SEE Optional Mathematics Nepal key terms

A rule that assigns to each element of one set exactly one element of another set; the set of allowed inputs is its domain and the set of outputs is its range.

The complete set of input values for which a function is defined; for example, the domain of 1/x excludes x = 0.

The set of all output values that a function actually produces when every allowed input in its domain is used; it is a subset of the codomain.

A function formed by applying one function to the result of another, written f∘g and evaluated as f(g(x)); its domain excludes inputs where g(x) is not allowed.

A function that reverses another function, sending each output back to its original input; it exists only when the original function is one-to-one.

An expression made by adding or subtracting terms of the form ax^n, where n is a non-negative integer and a is a constant; its highest power gives the degree.

The statement that dividing a polynomial p(x) by (x − a) leaves remainder p(a); it gives the remainder without carrying out long division.

A polynomial p(x) has (x − a) as a factor exactly when p(a) = 0; this links factors of a polynomial with its zeros.

A sequence in which the difference between consecutive terms is constant; that constant is called the common difference and is often denoted d.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed non-zero number called the common ratio.

The sum of a set of values divided by the number of values; between two numbers it equals half their sum.

For two positive numbers a and b, the positive square root of their product; more generally, the nth root of the product of n positive values.

An equation of the form ax² + bx + c = 0 with a ≠ 0; its solutions are called roots and can be found by factorising or using the quadratic formula.

The quantity b² − 4ac for a quadratic ax² + bx + c = 0; its sign shows whether the roots are real and distinct, real and equal, or non-real.

A method of finding the maximum or minimum of a linear objective function subject to linear inequalities called constraints, usually graphed as a feasible region.

The set of all points that satisfy every constraint of a linear programming problem at the same time; the optimum usually occurs at a vertex of this region.

The linear expression in a linear programming problem whose value is to be maximised or minimised, such as profit, cost, or production.

An equation involving trigonometric functions that is true for every value for which both sides are defined, such as sin²θ + cos²θ = 1.

The complete set of all angles satisfying a trigonometric equation, usually written using an integer n to show repetition every period.

The angle measured upward from a horizontal line to the line of sight when an observer looks at an object above the observer's level.

The angle measured downward from a horizontal line to the line of sight when an observer looks at an object below the observer's level.

In any triangle, the ratio of a side to the sine of the opposite angle is constant: a/sin A = b/sin B = c/sin C.

In any triangle, c² = a² + b² − 2ab cos C; it relates the three sides to one angle and is used when SAS or SSS information is known.

Triangles that have exactly the same shape and size, so all corresponding sides and angles are equal; standard tests include SSS, SAS, ASA, AAS, and RHS.

Triangles with equal corresponding angles and proportional corresponding sides; their areas are in the ratio of the squares of corresponding sides.

A quadrilateral whose four vertices lie on one circle; its opposite angles are supplementary, adding to 180 degrees.

A straight line that touches a circle at exactly one point; it is perpendicular to the radius drawn to that point of contact.

An angle formed inside a circle by two chords meeting at a point on the circle; it equals half the central angle standing on the same arc.

A rule that changes the position, size, or orientation of a figure in a plane; common types are translation, rotation, reflection, and enlargement.

The set of all points that satisfy a given geometric condition, such as all points a fixed distance from a fixed point.

The distance between points (x₁, y₁) and (x₂, y₂) in a plane, given by the square root of (x₂ − x₁)² + (y₂ − y₁)².

A formula giving the coordinates of a point that divides the segment joining two points in a given ratio, either internally or externally.

A measure of the steepness of a line, equal to the change in y divided by the change in x between two points on the line.

A quantity having both magnitude and direction, often represented by a directed line segment and written in component form.

For vectors a and b, the scalar a·b = |a||b| cos θ; it is also found by summing the products of corresponding components.

A measure of spread equal to the square root of the variance; it shows the typical distance of data values from the mean.

A number from 0 to 1 measuring how likely an event is, calculated for equally likely outcomes as favourable outcomes divided by total outcomes.

Events that cannot occur at the same time; for such events, P(A or B) = P(A) + P(B).

The set of all possible outcomes of a random experiment, usually denoted S; an event is a subset of the sample space.

The middle value of an ordered data set; if the number of values is even, it is the mean of the two middle values.