Useful Algebra I/II Formulas for the PSAT/SAT

Slope formula

Slope-intercept form of a line

Standard form of a line

Point-slope form

Quadratic formula

• Discriminant b² - 4ac tells you the number of real solutions

• > 0 → two real solutions

• = 0 → one real solution

• < 0 no real solution

Vertex form of a parabola

Standard form of a quadratic

Exponent rules

Difference of squares

Perfect square trinomials

Systems of equations

• Substitution: Solve one equation for a variable, plug into the other

• Elimination: Add/subtract equations to cancel a variable

• No solution → parallel lines (same slope, different intercept)

• Infinite solutions → same line

Functions

• f(3) means "plug in 3 for x"

• f(g(x)) = plug g(x) into f

• Linear function: f(x)=mx+b

• Exponential: f(x)=a⋅b^x

Percent change

Rate problems

• Distance=Rate×Time

• Or: d=rt

• Works for speed, work, production, etc

Mean (average)

Simple geometry things

Tricky quadratic problems with constants

Example of tricky quadratic problems with constants