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Contenido principal

STANDARDS

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US-WV

Math

West Virginia Math

High School Algebra II: Polynomial, Rational, and Radical Relationships

Perform arithmetic operations with complex numbers.

M.A2HS.1

Fully covered
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.

M.A2HS.2

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

Use complex numbers in polynomial identities and equations.

M.A2HS.3

Fully covered
Solve quadratic equations with real coefficients that have complex solutions.

M.A2HS.4

Fully covered
Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

M.A2HS.5

Fully covered
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Interpret the structure of expressions.

M.A2HS.6

Interpret expressions that represent a quantity in terms of its context.

M.A2HS.6.a

Fully covered
Interpret parts of an expression, such as terms, factors, and coefficients.

M.A2HS.6.b

Fully covered
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)^n as the product of P and a factor not depending on P.

M.A2HS.7

Fully covered
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).

Write expressions in equivalent forms to solve problems.

M.A2HS.8

Fully covered
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. For example, calculate mortgage payments.

Perform arithmetic operations on polynomials.

M.A2HS.9

Mostly covered
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.

Understand the relationship between zeros and factors of polynomials.

M.A2HS.10

Fully covered
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).

M.A2HS.11

Fully covered
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.

Use polynomial identities to solve problems.

M.A2HS.12

Fully covered
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.

M.A2HS.13

Fully covered
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.

Rewrite rational expressions.

M.A2HS.14

Fully covered
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.

M.A2HS.15

Fully covered
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.

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

M.A2HS.16

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

Represent and solve equations and inequalities graphically.

M.A2HS.17

Fully covered
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.

Analyze functions using different representations.

M.A2HS.18

Partially covered
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.