Math Digital SAT

Quadratic Equations

• (x+y)(x-y) = x²-y²

• (x+y)² = x² +2xy + y²

• (x-y)² = x² - 2xy + y²

sum of the roots

-b/a

product of the roots

c/a

positive discriminant

quadratic has 2 real solutions

discriminant = 0

quadratic has 1 real solution

negative discriminant

quadratic has no real solutions

growth/decay rate is a percent of the total population

final amount = original amount (1± rate) ^number of changes

growth/decay is a multiple of the total population

final amount = original amount (multiplier) ^number of changes

perpendicular lines

negative reciprocal of the other line’s slope

Inequality Rule

when multiple or dive an inequality by a negative number, must rever the inequality sign

Standard Form - Function

ax + by = c

• slope: -(-5/1)

• y-intercept: c/b

• x-intercept: c/a

Infinite Solutions

equations represent the same line

Standard Form - Parabola

y = ax² + bx + c

Factored Form - Parabola

y = a(x-r) (x-r)

• r are the two roots/ x-intercepts

Vertex Form - Parabola

y = a(x-h)² + k

Equation of Circle

(x-h)² + (y-k)² = r²

SOHCAHTOA

• sine = opp/hyp

• cosine = adj/hyp

• tangent = opp/adj

Pythagorean triples

• 3-4-5 (hypothenuse)

• 5-12-13 (hypothenuse)

Similar Triangles

• AAA - all angles congruent

• SAS - side, angle, side

• SSS - all sides are in proportion

Congruent Triangles

• SSS - all sides are equal

• ASA - angle, side, angle

• SAS - side, angle, side

• AAS - angle, angle, side

Arcs and Sectors

part/whole = central angle/360 = arc length/2πr = sector area/πr²

Conditional Probability

• P (A u B) = P(A) + P(B) - P (A n B)

• P (A l B) = P(A and B) / P(B)

Complementary Angle

Sin (x) = Cos (90-x)