Nepal SEE Mathematics key terms

The set that contains every element being considered in a particular problem. All other sets in that discussion are subsets of it, and it is usually denoted by U.

A set whose every element also belongs to another set. If A is a subset of B, then B contains all elements of A, written A ⊆ B.

The set of all elements in the universal set that are not in a given set A. It is written A' or A^c and depends on the universal set chosen.

A diagram that uses overlapping circles or closed curves inside a rectangle to show sets and their relationships. The rectangle usually represents the universal set.

The amount of money a trader pays to buy or produce an item before selling it. Profit or loss is calculated by comparing cost price with selling price.

The amount of money for which an item is actually sold to a customer. It may be equal to, greater than, or less than the cost price.

A reduction given on the marked price of an item, usually expressed as a percentage of the marked price. The customer pays marked price minus discount.

Interest calculated only on the original principal for the whole time, using the formula I = P × T × R / 100. It does not earn interest on interest.

Interest calculated on the principal plus any interest already added. Each period's interest is added to the amount before the next period's interest is found.

A tax charged on the value added to goods or services at each stage of sale. In Nepal it is usually a percentage added to the selling price.

The value of one country's currency expressed in another country's currency. It is used to convert money from one currency to another.

The amount of surface covered by a plane figure, measured in square units. Common formulas include length × breadth for rectangles and πr² for circles.

The sum of the areas of all the surfaces of a solid figure. For a closed solid it includes every face, such as the curved surface and bases of a cylinder.

The amount of space occupied by a solid figure, measured in cubic units. It is found by multiplying a base area by height or by using a formula for the solid.

The distance along the sloping surface from the vertex of a cone or pyramid to a point on the edge of its base. It is not the perpendicular height.

An equation in which the highest power of the variable is one, such as 2x + 3 = 11. It has a straight-line graph and usually one solution.

An equation of the form ax² + bx + c = 0, where a is not zero. It may be solved by factorization, completing the square, or the quadratic formula.

A number written above and to the right of a base that shows how many times the base is multiplied by itself. For example, in 5³ the index is 3.

An irrational number written as a root of a rational number that cannot be simplified to remove the root, such as √2 or 3√5. Surds are often simplified or combined in algebra.

A mathematical statement comparing two expressions that are not necessarily equal, using symbols such as <, >, ≤, or ≥. Its solution is a range of values.

Triangles that have exactly the same shape and size. Their corresponding sides and angles are equal, and they can be matched exactly by translation, rotation, or reflection.

Triangles that have the same shape but not necessarily the same size. Their corresponding angles are equal and corresponding sides are in the same ratio.

A quadrilateral whose four vertices lie on a single circle. Its opposite angles are supplementary, meaning each pair adds up to 180 degrees.

An angle formed by two chords of a circle that meet at a point on the circle. It is half the central angle standing on the same arc.

Drawing accurate geometric figures using only a compass and a straightedge, without measuring angles or lengths with a ruler. It often involves bisecting lines, angles, or drawing perpendiculars.

A ratio comparing two sides of a right-angled triangle, such as sine, cosine, or tangent. The ratio depends on one acute angle of the triangle.

The angle measured upward from the horizontal line of sight of an observer to an object above the observer's eye level. It is used in height-and-distance problems.

The angle measured downward from the horizontal line of sight of an observer to an object below the observer's eye level. It is equal to the angle of elevation from the object.

The arithmetic average of a set of data. It is found by adding all the values and dividing the total by the number of values.

The middle value of a data set when the values are arranged in order. If there is an even number of values, it is the average of the two middle values.

The value that occurs most frequently in a data set. A data set may have one mode, more than one mode, or no mode if all values occur equally often.

A number between 0 and 1 that measures how likely an event is. It is found by dividing the number of favourable outcomes by the total number of equally likely outcomes.

The set of all possible outcomes of a random experiment. For example, tossing a coin gives the sample space {Head, Tail}.

A transformation that moves every point of a figure the same distance in the same direction. The shape and size do not change.

A transformation that turns a figure about a fixed point through a given angle and direction. The distance from the centre and the shape remain unchanged.

A transformation that flips a figure across a line, producing its mirror image. Corresponding points are the same distance from the line of reflection.

A transformation that changes the size of a figure by a scale factor from a fixed centre. Angles stay the same, but lengths are multiplied by the scale factor.

A measure of how steep a straight line is. It is the change in y divided by the change in x between two points on the line.

A formula that gives the distance between two points on a coordinate plane. For points (x₁, y₁) and (x₂, y₂), it is √[(x₂ − x₁)² + (y₂ − y₁)²].

A vector written as a vertical column of two numbers, where the top number gives horizontal movement and the bottom number gives vertical movement.