 1 = Approximate match; wording or grain size differences
  • 2 = Clear match
8.5a
Explain the conceptual meaning of inverse functions using graphs, tables, in words, and arrow diagrams.

Precalculus
8.5b
Define what it means for a function to be one-to-one, identify examples and non-examples (algebraic and graphical), andgenerate examples (algebraic and graphical).

Precalculus
8.5c
Find and verify the inverse function algebraically, graphically, and numerically; restrict the domain of a function when necessary.

Precalculus

1
A2.4.A
Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

Component 8.6Recognize, analyze, interpret, and model with trigonometric functions.

Evidence of Learning

College Readiness Standards Wash. State K–12 Math Standards

Footer information goes here

Alignment Code Legend:

  • 0 = No match for CRS item
  • 1 = Approximate match; wording or grain size differences
  • 2 = Clear match
8.6a
Represent and interpret trig functions using the unit circle.
8.6b
Demonstrate an understanding of radians and degrees by converting between units, finding areas of sectors, and determining arc lengths of circles.
1
G.6.A
Derive and apply formulas for arc length and area of a sector of a
circle.
8.6c
Find exact values (without technology) of sine, cosine and tangent for unit circle and for multiples of π/6 and π/4;evaluate trigonometric ratios; and distinguish between exact and approximate values when evaluating trig ratios/functions.
8.6d
Sketch graphs of sine, cosine, and tangent functions, without technology; identify the domain, range, intercepts, and asymptotes.
8.6e
Use transformations (horizontal and vertical shifts, reflections about axes, period and amplitude changes) to create new trig functions (algebraic, tabular, and graphical).
8.6f
Know and apply the identity cos ² x+sin ² x=1 and generate related identities; apply sum and half-angle identities.
8.6g
Solve linear and quadratic equations involving trig functions.
8.6h
Generate algebraic and graphical representation of inverse trig functions (arcsin, arccos, arctan), and determine domain and range.
8.6i
Use trig and inverse trig functions to solve application problems.