Algebra 1

a brief outline

1. variables and algebraic expressions

order of operations

properties of real numbers

equality: reflexive, transitive, symmetric

addition and multiplication: identities, inverses, commutative, associative

distributive property of multiplication over addition

2. adding, subtracting, multiplying, dividing positive and negative integers

adding, subtracting, multiplying, dividing positive and negative rational numbers

3. solving linear equations in one variable

4. using equations to solve application problems

ratios and proportions

percentages

percent increase or decrease

similar triangles

probability and odds

weighted averages (mixture problems)

direct and inverse variation

uniform motion problems

5. relations and functions

definitions, domains, ranges, graphs of functions

6. linear equations

slope

point-slope form

standard form

slope-intercept form

graphs

parallel and perpendicular lines

midpoints

7. linear inequalities

solving linear inequalities

compound inequalities

absolute value in inequalities

graphing inequalities in two variables

8. solving systems of linear equations

by graphing, substitution, linear combination

solving systems of linear inequalities by graphing

9. polynomials

multiplying and dividing monomials B negative exponents

degrees of polynomials and monomials

adding, subtracting polynomials

multiplying a polynomial by a monomial

multiplying polynomials

recognizing Aspecial@ products

10. factoring

GCF

factoring using the distributive property

factoring trinomials

factoring Aspecial@ products

difference of two squares

perfect squares

solving equations by factoring

11. rational expressions and equations

simplifying, multiplying, dividing

rational equations

12. radical expressions

simplifying radical expressions

radical equations

solving quadratic equations by completing the square

derivation and use of the quadratic formula