A function is a relation between two sets that associates each element of the first set (the domain) with exactly one element of the second set (the range).

An expression is a mathematical phrase involving numbers, operations, and variables. An equation is a statement that two expressions are equal, with an equals sign (=) separating the two expressions.

The properties of real numbers are: commutative property, associative property, distributive property, existence of additive and multiplicative identities (0 and 1), existence of additive and multiplicative inverses, and closure under addition, subtraction, multiplication, and division (except division by 0).

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integral powers of variables.

A rational number is a number that can be expressed as a ratio of two integers (a/b, where a and b are integers and b is not equal to 0). An irrational number is a number that cannot be expressed as a ratio of two integers.

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. Matrices are used to represent and manipulate data in various areas of mathematics, science, and engineering.

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to 0. It is called quadratic because the highest power of the variable is 2.

A circle is a two-dimensional geometric shape consisting of a set of points equidistant from a given point (the center), while a sphere is a three-dimensional geometric shape consisting of a set of points equidistant from a given point (the center).

A derivative is a fundamental concept in calculus that represents the rate of change of a function at a particular point. It is a measure of how the function changes as its input changes.

A permutation is an arrangement of objects in a specific order, where the order matters. A combination is a selection of objects from a set, where the order does not matter.

Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number (approximately 3.14159) and is used extensively in geometry, trigonometry, and other areas of mathematics.

A prime number is a natural number greater than 1 that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are prime numbers.

A square is a quadrilateral with four equal sides and four right angles, while a rectangle is a quadrilateral with four right angles but opposite sides are equal in length (not necessarily all sides are equal).

An acute angle is an angle that measures less than 90 degrees, while an obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.

The Cartesian coordinate system is a system of perpendicular lines used to specify the position of a point in a plane or in space. Each point is represented by a set of coordinates, typically (x, y) in a two-dimensional plane or (x, y, z) in three-dimensional space.

Probability is a measure of the likelihood that an event will occur, quantified as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

A scalar is a quantity that has magnitude (size) but no direction, while a vector is a quantity that has both magnitude and direction.

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, or ≥) rather than the equal sign (=).

A logarithm is the inverse operation of exponentiation. It represents the power to which a base number must be raised to produce a given number.

The centroid of a triangle is the intersection point of the three medians (lines drawn from each vertex to the midpoint of the opposite side).

A square root is a value that, when multiplied by itself, gives the original number (e.g., √9 = 3 because 3^2 = 9). A cube root is a value that, when multiplied by itself twice, gives the original number (e.g., ∛27 = 3 because 3^3 = 27).

A parabola is a plane curve that is the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

A factor is a number that divides evenly into another number, while a multiple is the product of a number and an integer.

A line is an infinite set of points that extends indefinitely in both directions, while a ray is a part of a line that has a fixed starting point and extends infinitely in one direction.

A variable is a symbol that represents a quantity that can take on different values, while a constant is a fixed value that does not change.

In an arithmetic sequence, the difference between successive terms is constant. In a geometric sequence, the ratio between successive terms is constant.

A set is a collection of distinct objects or elements, which can be numbers, shapes, or any other mathematical objects.

A rational number is a number that can be expressed as a fraction of two integers, while an irrational number is a number that cannot be expressed as a fraction of two integers.

A triangle is a polygon with three sides and three angles, while a polygon is a closed shape with three or more straight sides.

An ordered pair is a set of two numbers, written in a specific order (e.g., (3, 4)). A coordinate is a set of values that specify the position of a point in a particular space, such as a two-dimensional plane or three-dimensional space.

A circle is a set of points in a plane that are equidistant from a given point (the center), while an ellipse is a closed curve in a plane that consists of points whose sum of distances from two fixed points (the foci) is constant.

Parallel lines are lines that never intersect and have the same direction, while perpendicular lines are lines that intersect at a 90-degree angle.

A fraction is a ratio of two integers, while a decimal is a way of representing a number using a decimal point and place values.

An algebraic expression is a combination of variables, constants, and operations, while an equation is a statement that two expressions are equal, separated by an equals sign.

A sum is the result of adding two or more numbers, while a product is the result of multiplying two or more numbers.

A square is the result of multiplying a number by itself (e.g., 3^2 = 9), while a cube is the result of multiplying a number by itself twice (e.g., 3^3 = 27).

The mean is the arithmetic average of a set of numbers, while the median is the middle value of a set of numbers arranged in order.

A positive number is greater than zero, while a negative number is less than zero.

A factor is a number that divides another number evenly, while a power is the result of multiplying a number by itself a certain number of times.

A triangle is a polygon with three sides and three angles, while a quadrilateral is a polygon with four sides and four angles.

A horizontal line is parallel to the x-axis, while a vertical line is parallel to the y-axis.

A prime number is a natural number greater than 1 that is only divisible by 1 and itself, while a composite number is a natural number greater than 1 that is divisible by other numbers besides 1 and itself.

Congruent figures are figures that have the same shape and size, while similar figures are figures that have the same shape but different sizes.

A linear equation is an equation that graphs as a straight line, while a quadratic equation is an equation that graphs as a curve (parabola) and contains a variable raised to the second power.

A monomial is an algebraic expression with only one term, while a polynomial is an algebraic expression with two or more terms.

A radical is a symbol (√) indicating the root of a number, while an exponent is a number or symbol indicating the power to which a base is raised.

The diameter is the length of a straight line segment that passes through the center of a circle and connects two points on the circle's circumference, while the circumference is the distance around the circle.