ny-regents-examination-integrated-algebra-august-2012-pt-iv-21-25

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Algebra Strand

Students will represent and analyze algebraically a wide variety of problem solving situations.

Variables and A.A.1 Translate a quantitative verbal phrase into an algebraic

Expressions expression

A.A.2 Write a verbal expression that matches a given

mathematical expression

Equations and A.A.3 Distinguish the difference between an algebraic

Inequalities expression and an algebraic equation

A.A.4 Translate verbal sentences into mathematical equations or

inequalities

A.A.5 Write algebraic equations or inequalities that represent a

situation

A.A.6 Analyze and solve verbal problems whose solution requires

solving a linear equation in one variable or linear inequality in

one variable

A.A.7 Analyze and solve verbal problems whose solution requires

solving systems of linear equations in two variables

A.A.8 Analyze and solve verbal problems that involve quadratic

equations

A.A.9 Analyze and solve verbal problems that involve exponential

growth and decay

A.A.10 Solve systems of two linear equations in two variables

algebraically (See A.G.7)

A.A.11 Solve a system of one linear and one quadratic equation

in two variables, where only factoring is required Note: The

quadratic equation should represent a parabola and the

solution(s) should be integers.

Students will perform algebraic procedures accurately.

Variables and A.A.12 Multiply and divide monomial expressions with a common

Expressions base, using the properties of exponents Note: Use integral

exponents only.

A.A.13 Add, subtract, and multiply monomials and polynomials

A.A.14 Divide a polynomial by a monomial or binomial, where the

quotient has no remainder

A.A.15 Find values of a variable for which an algebraic fraction is

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A.A.16 Simplify fractions with polynomials in the numerator and

denominator by factoring both and renaming them to lowest

terms

A.A.17 Add or subtract fractional expressions with monomial or like

binomial denominators

A.A.18 Multiply and divide algebraic fractions and express the product

or quotient in simplest form

A.A.19 Identify and factor the difference of two perfect squares

A.A.20 Factor algebraic expressions completely, including trinomials

with a lead coefficient of one (after factoring a GCF)

Equations and A.A.21 Determine whether a given value is a solution to a given

Inequalities linear equation in one variable or linear inequality in one

variable

A.A.22 Solve all types of linear equations in one variable

A.A.23 Solve literal equations for a given variable

A.A.24 Solve linear inequalities in one variable

A.A.25 Solve equations involving fractional expressions Note:

Expressions which result in linear equations in one variable.

A.A.41 Determine the vertex and axis of symmetry of a parabola,

given its equation (See A.G.10 )

Trigonometric A.A.42 Find the sine, cosine, and tangent ratios of an angle of

Functions a right triangle, given the lengths of the sides

A.A.43 Determine the measure of an angle of a right triangle, given the

length of any two sides of the triangle

A.A.44 Find the measure of a side of a right triangle, given an acute

angle and the length of another side

A.A.45 Determine the measure of a third side of a right triangle using

the Pythagorean theorem, given the lengths of any two sides

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