Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Reasoning with Equations and Inequalities

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Reasoning with Equations and Inequalities

Standard: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Reasoning with Equations and Inequalities

Standard: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Reasoning with Equations and Inequalities

Standard: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Algebra: Seeing Structure in Expressions

Standard: Use the structure of an expression to identify ways to rewrite it. For example, see x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 - y^2)(x^2 + y^2).

Degree of Alignment: Not Rated (0 users)

Learning Domain: Functions: Interpreting Functions

Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Expressing Geometric Properties with Equations

Standard: Derive the equation of a parabola given a focus and directrix.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Number and Quantity: The Complex Number System

Standard: Know there is a complex number i such that i^2 = ‰öŐ1, and every complex number has the form a + bi with a and b real.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Number and Quantity: The Complex Number System

Standard: Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Number and Quantity: The Complex Number System

Standard: Solve quadratic equations with real coefficients that have complex solutions.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Number and Quantity: Quantities

Standard: Define appropriate quantities for the purpose of descriptive modeling.*

Degree of Alignment: Not Rated (0 users)

Cluster: Reason quantitatively and use units to solve problems

Standard: Define appropriate quantities for the purpose of descriptive modeling.*

Degree of Alignment: Not Rated (0 users)

Cluster: Perform arithmetic operations with complex numbers

Standard: Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.

Degree of Alignment: Not Rated (0 users)

Cluster: Perform arithmetic operations with complex numbers

Standard: Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Degree of Alignment: Not Rated (0 users)

Cluster: Use complex numbers in polynomial identities and equations

Standard: Solve quadratic equations with real coefficients that have complex solutions.

Degree of Alignment: Not Rated (0 users)

Cluster: Interpret the structure of expressions.

Standard: Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).

Degree of Alignment: Not Rated (0 users)

Cluster: Understand the relationship between zeros and factors of polynomial

Standard: 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).

Degree of Alignment: Not Rated (0 users)

Cluster: Understand the relationship between zeros and factors of polynomial

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Use polynomial identities to solve problems

Standard: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

Degree of Alignment: Not Rated (0 users)

Cluster: Rewrite rational expressions

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Standard: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve systems of equations

Standard: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve systems of equations

Standard: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze functions using different representations

Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*

Degree of Alignment: Not Rated (0 users)

Cluster: Translate between the geometric description and the equation for a conic section

Standard: Derive the equation of a parabola given a focus and directrix.

Degree of Alignment: Not Rated (0 users)