Slant Height Formula Explained: Cone & Pyramid The Formula, Step by Step The slant height is the diagonal distance from the apex of a cone or pyramid down to the edge of the base measured along the surface of the shape, not straight down through the middle. It always forms the hypotenuse of a right triangle… Continue reading “Slant Height” Explained
Trigonometric ratios (trig ratios) define the relationship between the angles and side lengths of a right triangle. The three primary trig ratios are remembered using SOH-CAH-TOA: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent. These ratios are foundational in Florida MAFS Geometry standards (MAFS.912.G-SRT) and appear on the SAT Math “Additional Topics in… Continue reading “Trigonometric Ratios” Explained
In mathematics, scaling means multiplying a figure’s dimensions by a constant called the scale factor (k) to produce an enlarged or reduced version that maintains the original’s shape and proportions. When a figure is scaled by k, its side lengths multiply by k, its area multiplies by k², and its volume multiplies by k³. Scaling is a core concept… Continue reading “Scaling Dimensions” Explained
A quadratic function is a polynomial function of degree 2 written in standard form as f(x) = ax² + bx + c (where a ≠ 0). Its graph is a parabola — a U-shaped curve that opens upward when a > 0 and downward when a < 0. Quadratic functions have three equivalent forms (standard, vertex, and factored), are solved using factoring, completing the… Continue reading “Quadratic Functions” Explained
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the two legs: a² + b² = c². To use it, substitute the two known sides and solve for the unknown side by taking the square root. The Pythagorean Theorem is tested on… Continue reading “Pythagorean Theorem” Explained
In mathematics, probability is a measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). The basic probability formula is: P(A) = number of favorable outcomes ÷ total number of possible outcomes. To calculate probability, count how many outcomes satisfy your event, then divide by all possible outcomes. Probability appears on… Continue reading “Probability” Explained
A prism is a 3D solid with two identical parallel bases connected by rectangular lateral faces. The volume of a prism is V = Bh, where B is the area of the base and h is the height. The surface area of a prism is SA = 2B + Ph, where P is the perimeter of the base. Prisms are tested on the… Continue reading “Prisms” Explained
The perimeter of a shape is the total distance around its outside edge — the sum of all its side lengths. The perimeter formula is P = sum of all sides. For a rectangle: P = 2l + 2w. For a square: P = 4s. For any polygon, add all side lengths. Perimeter is tested on the Florida FSA, Florida Geometry EOC,… Continue reading “Perimeter” Explained
A quadratic system of equations is a system containing at least one quadratic equation (with an x² term) paired with a linear equation. Unlike linear systems, quadratic systems are solved using substitution only — not elimination. Substitute the linear equation into the quadratic, simplify to standard form, then solve using factoring, the quadratic formula, or completing the square. Quadratic systems… Continue reading “Quadratic Systems” Explained
A linear system of equations is a set of two or more equations in which every term is degree 1 (no x², no xy), written in standard form Ax + By = C. Graphed on a coordinate plane, each equation is a straight line — the solution is the point where the lines intersect. Lines that intersect at one… Continue reading “Linear Systems” Explained
