AP SSC Mathematics key terms

For any two positive integers a and b, there exist unique whole numbers q and r such that a = bq + r, where r is greater than or equal to 0 and less than b.

Every composite number can be written as a product of prime numbers, and this factorisation is unique except for the order in which the primes are written.

A real number that cannot be written in the form p/q, where p and q are integers and q is not zero; its decimal expansion is non-terminating and non-repeating.

The largest positive integer that divides two or more given numbers exactly, leaving no remainder; it equals the product of the smallest powers of the common prime factors.

The exponent to which a fixed base must be raised to produce a given number; if a to the power x equals N, then log base a of N equals x, with a positive and not equal to one.

A way of writing a set by listing all its elements inside curly brackets, separated by commas, with each element written only once and order not mattering.

A way of writing a set by stating a rule or property that every element satisfies, usually written as the set of all x such that x has that property.

The set that contains all the elements under consideration in a particular discussion; every other set in that discussion is a subset of it.

The set of all elements of the universal set that are not present in the given set A, written as A dash; it depends on which universal set is chosen.

Two sets that have no element in common, so their intersection is the empty set; for example, the set of odd numbers and the set of even numbers.

The highest power of the variable having a non-zero coefficient in a polynomial; it decides the polynomial's name, such as linear, quadratic or cubic.

A value of the variable at which the polynomial gives the result zero; for a polynomial p of x, the number k is a zero when p of k equals 0.

If p of x and g of x are polynomials with g of x not the zero polynomial, then p of x equals g of x times q of x plus r of x, where the degree of r of x is less than that of g of x.

A list of numbers in which each term after the first is obtained by adding a fixed number to the term just before it, so consecutive differences stay equal.

The fixed number added to each term of an arithmetic progression to get the next term; it equals any term minus the term immediately before it.

The term at position n in an arithmetic progression, given by a plus (n minus 1) times d, where a is the first term and d is the common difference.

The total of the first n terms of an arithmetic progression, found as n by 2 times (2a plus (n minus 1)d), or as n by 2 times the first term plus the last term.

A list of numbers in which each term after the first is obtained by multiplying the term before it by a fixed non-zero number called the common ratio.

The rule giving the distance between two points with coordinates x1, y1 and x2, y2 as the square root of (x2 minus x1) squared plus (y2 minus y1) squared.

The rule that gives the coordinates of the point dividing the line segment joining two given points internally in a stated ratio m to n.

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

Three or more points that lie on the same straight line; in coordinate geometry the slope between every pair of them works out to be the same value.

A pair of linear equations that has at least one common solution; the graphs of the two equations either meet at exactly one point or lie on top of each other.

A method of solving simultaneous equations in which one variable is removed by adding or subtracting suitably multiplied forms of the two given equations.

Triangles whose corresponding angles are equal and whose corresponding sides are in the same ratio; they have the same shape but not necessarily the same size.

If a line is drawn parallel to one side of a triangle and cuts the other two sides, then it divides those two sides in the same ratio.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides; its converse tests whether an angle is a right angle.

A quadrilateral whose four vertices all lie on one circle; its opposite angles are supplementary, adding up to 180 degrees, and its exterior angle equals the interior opposite angle.

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

The region enclosed by two radii of a circle and the arc between their endpoints; its area is theta by 360 times pi r squared and its arc length is theta by 360 times 2 pi r.

The part of a cone or pyramid left after cutting off the top by a plane parallel to the base; it has two parallel circular faces of different radii.

The sum of the areas of all the faces or surfaces of a solid, including its curved or lateral surface together with any flat bases it has.

A ratio of two sides of a right-angled triangle that depends on an acute angle, such as sine, cosine, tangent, cosecant, secant and cotangent.

The angle between the horizontal line drawn through the observer's eye and the line of sight when the observer looks upward at an object above eye level.

The angle between the horizontal line drawn through the observer's eye and the line of sight when the observer looks downward at an object below eye level.

An equation involving trigonometric ratios that is true for every value of the angle for which the ratios are defined, for example sine squared theta plus cosine squared theta equals one.

The average of a grouped frequency distribution, calculated as the sum of each class mark multiplied by its frequency, divided by the total of all frequencies.

The middle value of a grouped distribution, estimated by l plus (n by 2 minus cumulative frequency before the median class) divided by median class frequency, all multiplied by class size h.

The value that occurs most often in a grouped distribution, estimated by l plus (f1 minus f0) divided by (2f1 minus f0 minus f2), all multiplied by class size h.

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