Graphing Basics

create a scatter plot from ordered pairs of numbers
graph inequalities on the number line
create a line graph from a table
read line and bar graphs and draw conclusions
find distance on the real number line

Linear Equations and Inequalities

solve an equation with variables on both sides by adding/subtracting a variable to both sides, and/or adding/subtracting/multiplying/dividing both sides by a constant to simplify it down and isolate the unknown on one side
solve an inequality, compound inequality (e.g. 1<x<3), inequality with absolute value, inequality with two variables by adding/subtracting/multiplying/dividing both sides of the inequality
solve a word problem by modeling it algebraically, then solving that algebraic model.
re-arrange formulas/functions to find how to express one term in terms of the other
V=PI*r^2*h/3 => h = 3*V / PI*r^2

for two numbers x and y, solve for k such that y=kx, and check

Linear Graphs

graph a linear equation given:
a function in the form y=mx+b
the x and y intercepts, connecting the two points
the x and y intercepts, by finding them using an equation in the form y=mx+b
the slope and intercept, by finding them using an equation in the form y=mx+b
graph a linear inequality
use a graph to solve problems involving linear expressions
derive an equation for a relation between two sets of numbers by deriving the pattern that describes the relationship
x={1,2,3,4,5}, y={3,5,7,9,11}
2(1)+1 = 3
2(2)+1 = 5
2(3)+1 = 7
...
2(x)+1 = y

Systems of Linear Equations

Solve a system of two linear equations by:
finding the intersection of two lines on a graph
substituting one equation into the other
using linear combinations (add two equations to each other, hoping one variable will cancel out)
multiplying one equation by a constant, so that when both equations are added together, one variable cancels out
Find if a system of linear equations has no solutions, one solution, or infinite solutions
graph a system of inequalities, and the solution area

Factoring

Factoring using the distributive property
2x^2+8=2(x^2+4)

Factoring Trinomials
Factoring x^2+bx+c
Factoring ax^2+bx+c

Factoring special products
Difference of two squares a^2-b^2=(a+b)(a-b)
Perfect square trinomial pattern (a+b)^2=a^2+2ab+b^2 and (a-b)^2=a^2-2ab+b^2

Proportions

solve a proportion using the cross-product rule
12/7 = 5/x; 12x = 35; x=35/12

find how much percent is a of b, what is x percent of a
Calculate relative frequencies or probabilities in situations with a finite number of equally likely outcomes
multiply and divide expressions by cancelling out common factors
(2x^2+3x-2)/(2x^2+5x+2) => (2x-1)/(2x+1)

simplify the addition/subtraction of two rationals by finding LCD, rewriting and simplifying
(x+3)/(3x-1) + 4/(x-3)
((x^2-9) + 4(3x-1)) / (3x-1)(x-3)
(x^2 + 12x - 13) / (3x-1)(x-3)
(x-1)(x+13) / (3x-1)(x-3)

solve a rational equation by multiplying by LCD

Exponents

evaluate expressions with negative or zero exponents
write and evaluate (for some given x) exponential growth and decay functions
graph exponential functions
Simplify products, quotients, and powers of powers
Calculate compound interest

Quadratics and Radicals
find the GCF of two monomials
12ab, 4a^2b^2 => 4ab

multiply two binomials that fit either the square of a difference pattern, or product of sum and difference
(x-6)(x+6) = x^2 - 36
(4x+7)^2 = 16x^2 + 56x + 49

identify if a quadratic has a minimum or maximum vertex (is the vertex the minimum or maximum of the function)
find the number of solutions to a quadratic by using the discriminant (b^2-4ac)
solve a quadatic by:
simplifying and finding a square root
graphing and finding the 0's
using the quadratic formula
completing the square

Polynomials

add/subtract/multiply polynomials (multiply using distributive property/FOIL)
Multiply a polynomial by a monomial or multiply two binomials
use the distributive property to factor a polynomial by creating a common term, then adding
2x^2 - 3xz - 2xy + 3yz
x*(2x-3z) - y(2x-3z)
(x-y)(2x-3z)

solve an equation involving polynomials
multiply two scientific notation numbers by multiplying the significands and adding the exponents

Functions

evaluate functions and solve equations involving function notation
determine whether or not a graph represents a function
determine the domain and range of a function
Use a graph to locate local maxima and minima
Determine even and odd functions from a graph
even functions: f(-x) = f(x)
odd functions: f(-x) = -f(x)
Form the sum, difference, product, and quotient of two functions