SAT Math Formulas

Circle

The area of a circle is given by the formula $A = \pi r^2$ where $r$ is the radius of the circle. This formula calculates the space enclosed within the circle.

The circumference of a circle is calculated using $C = 2\pi r$, which gives the distance around the circle. This is crucial for problems involving the perimeter of circular shapes.

Rectangle

The area of a rectangle is found using $A = lw$, where $l$ is the length and $w$ is the width. This formula helps determine the amount of space within the rectangle.

Understanding this formula is essential for solving problems related to rectangular plots, rooms, or any scenarios involving rectangular dimensions.

Triangle

The area of a triangle is given by $A = \frac{1}{2}bh$, where $b$ is the base and $h$ is the height. This formula calculates the space within the triangle.

The sum of the measures in degrees of the angles of a triangle is 180, a fundamental property for solving problems involving triangles.

The Pythagorean Theorem, $c^2 = a^2 + b^2$, is used to find the length of the sides in a right triangle. This is crucial for solving problems involving distances and lengths in geometry.

Special Right Triangles

The 30-60-90 triangle has sides in the ratio $x, x\sqrt{3}, 2x$, which simplifies many trigonometry problems by providing consistent side ratios.

The 45-45-90 triangle has sides in the ratio $s, s, s\sqrt{2}$, which is useful for problems involving isosceles right triangles.

Rectangular Prism

The volume of a rectangular prism is found using $V = lwh$, where $l$ is the length, $w$ is the width, and $h$ is the height. This formula calculates the space within the prism.

This is important for solving problems related to the capacity of boxes, rooms, and other rectangular objects.

Cylinder

The volume of a cylinder is given by $V = \pi r^2h$, where $r$ is the radius of the base and $h$ is the height. This formula calculates the space within the cylinder.

This is essential for problems involving cylindrical containers, pipes, and similar objects.

Sphere

The volume of a sphere is calculated using $V = \frac{4}{3}\pi r^3$, where $r$ is the radius. This formula determines the space within the sphere.

Understanding this formula is crucial for solving problems involving balls, planets, and other spherical objects.

Cone

The volume of a cone is found using $V = \frac{1}{3}\pi r^2h$, where $r$ is the radius of the base and $h$ is the height. This formula calculates the space within the cone.

This is important for problems related to conical containers, ice cream cones, and similar shapes.

Pyramid

The volume of a pyramid is given by $V = \frac{1}{3}lwh$, where $l$ is the length, $w$ is the width, and $h$ is the height. This formula calculates the space within the pyramid.

Understanding this formula helps in solving problems related to pyramidal structures and objects.

Arcs and Radians

The number of degrees of arc in a circle is 360, which is essential for problems involving angles and circles.

The number of radians of arc in a circle is $2\pi$, providing an alternative way to measure angles in trigonometry problems.