# Mathematics

## Acute Triangles

An acute triangle is a triangle whose all interior three angles are less than 90 degrees. In most cases, the tip of the triangle aligns with the middle of the length opposite it.

Adjacent angles are angles that share a common vertex and arm or side and do not overlap.

## Arithmetic Sequences

Arithmetic sequences are ordered lists of numbers with a constant difference between consecutive terms. Each term is found by adding or subtracting the common difference from the previous term.

## Averages

The average refers to the sum of values divided by the number of values, providing a representative value indicative of the collective set or distribution of data.

## Collinear Points

Collinear points are points that lie on the same line. This means if you draw a straight line connecting any of these points, it will pass through the other points.

## Compound Interest

Compound interest is the interest calculated on both the principal amount and the accumulated interest, leading to exponential growth or debt increase over time in financial transactions.

## Congruent Triangles

Congruent triangles are triangles that have the same size and shape, with corresponding sides and angles equal in measure, representing identical configurations when overlapped or superimposed.

## Corresponding Angles

Corresponding angles are formed when a third line, known as a transversal, intersects two parallel lines.

## Cubes and Cube Roots

A cube of a number is the product obtained when a number is multiplied by itself thrice. The cube root of a number is defined as the number which when multiplied by itself three times outputs the number.

## Decimals

Decimal numbers are numbers with a point placed in them to separate some of their digits.

## Derivatives

A derivative in mathematics can be defined as a measure of the rate at which a function will change with respect to a variable.

## Dilation

Dilations are a special kind of transformation in mathematics that makes a figure bigger or smaller without changing its original shape.

## Direct Variation

Direct variation describes a relationship between two variables where one variable is directly proportional to the other, changing in a consistent manner as the other changes.

## Ellipses

Ellipses represent a closed curve formed by points where the sum of the distances from two fixed points (foci) to any point on the curve remains constant.

## Equilateral Triangles

An equilateral triangle has all three sides equal. To achieve this, all the interior angles are equal too. Therefore, each interior angle is 60 degrees.

## Functions and Relations

Functions are mathematical relationships where each input (from a set called the domain) corresponds to exactly one output (from a set called the range), while relations allow multiple outputs for an input.

## Hyperbola

A hyperbola is formed when a plane slices through the edges of a right circular double cone at an angle greater than the slope of the cone.

## Inverse Variation

An inverse variation is a kind of relationship where one value increases while the other one decreases.

## Isosceles Triangles

An isosceles triangle is a type of triangle that has two sides that are of equal length. These two equal sides form what people often refer to as the legs of the triangle.

## Linear Equations

Linear equations are special type of equations that contains only one or two variables/ unknowns which are of degree one.

## Linear Models

Linear models in mathematics are representations of relationships between variables using linear equations or functions. They involve straight-line relationships and are characterized by their simplicity and ease of interpretation.

## Linear Regression

Linear regression is a statistical method to model the relationship between two variables, utilizing a linear equation to predict the value of one variable based on the other’s values.

## Linear Relationships

Linear relationships describe a direct correlation between two variables, wherein a change in one variable results in a proportional change in the other, following a straight-line pattern on a graph.

## Non-Collinear Points

Non-collinear points are a set of three or more points that do not fall on the same straight line. In other words, they are not in a straight line and cannot be connected by drawing a single straight line through all of them.

## Obtuse Angles

An obtuse angle is formed when the number of degrees measured at or near the vertex is between 90° and 180°.

## Optimization Problem

In mathematics, an optimization problem involves finding the best solution among feasible options, aiming to maximize or minimize a certain objective function while adhering to constraints or limitations.

## Parallel Lines

Parallel lines in geometry are two or more straight lines in the same plane that never intersect, maintaining a consistent, equidistant relationship throughout their length, denoting no meeting point.

## Permutations

Permutations represent the arrangements of a set of elements in a particular order, where the order matters. It calculates the number of possible arrangements without repetition.

## Perpendicular Lines

Two lines are perpendicular to each other when a right angle is formed at their point of connection.

## Plane (Geometry)

A plane is any flat surface with two dimensions that are extended infinitely.

## Point (Geometry)

Points can be described as positions represented by dots to indicate exact location.

Quadrilaterals are polygons with four sides and four angles. They vary in shapes and properties, including squares, rectangles, parallelograms, trapezoids, and rhombuses, each defined by specific side lengths and angle measures.

## Rates

Rates are measures of change in quantities over time or other variables, expressed as ratios or comparisons, often depicting how one quantity changes concerning another, like speed, growth, or proportion.

## Rational Functions

Rational functions are defined as functions that can be written as the ratio of two polynomial functions i.e. f(x) = P(x) /Q(x).

## Ratios

Ratios represent a comparison between two quantities, typically expressed as the quotient or fraction of one quantity to another, showing their proportional relationship or relative sizes.

## Ray (Geometry)

A ray is any line that has an endpoint called a point of origin and extends forever in a single direction.

## Rectangular Prism

A rectangular prism is a three-dimensional geometric solid characterized by six rectangular faces, where opposite faces are congruent and parallel, forming a solid shape with 12 edges and 8 vertices.

## Reflection

A reflection is a transformation that maps all the points of a figure to an image across a fixed line, known as the line of reflection.

## Rhombus

A rhombus is a quadrilateral (four-sided figure) with four equal sides.

## Right Triangles

Right triangles are triangles with one angle measuring 90 degrees, called a right angle. They follow the Pythagorean theorem and have a side called the hypotenuse opposite the right angle.

## Rotation

Rotation is a mathematical concept that involves the turning of a shape about a fixed point.

## Scalene Triangles

Scalene triangles are triangles in which all three sides are of different lengths. The three angles within scalene triangles are also of different measures.

## Scientific Notation

Scientific notation is a way to express numbers as a product of a decimal number and a power of ten, making large or small numbers more manageable for calculation and representation.

## Similarity Statement

Similarity statements are logical arguments that show how two or more shapes are similar.

## Slope

Slope refers to the measure of steepness or inclination of a line, expressed as the ratio of vertical change (rise) to horizontal change (run) between two points on the line.

## Surface Area

Surface area is the total measure of all the exposed areas of a three-dimensional object, calculated by summing the areas of its individual faces, including curved surfaces if applicable.

## Supplementary Angles

Supplementary angles in geometry are angles whose sum is 180 degrees. They form a straight line when joined together.

## Square Pyramid

A square pyramid is a three-dimensional geometric figure with a square base and four triangular faces that meet at a single point called the apex, creating a pyramid with five faces.

## Translation

In mathematics, translation refers to shifting a figure or object in a specific direction without altering its shape, size, or orientation. It involves moving every point of the figure by the same distance.

## Trigonometry

Trigonometry is a branch of mathematics dealing with the study of angles and relationships between sides and angles in triangles, often used in geometry, physics, engineering, and other fields.

## Triangular Prism

A triangular prism is a three-dimensional geometric solid characterized by two triangular bases and three rectangular lateral faces, forming a prism with six faces, nine edges, and six vertices.

## Vertical Angles

Vertical angles are a pair of angles that are formed by two intersecting lines.

## Volume

Volume is the measure of the space occupied by a three-dimensional object, calculated by multiplying its dimensions (length, width, and height) or using specific formulas based on the object’s shape.