Kerala SSLC Mathematics key terms

A list of numbers in which the same amount is added to each term to get the next one, so the gap between neighbouring terms never changes.

The fixed number added each time in an arithmetic sequence; it is found by subtracting any term from the term that comes after it.

A rule giving the term in position n of an arithmetic sequence, usually aₙ = a + (n − 1)d, where a is the first term and d the common difference.

The total of the first n terms of an arithmetic sequence, equal to n/2 multiplied by the sum of the first term and the nth term.

A straight line segment joining two points on a circle; the longest chord passes through the centre and is called a diameter.

A quadrilateral whose four vertices all lie on the same circle; each pair of opposite angles adds up to 180 degrees.

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

The region inside a circle bounded by two radii and the arc between them; its area is that fraction of the whole circle given by the central angle.

A number from 0 to 1 saying how likely an event is; it equals the number of favourable outcomes divided by the total number of equally likely outcomes.

The complete set of all possible outcomes of a random experiment, written so that every outcome is listed once and no outcome is missed.

The event that the given event does not happen; its probability is 1 minus the probability of the event, so the two probabilities add to 1.

An equation in one variable in which the highest power is two, usually written ax² + bx + c = 0 with a not equal to zero.

The values of the variable that satisfy a quadratic equation; there are at most two of them, and they may be equal or not real.

The quantity b² − 4ac for a quadratic ax² + bx + c = 0; whether it is positive, zero or negative decides the nature of the roots.

The rule x = (−b ± √(b² − 4ac)) / 2a giving the roots of a quadratic equation directly from its coefficients a, b and c.

A ratio of two sides of a right-angled triangle that depends only on one acute angle of the triangle, not on its size.

In a right-angled triangle, the length of the side opposite the angle divided by the length of the hypotenuse; written sin θ.

In a right-angled triangle, the length of the side opposite the angle divided by the length of the side next to it; written tan θ.

The angle between the horizontal line through an observer's eye and the line of sight to an object above that level.

The rule for the distance between two points (x₁, y₁) and (x₂, y₂): the square root of (x₂ − x₁)² + (y₂ − y₁)².

The point exactly halfway between two given points; each coordinate of it is the average of the matching coordinates of the two points.

A number describing how steep a straight line is, found by dividing the change in y by the change in x between two points on the line.

A straight line that touches a circle at exactly one point and does not cut through the circle; that point is called the point of contact.

The single point at which a tangent line touches a circle; the radius drawn to this point is perpendicular to the tangent line.

The two tangent segments drawn from a point outside a circle to touch the circle are always equal in length.

The amount of space occupied by a solid, measured in cubic units; for a prism or a cylinder it equals base area multiplied by height.

The distance from the top point of a cone or pyramid, measured along the sloping side, to a point on the edge of the base.

The solid left when the top of a cone or pyramid is sliced off by a plane parallel to the base; a bucket is a common example.

An expression built from terms of the form a·xⁿ added together, where n is a whole number and a is a fixed number, such as 3x² − 5x + 2.

The largest power of the variable that appears in a polynomial with a non-zero coefficient; it also gives the greatest number of zeros the polynomial can have.

A value of the variable at which the polynomial takes the value zero; it is the same as a root of the equation formed by setting the polynomial equal to zero.

When a polynomial p(x) is divided by x − a, the remainder is p(a), the value obtained by substituting a for x.

Triangles whose corresponding angles are equal and whose corresponding sides are in the same ratio; one is an enlarged or shrunken copy of the other.

The ratio by which a figure is enlarged or reduced to produce a similar figure; it equals the ratio of any pair of corresponding sides.

A line drawn parallel to one side of a triangle, cutting the other two sides, divides those two sides in the same ratio.

The average of a set of values, found by adding all the values and dividing by how many there are; for grouped data, class marks are used.

The middle value of data arranged in order of size; for grouped data it is read from the cumulative frequency table.

The value that occurs most often in a set of data; in grouped data it lies in the class with the highest frequency.