Algebra I
ALGEBRA I
PROFICIENCIES
The student will be able to:
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simplify numerical expressions and evaluate algebraic expressions.
simplify expressions with and without grouping symbols.
find solution sets of equations over a given domain.
translate phrases into variable expressions.
translate word sentences into equations.
translate simple word problems into equations.
graph real numbers on a number line and compare real numbers.
opposites and absolute values.
number properties to simplify expressions.
add real numbers using number line or properties about opposites.
add real numbers using rules for addition.
subtract real numbers and simplify expressions involved.
the distributive property to simplify expressions.
multiply real numbers.
write equations representing relationships among integers.
simplify expressions involving reciprocals.
solve equations using addition or subtraction.
solve equations using multiplication or division.
solve equations by using more than one transformation.
solve equations with the variable on both sides.
organize the facts of a problem.
solve problems involving costs, income, and value.
write and simplify expressions involving exponents.
add and subtract polynomials.
multiply monomials.
transform formulas.
solve word problems involving uniform motion and others involving area and
identify problems without solutions.
factor integers, find the greatest common factor of several integers, and simplify
quotients of monomials and find the GCF of several monomials.
divide polynomials by monomials and find monomial factors of polynomials.
find the product of two binomials mentally.
simplify products of the form (a + b) (a - b) and factor difference of two squares.
find squares of binomials and factor perfect square.
factor any trinomial (not by type).
use factoring in solving polynomial equations.
solve problems by writing and factoring quadratic equations.
simplify algebraic fractions and identify restrictions.
multiply algebraic fractions.
Algebra I
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divide algebraic fractions.
express two or more fractions with their least common denominator.
add and subtract algebraic fractions.
divide polynomials.
solve problems involving ratios.
solve problems using proportions.
solve equations with fractional coefficients.
solve fractional equations.
work with percents and decimals.
solve problems involving percents.
solve mixture and work problems.
use negative exponents.
use scientific notation.
graph ordered pairs and linear equation in two variables.
find the slope of a line.
use the slope-intercept form of a linear equation.
find an equation of a line given the slope and one point on the line, given two
points on the line, or knowing two lines as parallel.
use graphs to solve systems of linear equations.
use the substitution method to solve systems of linear equations.
use linear combination to solve systems of linear equations in two variables.
use multiplication with the linear combination method to solve systems of linear
equations.
apply some properties of rational numbers.
express rational numbers as decimals or fractions.
find the square root of numbers that have rational square roots.
simplify radicals and find decimal approximations of irrational square roots.
find square roots of variable expressions and use them to solve equations and
problems.
use the Pythagorean Theorem and its converse to solve geometric problems.
simplify products and quotients of radicals.
simplify sums and differences of radicals.
multiply binomials containing square-root-radicals and to rationalize binomial
denominators that contains square-root radicals.
graph inequalities in one variable..
transform inequalities in order to solve them.
solve problems that involve inequalities.
find the solution sets of combined inequalities.
solve equations and inequalities involving a absolute value.
learn the names and properties of special pairs of angles.
learn some properties of triangles.
solve problems involving similar triangles.