High School Algebra 1 – CA Common Core – Standards & Learning Objectives

9-12.N Number and Quantity

9-12.N-RN The Real Number System

9-12. Extend the properties of exponents to rational exponents.

9-12.N-RN.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.

Evaluate integers raised to rational exponents (Algebra 1 – V.10)

Evaluate rational exponents (Algebra 2 – M.1)

Evaluate rational exponents (Precalculus – H.4)

 

9-12.N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Simplify radical expressions (Algebra 1 – EE.1)

Simplify radical expressions involving fractions (Algebra 1 – EE.2)

Multiply radical expressions (Algebra 1 – EE.3)

Add and subtract radical expressions (Algebra 1 – EE.4)

Simplify radical expressions using the distributive property (Algebra 1 – EE.5)

Simplify radical expressions: mixed review (Algebra 1 – EE.7)

Simplify radical expressions (Geometry – A.4)

Roots of integers (Algebra 2 – L.1)

Roots of rational numbers (Algebra 2 – L.2)

Nth roots (Algebra 2 – L.4)

Simplify radical expressions with variables I (Algebra 2 – L.5)

Simplify radical expressions with variables II (Algebra 2 – L.6)

Multiply radical expressions (Algebra 2 – L.7)

Divide radical expressions (Algebra 2 – L.8)

Add and subtract radical expressions (Algebra 2 – L.9)

Simplify radical expressions using the distributive property (Algebra 2 – L.10)

Simplify radical expressions using conjugates (Algebra 2 – L.11)

Multiplication with rational exponents (Algebra 2 – M.2)

Division with rational exponents (Algebra 2 – M.3)

Power rule (Algebra 2 – M.4)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Operations with rational exponents (Precalculus – H.5)

Nth roots (Precalculus – H.6)

Simplify radical expressions with variables (Precalculus – H.7)

Simplify expressions involving rational exponents (Precalculus – H.8)

 

9-12. Use properties of rational and irrational numbers.

9-12.N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Classify rational and irrational numbers (Precalculus – Q.1)

Sort rational and irrational numbers (Precalculus – Q.2)

Properties of operations on rational and irrational numbers (Precalculus – Q.3)

 

9-12.N-Q Quantities

 

9-12. Reason quantitatively and use units to solve problems.

 

9-12.N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Scale drawings and scale factors (Algebra 1 – C.7)

Convert rates and measurements: customary units (Algebra 1 – E.1)

Convert rates and measurements: metric units (Algebra 1 – E.2)

Unit prices with unit conversions (Algebra 1 – E.3)

Scale maps and drawings (Geometry – A.2)

Convert rates and measurements: customary units (Geometry – W.1)

Convert rates and measurements: metric units (Geometry – W.2)

Convert square and cubic units of length (Geometry – W.3)

 

9-12.N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.

Interpret bar graphs, line graphs, and histograms (Algebra 1 – N.1)

Create bar graphs, line graphs, and histograms (Algebra 1 – N.2)

Interpret stem-and-leaf plots (Algebra 1 – N.4)

Interpret box-and-whisker plots (Algebra 1 – N.5)

Interpret a scatter plot (Algebra 1 – N.6)

Scatter plots: line of best fit (Algebra 1 – N.7)

 

9-12.N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Precision (Algebra 1 – E.4)

Greatest possible error (Algebra 1 – E.5)

Precision (Geometry – W.4)

Greatest possible error (Geometry – W.5)

Minimum and maximum area and volume (Geometry – W.6)

Percent error (Geometry – W.7)

Percent error: area and volume (Geometry – W.8)

9-12.A. Algebra

9-12.A-SSE Seeing Structure in Expressions

9-12. Interpret the structure of expressions

9-12.A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

 

9-12.A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

Polynomial vocabulary (Algebra 1 – Z.1)

Polynomial vocabulary (Algebra 2 – K.1)

 

9-12.A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

Factor using a quadratic pattern (Algebra 2 – I.4)

Factor using a quadratic pattern (Precalculus – D.14)

 

9-12.A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

Simplify variable expressions using properties (Algebra 1 – H.3)

Simplify variable expressions involving like terms and the distributive property (Algebra 1 – I.2)

Simplify expressions involving exponents (Algebra 1 – V.8)

Powers of monomials (Algebra 1 – Y.5)

Factor out a monomial (Algebra 1 – AA.2)

Simplify variable expressions using properties (Algebra 2 – A.3)

Pascal’s triangle and the Binomial Theorem (Algebra 2 – K.17)

Binomial Theorem I (Algebra 2 – K.18)

Binomial Theorem II (Algebra 2 – K.19)

Simplify radical expressions with variables I (Algebra 2 – L.5)

Simplify radical expressions with variables II (Algebra 2 – L.6)

Simplify radical expressions using conjugates (Algebra 2 – L.11)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Simplify rational expressions (Algebra 2 – N.4)

Pascal’s triangle and the Binomial Theorem (Precalculus – D.17)

Binomial Theorem I (Precalculus – D.18)

Binomial Theorem II (Precalculus – D.19)

Simplify radical expressions with variables (Precalculus – H.7)

Simplify expressions involving rational exponents (Precalculus – H.8)

 

9-12. Write expressions in equivalent forms to solve problems

 

9-12.A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

 

9-12.A-SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

Factor quadratics with leading coefficient 1 (Algebra 1 – AA.3)

Factor quadratics with other leading coefficients (Algebra 1 – AA.4)

Factor quadratics: special cases (Algebra 1 – AA.5)

Solve a quadratic equation by factoring (Algebra 1 – BB.6)

Factor quadratics (Algebra 2 – I.2)

Solve a quadratic equation by factoring (Algebra 2 – J.8)

Solve a quadratic equation by factoring (Precalculus – C.6)

 

9-12.A-SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Complete the square (Algebra 1 – BB.7)

Complete the square (Algebra 2 – J.9)

Convert equations of parabolas from general to vertex form (Algebra 2 – T.7)

Find properties of a parabola from equations in general form (Algebra 2 – T.8)

 

9-12.A-SSE.3.c Use the properties of exponents to transform expressions for exponential functions.

Negative exponents (Algebra 1 – V.3)

Multiplication with exponents (Algebra 1 – V.4)

Division with exponents (Algebra 1 – V.5)

Multiplication and division with exponents (Algebra 1 – V.6)

Power rule (Algebra 1 – V.7)

Simplify expressions involving exponents (Algebra 1 – V.8)

Evaluate an exponential function (Algebra 1 – X.1)

Match exponential functions and graphs (Algebra 1 – X.2)

Properties of exponents (Geometry – A.3)

Evaluate rational exponents (Algebra 2 – M.1)

Multiplication with rational exponents (Algebra 2 – M.2)

Division with rational exponents (Algebra 2 – M.3)

Power rule (Algebra 2 – M.4)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Evaluate exponential functions (Algebra 2 – S.2)

Match exponential functions and graphs (Algebra 2 – S.3)

Solve exponential equations using factoring (Algebra 2 – S.4)

Solve exponential equations using factoring (Precalculus – F.9)

 

9-12.A-APR Arithmetic with Polynomials and Rational Expressions

 

9-12. Perform arithmetic operations on polynomials

 

9-12.A-APR.1 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.

Model polynomials with algebra tiles (Algebra 1 – Z.2)

Add and subtract polynomials using algebra tiles (Algebra 1 – Z.3)

Add and subtract polynomials (Algebra 1 – Z.4)

Add polynomials to find perimeter (Algebra 1 – Z.5)

Multiply a polynomial by a monomial (Algebra 1 – Z.6)

Multiply two polynomials using algebra tiles (Algebra 1 – Z.7)

Multiply two binomials (Algebra 1 – Z.8)

Multiply two binomials: special cases (Algebra 1 – Z.9)

Multiply polynomials (Algebra 1 – Z.10)

Add and subtract polynomials (Algebra 2 – K.2)

Multiply polynomials (Algebra 2 – K.3)

 

9-12.A-CED Creating Equations

 

9-12. Create equations that describe numbers or relationships

 

9-12.A-CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

Write variable equations (Algebra 1 – I.4)

Model and solve equations using algebra tiles (Algebra 1 – J.1)

Write and solve equations that represent diagrams (Algebra 1 – J.2)

Solve linear equations: word problems (Algebra 1 – J.8)

Write inequalities from graphs (Algebra 1 – K.2)

Write compound inequalities from graphs (Algebra 1 – K.13)

Weighted averages: word problems (Algebra 1 – O.5)

Write variable expressions and equations (Geometry – A.5)

Solve linear equations (Geometry – A.6)

Solve linear inequalities (Geometry – A.7)

Solve linear equations (Algebra 2 – B.1)

Solve linear equations: word problems (Algebra 2 – B.2)

Write inequalities from graphs (Algebra 2 – C.3)

Solve linear inequalities (Algebra 2 – C.5)

Solve equations with sums and differences of cubes (Precalculus – D.13)

Solve equations using a quadratic pattern (Precalculus – D.15)

 

9-12.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Graph a function (Algebra 1 – Q.9)

Write a function rule: word problems (Algebra 1 – Q.10)

Write a rule for a function table (Algebra 1 – Q.12)

Write direct variation equations (Algebra 1 – R.4)

Write inverse variation equations (Algebra 1 – R.7)

Write and solve inverse variation equations (Algebra 1 – R.8)

Find a missing coordinate using slope (Algebra 1 – S.4)

Slope-intercept form: graph an equation (Algebra 1 – S.6)

Slope-intercept form: write an equation from a graph (Algebra 1 – S.7)

Slope-intercept form: write an equation (Algebra 1 – S.8)

Linear function word problems (Algebra 1 – S.10)

Write equations in standard form (Algebra 1 – S.11)

Standard form: graph an equation (Algebra 1 – S.13)

Point-slope form: graph an equation (Algebra 1 – S.16)

Point-slope form: write an equation (Algebra 1 – S.18)

Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)

Graph an absolute value function (Algebra 1 – DD.3)

Graph a linear equation (Geometry – E.3)

Equations of lines (Geometry – E.4)

Graph a linear inequality in the coordinate plane (Algebra 2 – C.2)

Graph a quadratic function (Algebra 2 – J.4)

Write and solve direct variation equations (Algebra 2 – Q.1)

Write and solve inverse variation equations (Algebra 2 – Q.2)

Write joint and combined variation equations I (Algebra 2 – Q.4)

Write joint and combined variation equations II (Algebra 2 – Q.6)

Solve variation equations (Algebra 2 – Q.7)

Graph parabolas (Algebra 2 – T.9)

Graph circles (Algebra 2 – U.7)

Graph sine functions (Algebra 2 – Z.4)

Graph cosine functions (Algebra 2 – Z.8)

Graph sine and cosine functions (Algebra 2 – Z.9)

Graph a quadratic function (Precalculus – C.3)

Graph sine functions (Precalculus – N.4)

Graph cosine functions (Precalculus – N.8)

Graph sine and cosine functions (Precalculus – N.9)

Graph parabolas (Precalculus – P.3)

Graph circles (Precalculus – P.6)

 

9-12.A-CED.3 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.

Solve a system of equations by graphing: word problems (Algebra 1 – U.3)

Solve a system of equations using substitution: word problems (Algebra 1 – U.9)

Solve a system of equations using elimination: word problems (Algebra 1 – U.11)

Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)

Solve a system of equations using any method: word problems (Algebra 1 – U.15)

Solve systems of linear equations (Geometry – A.8)

Solve a system of equations by graphing: word problems (Algebra 2 – E.3)

Solve a system of equations using substitution: word problems (Algebra 2 – E.7)

Solve a system of equations using elimination: word problems (Algebra 2 – E.9)

Solve a system of equations using any method: word problems (Algebra 2 – E.11)

Solve systems of linear inequalities by graphing (Algebra 2 – F.2)

Solve systems of linear and absolute value inequalities by graphing (Algebra 2 – F.3)

Find the vertices of a solution set (Algebra 2 – F.4)

Linear programming (Algebra 2 – F.5)

Solve a system of equations by graphing (Precalculus – I.1)

Solve a system of equations by graphing: word problems (Precalculus – I.2)

Solve a system of equations using substitution (Precalculus – I.4)

Solve a system of equations using substitution: word problems (Precalculus – I.5)

Solve a system of equations using elimination (Precalculus – I.6)

Solve a system of equations using elimination: word problems (Precalculus – I.7)

Solve systems of linear inequalities by graphing (Precalculus – J.1)

Solve systems of linear and absolute value inequalities by graphing (Precalculus – J.2)

Find the vertices of a solution set (Precalculus – J.3)

Linear programming (Precalculus – J.4)

 

9-12.A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Rate of travel: word problems (Algebra 1 – O.4)

Solve multi-variable equations (Algebra 2 – B.5)

 

9-12.A-REI Reasoning with Equations and Inequalities

 

9-12. Understand solving equations as a process of reasoning and explain the reasoning

 

9-12.A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Properties of equality (Algebra 1 – H.4)

Weighted averages: word problems (Algebra 1 – O.5)

 

9-12. Solve equations and inequalities in one variable

 

9-12.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Model and solve equations using algebra tiles (Algebra 1 – J.1)

Write and solve equations that represent diagrams (Algebra 1 – J.2)

Solve one-step linear equations (Algebra 1 – J.3)

Solve two-step linear equations (Algebra 1 – J.4)

Solve advanced linear equations (Algebra 1 – J.5)

Solve equations with variables on both sides (Algebra 1 – J.6)

Identities and equations with no solutions (Algebra 1 – J.7)

Solve linear equations: word problems (Algebra 1 – J.8)

Solve linear equations: mixed review (Algebra 1 – J.9)

Identify solutions to inequalities (Algebra 1 – K.3)

Solve one-step linear inequalities: addition and subtraction (Algebra 1 – K.4)

Solve one-step linear inequalities: multiplication and division (Algebra 1 – K.5)

Solve one-step linear inequalities (Algebra 1 – K.6)

Graph solutions to one-step linear inequalities (Algebra 1 – K.7)

Solve two-step linear inequalities (Algebra 1 – K.8)

Graph solutions to two-step linear inequalities (Algebra 1 – K.9)

Solve advanced linear inequalities (Algebra 1 – K.10)

Graph solutions to advanced linear inequalities (Algebra 1 – K.11)

Graph compound inequalities (Algebra 1 – K.12)

Write compound inequalities from graphs (Algebra 1 – K.13)

Solve compound inequalities (Algebra 1 – K.14)

Graph solutions to compound inequalities (Algebra 1 – K.15)

Solve linear equations (Geometry – A.6)

Solve linear inequalities (Geometry – A.7)

Solve linear equations (Algebra 2 – B.1)

Solve linear equations: word problems (Algebra 2 – B.2)

Solve linear inequalities (Algebra 2 – C.5)

Graph solutions to linear inequalities (Algebra 2 – C.6)

 

9-12.A-REI.3.1 Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

Solve absolute value equations (Algebra 1 – L.1)

Graph solutions to absolute value equations (Algebra 1 – L.2)

Solve absolute value inequalities (Algebra 1 – L.3)

Graph solutions to absolute value inequalities (Algebra 1 – L.4)

Solve absolute value equations (Algebra 2 – B.3)

Graph solutions to absolute value equations (Algebra 2 – B.4)

Solve absolute value inequalities (Algebra 2 – C.7)

Graph solutions to absolute value inequalities (Algebra 2 – C.8)

 

9-12.A-REI.4 Solve quadratic equations in one variable.

 

9-12.A-REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

Complete the square (Algebra 1 – BB.7)

Complete the square (Algebra 2 – J.9)

 

9-12.A-REI.4.b Solve quadratic equations by inspection (e.g., for x² = 49), 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 a ± bi for real numbers a and b.

Solve a quadratic equation using square roots (Algebra 1 – BB.4)

Solve an equation using the zero product property (Algebra 1 – BB.5)

Solve a quadratic equation by factoring (Algebra 1 – BB.6)

Complete the square (Algebra 1 – BB.7)

Solve a quadratic equation by completing the square (Algebra 1 – BB.8)

Solve a quadratic equation using the quadratic formula (Algebra 1 – BB.9)

Using the discriminant (Algebra 1 – BB.10)

Solve quadratic equations (Geometry – A.9)

Solve a quadratic equation using square roots (Algebra 2 – J.6)

Solve a quadratic equation using the zero product property (Algebra 2 – J.7)

Solve a quadratic equation by factoring (Algebra 2 – J.8)

Solve a quadratic equation using the quadratic formula (Algebra 2 – J.11)

Using the discriminant (Algebra 2 – J.12)

Solve a quadratic equation using square roots (Precalculus – C.5)

Solve a quadratic equation by factoring (Precalculus – C.6)

Solve a quadratic equation by completing the square (Precalculus – C.7)

Solve a quadratic equation using the quadratic formula (Precalculus – C.8)

 

9-12. Solve systems of equations

 

9-12.A-REI.5 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.

Solve a system of equations using elimination (Algebra 1 – U.10)

Solve a system of equations using elimination: word problems (Algebra 1 – U.11)

Solve a system of equations using augmented matrices (Algebra 1 – U.12)

Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)

Solve a system of equations using elimination (Algebra 2 – E.8)

Solve a system of equations using elimination: word problems (Algebra 2 – E.9)

Solve a system of equations using elimination (Precalculus – I.6)

Solve a system of equations using elimination: word problems (Precalculus – I.7)

 

9-12.A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Is (x, y) a solution to the system of equations? (Algebra 1 – U.1)

Solve a system of equations by graphing (Algebra 1 – U.2)

Solve a system of equations by graphing: word problems (Algebra 1 – U.3)

Find the number of solutions to a system of equations by graphing (Algebra 1 – U.4)

Find the number of solutions to a system of equations (Algebra 1 – U.5)

Classify a system of equations by graphing (Algebra 1 – U.6)

Classify a system of equations (Algebra 1 – U.7)

Solve a system of equations using substitution (Algebra 1 – U.8)

Solve a system of equations using substitution: word problems (Algebra 1 – U.9)

Solve a system of equations using elimination (Algebra 1 – U.10)

Solve a system of equations using elimination: word problems (Algebra 1 – U.11)

Solve a system of equations using augmented matrices (Algebra 1 – U.12)

Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)

Solve a system of equations using any method (Algebra 1 – U.14)

Solve a system of equations using any method: word problems (Algebra 1 – U.15)

Solve systems of linear equations (Geometry – A.8)

Is (x, y) a solution to the system of equations? (Algebra 2 – E.1)

Solve a system of equations by graphing (Algebra 2 – E.2)

Solve a system of equations by graphing: word problems (Algebra 2 – E.3)

Find the number of solutions to a system of equations (Algebra 2 – E.4)

Classify a system of equations (Algebra 2 – E.5)

Solve a system of equations using substitution (Algebra 2 – E.6)

Solve a system of equations using substitution: word problems (Algebra 2 – E.7)

Solve a system of equations using elimination (Algebra 2 – E.8)

Solve a system of equations using elimination: word problems (Algebra 2 – E.9)

Solve a system of equations using any method (Algebra 2 – E.10)

Solve a system of equations using any method: word problems (Algebra 2 – E.11)

Solve a system of equations by graphing (Precalculus – I.1)

Solve a system of equations by graphing: word problems (Precalculus – I.2)

Classify a system of equations (Precalculus – I.3)

Solve a system of equations using substitution (Precalculus – I.4)

Solve a system of equations using substitution: word problems (Precalculus – I.5)

Solve a system of equations using elimination (Precalculus – I.6)

Solve a system of equations using elimination: word problems (Precalculus – I.7)

 

9-12.A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Solve a non-linear system of equations (Algebra 2 – E.15)

 

9-12. Represent and solve equations and inequalities graphically

 

9-12.A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Relations: convert between tables, graphs, mappings, and lists of points (Algebra 1 – Q.1)

Complete a function table (Algebra 1 – Q.6)

Graph a function (Algebra 1 – Q.9)

Find points on a function graph (Algebra 1 – Q.11)

 

9-12.A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Solve a system of equations by graphing (Algebra 1 – U.2)

Solve a system of equations by graphing: word problems (Algebra 1 – U.3)

Find the number of solutions to a system of equations by graphing (Algebra 1 – U.4)

Solve a system of equations by graphing (Precalculus – I.1)

Solve a system of equations by graphing: word problems (Precalculus – I.2)

 

9-12.A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Graph a linear inequality in the coordinate plane (Algebra 1 – T.3)

Graph a linear inequality in the coordinate plane (Algebra 2 – C.2)

Solve systems of linear inequalities by graphing (Algebra 2 – F.2)

Solve systems of linear inequalities by graphing (Precalculus – J.1)

9-12.F Functions

 

9-12.F-IF Interpreting Functions

 

9-12. Understand the concept of a function and use function notation

 

9-12.F-IF.1 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 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).

Domain and range of relations (Algebra 1 – Q.2)

Identify independent and dependent variables (Algebra 1 – Q.3)

Identify functions (Algebra 1 – Q.4)

Identify functions: vertical line test (Algebra 1 – Q.5)

Domain and range of absolute value functions (Algebra 1 – DD.2)

Domain and range of radical functions (Algebra 1 – FF.2)

Domain and range (Algebra 2 – D.1)

Identify functions (Algebra 2 – D.2)

Domain and range (Precalculus – A.1)

Identify functions (Precalculus – A.2)

Domain and range of exponential and logarithmic functions (Precalculus – F.1)

Domain and range of radical functions (Precalculus – G.1)

 

9-12.F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Complete a function table (Algebra 1 – Q.6)

Evaluate function rules I (Algebra 1 – Q.7)

Evaluate function rules II (Algebra 1 – Q.8)

Evaluate an exponential function (Algebra 1 – X.1)

Complete a function table: quadratic functions (Algebra 1 – BB.2)

Complete a function table: absolute value functions (Algebra 1 – DD.1)

Evaluate a radical function (Algebra 1 – FF.1)

Evaluate functions (Algebra 2 – D.3)

Evaluate logarithms (Algebra 2 – R.4)

Evaluate natural logarithms (Algebra 2 – R.5)

Evaluate logarithms: mixed review (Algebra 2 – R.12)

Evaluate exponential functions (Algebra 2 – S.2)

Evaluate functions (Precalculus – A.5)

 

9-12.F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Identify arithmetic and geometric sequences (Algebra 1 – P.1)

Arithmetic sequences (Algebra 1 – P.2)

Geometric sequences (Algebra 1 – P.3)

Evaluate variable expressions for number sequences (Algebra 1 – P.4)

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Number sequences: mixed review (Algebra 1 – P.7)

Classify formulas and sequences (Algebra 2 – BB.1)

Find terms of an arithmetic sequence (Algebra 2 – BB.2)

Find terms of a geometric sequence (Algebra 2 – BB.3)

Find terms of a recursive sequence (Algebra 2 – BB.4)

Evaluate formulas for sequences (Algebra 2 – BB.5)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Write a formula for a recursive sequence (Algebra 2 – BB.8)

Sequences: mixed review (Algebra 2 – BB.9)

Find terms of a sequence (Precalculus – W.1)

Find terms of a recursive sequence (Precalculus – W.2)

Identify a sequence as explicit or recursive (Precalculus – W.3)

Find a recursive formula (Precalculus – W.4)

 

9-12. Interpret functions that arise in applications in terms of the context

 

9-12.F-IF.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.

Identify proportional relationships (Algebra 1 – R.1)

Find the constant of variation (Algebra 1 – R.2)

Graph a proportional relationship (Algebra 1 – R.3)

Identify direct variation and inverse variation (Algebra 1 – R.6)

Slope-intercept form: find the slope and y-intercept (Algebra 1 – S.5)

Standard form: find x- and y-intercepts (Algebra 1 – S.12)

Slopes of parallel and perpendicular lines (Algebra 1 – S.19)

Characteristics of quadratic functions (Algebra 1 – BB.1)

Identify linear, quadratic, and exponential functions from graphs (Algebra 1 – CC.1)

Identify linear, quadratic, and exponential functions from tables (Algebra 1 – CC.2)

Graph an absolute value function (Algebra 1 – DD.3)

Rational functions: asymptotes and excluded values (Algebra 1 – GG.1)

Slopes of lines (Geometry – E.2)

Characteristics of quadratic functions (Algebra 2 – J.1)

Graph a quadratic function (Algebra 2 – J.4)

Match quadratic functions and graphs (Algebra 2 – J.5)

Match polynomials and graphs (Algebra 2 – K.14)

Rational functions: asymptotes and excluded values (Algebra 2 – N.1)

Classify variation (Algebra 2 – Q.3)

Find the constant of variation (Algebra 2 – Q.5)

Match exponential functions and graphs (Algebra 2 – S.3)

Linear functions (Precalculus – A.3)

Characteristics of quadratic functions (Precalculus – C.1)

Find the maximum or minimum value of a quadratic function (Precalculus – C.2)

Match quadratic functions and graphs (Precalculus – C.4)

Match polynomials and graphs (Precalculus – D.11)

Rational functions: asymptotes and excluded values (Precalculus – E.1)

 

9-12.F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Domain and range of absolute value functions (Algebra 1 – DD.2)

Domain and range of radical functions (Algebra 1 – FF.2)

Domain and range (Algebra 2 – D.1)

Domain and range of radical functions (Algebra 2 – L.12)

Domain and range of exponential and logarithmic functions (Algebra 2 – S.1)

Domain and range (Precalculus – A.1)

Domain and range of exponential and logarithmic functions (Precalculus – F.1)

Domain and range of radical functions (Precalculus – G.1)

 

9-12.F-IF.6 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.

Find the constant of variation (Algebra 1 – R.2)

Find the slope of a graph (Algebra 1 – S.2)

Find the slope from two points (Algebra 1 – S.3)

Slope-intercept form: find the slope and y-intercept (Algebra 1 – S.5)

Find the slope of a linear function (Algebra 2 – D.4)

Linear functions (Precalculus – A.3)

 

9-12. Analyze functions using different representations

 

9-12.F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

 

9-12.F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

Slope-intercept form: graph an equation (Algebra 1 – S.6)

Standard form: graph an equation (Algebra 1 – S.13)

Point-slope form: graph an equation (Algebra 1 – S.16)

Characteristics of quadratic functions (Algebra 1 – BB.1)

Graph a linear equation (Geometry – E.3)

Graph a linear function (Algebra 2 – D.5)

Graph a quadratic function (Algebra 2 – J.4)

Match quadratic functions and graphs (Algebra 2 – J.5)

Characteristics of quadratic functions (Precalculus – C.1)

Find the maximum or minimum value of a quadratic function (Precalculus – C.2)

Graph a quadratic function (Precalculus – C.3)

Match quadratic functions and graphs (Precalculus – C.4)

 

9-12.F-IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Graph an absolute value function (Algebra 1 – DD.3)

 

9-12.F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Match exponential functions and graphs (Algebra 1 – X.2)

Find properties of sine functions (Algebra 2 – Z.1)

Graph sine functions (Algebra 2 – Z.4)

Find properties of cosine functions (Algebra 2 – Z.5)

Graph cosine functions (Algebra 2 – Z.8)

Graph sine and cosine functions (Algebra 2 – Z.9)

Find properties of sine functions (Precalculus – N.1)

Graph sine functions (Precalculus – N.4)

Find properties of cosine functions (Precalculus – N.5)

Graph cosine functions (Precalculus – N.8)

Graph sine and cosine functions (Precalculus – N.9)

 

9-12.F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

 

9-12.F-IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Characteristics of quadratic functions (Algebra 1 – BB.1)

Solve a quadratic equation by factoring (Algebra 1 – BB.6)

Complete the square (Algebra 1 – BB.7)

Solve a quadratic equation by completing the square (Algebra 1 – BB.8)

Characteristics of quadratic functions (Algebra 2 – J.1)

Solve a quadratic equation by factoring (Algebra 2 – J.8)

Complete the square (Algebra 2 – J.9)

Convert equations of parabolas from general to vertex form (Algebra 2 – T.7)

Find properties of a parabola from equations in general form (Algebra 2 – T.8)

Characteristics of quadratic functions (Precalculus – C.1)

Find the maximum or minimum value of a quadratic function (Precalculus – C.2)

Solve a quadratic equation by factoring (Precalculus – C.6)

Solve a quadratic equation by completing the square (Precalculus – C.7)

 

9-12.F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions.

Match exponential functions and graphs (Algebra 1 – X.2)

Match exponential functions and graphs (Algebra 2 – S.3)

 

9-12.F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Match quadratic functions and graphs (Algebra 2 – J.5)

Match polynomials and graphs (Algebra 2 – K.14)

Match quadratic functions and graphs (Precalculus – C.4)

Match polynomials and graphs (Precalculus – D.11)

 

9-12.F-BF Building Functions

 

9-12. Build a function that models a relationship between two quantities

 

9-12.F-BF.1 Write a function that describes a relationship between two quantities.

 

9-12.F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Write inverse variation equations (Algebra 1 – R.7)

Write and solve inverse variation equations (Algebra 1 – R.8)

Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Write a formula for a recursive sequence (Algebra 2 – BB.8)

Find a recursive formula (Precalculus – W.4)

 

9-12.F-BF.1.b Combine standard function types using arithmetic operations.

Add and subtract functions (Algebra 2 – O.1)

Multiply functions (Algebra 2 – O.2)

Divide functions (Algebra 2 – O.3)

Add, subtract, multiply, and divide functions (Precalculus – A.6)

 

9-12.F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Write a formula for a recursive sequence (Algebra 2 – BB.8)

Find a recursive formula (Precalculus – W.4)

Find recursive and explicit formulas (Precalculus – W.5)

Convert a recursive formula to an explicit formula (Precalculus – W.6)

Convert an explicit formula to a recursive formula (Precalculus – W.7)

Convert between explicit and recursive formulas (Precalculus – W.8)

 

9-12. Build new functions from existing functions

 

9-12.F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Transformations of quadratic functions (Algebra 1 – BB.3)

Transformations of absolute value functions (Algebra 1 – DD.4)

Translations of functions (Algebra 2 – P.1)

Reflections of functions (Algebra 2 – P.2)

Dilations of functions (Algebra 2 – P.3)

Transformations of functions (Algebra 2 – P.4)

Function transformation rules (Algebra 2 – P.5)

Describe function transformations (Algebra 2 – P.6)

Translations of functions (Precalculus – B.1)

Reflections of functions (Precalculus – B.2)

Dilations of functions (Precalculus – B.3)

Transformations of functions (Precalculus – B.4)

Function transformation rules (Precalculus – B.5)

Describe function transformations (Precalculus – B.6)

 

9-12.F-BF.4 Find inverse functions.

 

9-12.F-BF.4.a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Find inverse functions and relations (Algebra 2 – O.9)

Solve exponential equations using common logarithms (Algebra 2 – S.5)

Solve exponential equations using natural logarithms (Algebra 2 – S.6)

Solve logarithmic equations I (Algebra 2 – S.7)

Solve logarithmic equations II (Algebra 2 – S.8)

Solve logarithmic equations with one logarithm (Precalculus – F.11)

 

9-12.F-LE Linear, Quadratic, and Exponential Models

 

9-12. Construct and compare linear, quadratic, and exponential models and solve problems

 

9-12.F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

 

9-12.F-LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Describe linear and exponential growth and decay (Algebra 1 – CC.6)

Identify linear and exponential functions (Algebra 2 – S.9)

Describe linear and exponential growth and decay (Algebra 2 – S.11)

Identify linear and exponential functions (Precalculus – F.13)

Describe linear and exponential growth and decay (Precalculus – F.15)

 

9-12.F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Solve linear equations: word problems (Algebra 1 – J.8)

Linear functions over unit intervals (Algebra 1 – CC.4)

Solve linear equations: word problems (Algebra 2 – B.2)

Linear functions over unit intervals (Algebra 2 – D.7)

Linear functions over unit intervals (Precalculus – A.4)

 

9-12.F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Exponential growth and decay: word problems (Algebra 1 – X.3)

Identify linear, quadratic, and exponential functions from graphs (Algebra 1 – CC.1)

Identify linear, quadratic, and exponential functions from tables (Algebra 1 – CC.2)

Exponential functions over unit intervals (Algebra 1 – CC.5)

Exponential functions over unit intervals (Algebra 2 – S.10)

Exponential growth and decay: word problems (Algebra 2 – S.12)

Exponential functions over unit intervals (Precalculus – F.14)

Exponential growth and decay: word problems (Precalculus – F.16)

 

9-12.F-LE.2 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).

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Write a rule for a function table (Algebra 1 – Q.12)

Slope-intercept form: write an equation (Algebra 1 – S.8)

Point-slope form: write an equation from a graph (Algebra 1 – S.17)

Point-slope form: write an equation (Algebra 1 – S.18)

Match exponential functions and graphs (Algebra 1 – X.2)

Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)

Equations of lines (Geometry – E.4)

Equations of parallel and perpendicular lines (Geometry – E.6)

Write the equation of a linear function (Algebra 2 – D.6)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Linear functions (Precalculus – A.3)

 

9-12.F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

 

9-12. Interpret expressions for functions in terms of the situation they model

 

9-12.F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Solve linear equations: word problems (Algebra 1 – J.8)

Exponential growth and decay: word problems (Algebra 1 – X.3)

Solve linear equations: word problems (Algebra 2 – B.2)

Exponential growth and decay: word problems (Algebra 2 – S.12)

Compound interest: word problems (Algebra 2 – S.13)

Continuously compounded interest: word problems (Algebra 2 – S.14)

Exponential growth and decay: word problems (Precalculus – F.16)

Compound interest: word problems (Precalculus – F.17)

 

9-12.F-LE.6 Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.

9-12.S Statistics and Probability

 

9-12.S-ID Interpreting Categorical and Quantitative Data

 

9-12. Summarize, represent, and interpret data on a single count or measurement variable

 

9-12.S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

Create bar graphs, line graphs, and histograms (Algebra 1 – N.2)

 

9-12.S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Mean, median, mode, and range (Algebra 1 – KK.1)

Quartiles (Algebra 1 – KK.2)

Mean absolute deviation (Algebra 1 – KK.7)

Variance and standard deviation (Algebra 1 – KK.8)

Variance and standard deviation (Algebra 2 – DD.2)

Variance and standard deviation (Precalculus – Z.2)

 

9-12.S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Interpret box-and-whisker plots (Algebra 1 – N.5)

Identify an outlier (Algebra 1 – KK.3)

Identify an outlier and describe the effect of removing it (Algebra 1 – KK.4)

Identify an outlier (Algebra 2 – DD.3)

Identify an outlier and describe the effect of removing it (Algebra 2 – DD.4)

Identify an outlier (Precalculus – Z.3)

Identify an outlier and describe the effect of removing it (Precalculus – Z.4)

 

9-12. Summarize, represent, and interpret data on two categorical and quantitative variables

 

9-12.S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

 

9-12.S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Outliers in scatter plots (Algebra 1 – KK.5)

Outliers in scatter plots (Algebra 2 – DD.5)

Outliers in scatter plots (Precalculus – Z.5)

 

9-12.S-ID.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Find the equation of a regression line (Precalculus – Z.8)

Interpret regression lines (Precalculus – Z.9)

Analyze a regression line of a data set (Precalculus – Z.10)

Analyze a regression line using statistics of a data set (Precalculus – Z.11)

 

9-12.S-ID.6.b Informally assess the fit of a function by plotting and analyzing residuals.

Interpret a scatter plot (Algebra 1 – N.6)

 

9-12.S-ID.6.c Fit a linear function for a scatter plot that suggests a linear association.

Scatter plots: line of best fit (Algebra 1 – N.7)

Find the equation of a regression line (Precalculus – Z.8)

 

9-12. Interpret linear models

 

9-12.S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Interpret regression lines (Precalculus – Z.9)

Analyze a regression line using statistics of a data set (Precalculus – Z.11)

 

9-12.S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

Match correlation coefficients to scatter plots (Precalculus – Z.6)

Calculate correlation coefficients (Precalculus – Z.7)

 

9-12.S-ID.9 Distinguish between correlation and causation.