psat math formulas

Linear equation

a straight line, y = mx + b, where m is the slope and b is the y-intercept.

Quadratic equation

ax² + bx + c = 0, where a, b, and c are constants.

Quadratic formula

x = (-b ± √(b² - 4ac)) / 2a.

Pythagorean theorem

a² + b² = c²

Area of a triangle

A = (1/2)bh, where b is the base and h is the height.

Area of a rectangle

A = lw, where l is the length and w is the width.

Area of a trapezoid

A = (1/2)(b₁ + b₂)h, where b₁ and b₂ are the bases and h is the height.

Circumference of a circle

C = 2πr, where r is the radius.

Area of a circle

A = πr².

Volume of a rectangular prism

V = lwh.

Volume of a cylinder

V = πr²h.

Volume of a cone

V = (1/3)πr²h.

Volume of a sphere

V = (4/3)πr³.

Volume of a pyramid

V = (1/3)lwh.

Slope formula

between 2 given points, m = (y₂ - y₁) / (x₂ - x₁).

Distance formula

d = √((x₂ - x₁)² + (y₂ - y₁)²).

Percent increase/decrease

Calculated using the formula (New - Old) / Old.

Degrees in a circle

A full circle contains 360 degrees.

Radians in a circle

A full circle contains 2π radians.

Sum of angles in a triangle

180 degrees.

30-60-90 triangle

he hypotenuse is 2x, the short side is x, and the long side is x√3.

45-45-90 triangle

the equal sides are s, and the hypotenuse is s√2.