Tamil Nadu HSE First Year Business Mathematics and Statistics key terms

A rectangular arrangement of numbers in rows and columns, enclosed in brackets and described by its order, such as m by n. It is used to organise and combine business data.

A single number calculated from the entries of a square matrix by fixed expansion rules. It tells whether the matrix has an inverse and helps solve simultaneous equations.

The signed minor of an element of a square matrix, obtained by multiplying its minor by plus or minus one according to the element's row and column position.

The transpose of the matrix formed by replacing each element of a square matrix with its cofactor. It is used in the formula for the inverse matrix.

A square matrix which, when multiplied by the original matrix, gives the identity matrix. It exists only when the determinant is not zero.

A method of solving simultaneous linear equations using determinants. Each unknown is found as a ratio of two determinants, with the coefficient determinant as denominator.

The process of expressing a rational algebraic fraction as a sum of simpler fractions with known denominators. It is useful before integrating rational functions and in business applications.

An arrangement of a chosen number of objects in a definite order. The number of arrangements of r objects selected from n distinct objects is written nPr.

A selection of objects in which the order of choosing does not matter. The number of selections of r objects from n distinct objects is written nCr.

A formula that expands a binomial raised to a positive integer power as a sum of terms involving binomial coefficients. It is used for expansion and approximation in business calculations.

The term in a binomial expansion that contains a stated power of one part, usually written using nCr with powers adding to n. It finds a particular term without expanding everything.

A sequence in which each term after the first is obtained by adding a fixed number called the common difference. Fixed annual increments in salary follow this pattern.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio. Compound growth and depreciation are modelled this way.

A formula giving the total of the first n terms of a sequence. For an arithmetic progression it uses the first term and common difference; for a geometric progression it uses the first term and common ratio.

A unit of angle measure defined so that an arc equal in length to the radius subtends one radian at the centre. One full revolution equals two pi radians.

An equation involving trigonometric ratios that is true for every angle where both sides are defined. Standard identities are used to simplify expressions and solve trigonometric equations.

A rule expressing a trigonometric ratio of the sum or difference of two angles in terms of ratios of the separate angles, such as sine of A plus B.

A measure of the steepness of a straight line, equal to the change in the vertical coordinate divided by the corresponding change in the horizontal coordinate. Parallel lines have equal slopes.

A formula giving the straight-line distance between two points from their coordinates. It equals the square root of the sum of the squared differences of the coordinates.

An algebraic relation satisfied by every point on a straight line, often written in slope-intercept or two-point form. It is used in cost, revenue and break-even analysis.

The value that the output of a function approaches as the input approaches a stated number. Limits are the basis for defining continuity and the derivative.

The instantaneous rate of change of a function with respect to its variable, defined as the limit of a difference quotient. It measures marginal change in business functions.

A differentiation rule giving the derivative of a product of two functions as first function times derivative of second plus second function times derivative of first.

The family of all antiderivatives of a function, written with an arbitrary constant of integration. It reverses differentiation and recovers a total from a marginal function.

The integral of a function between two limits, giving a single number that represents accumulated change or area under a curve between those limits.

A technique for integrating a product of two functions using a formula derived from the product rule. Choosing the two parts wisely makes the integral simpler.

Interest calculated only on the original principal for the whole period, using principal multiplied by rate multiplied by time. It does not earn interest on interest already received.

Interest calculated on both the original principal and the interest already added, so the amount grows faster than under simple interest over several periods.

A series of equal payments made at regular intervals over a fixed period. Annuities are used for loan repayments, savings plans and pension payments.

The value today of a future sum or series of payments after discounting at a given interest rate. It allows cash flows occurring at different times to be compared.

The middle value of a data set arranged in ascending or descending order. For an even number of observations it is the average of the two middle values.

The positive square root of the variance, measuring how far observations typically lie from the mean. It is expressed in the same units as the original data.

The ratio of the standard deviation to the mean, usually expressed as a percentage. It compares variability between data sets with different units or very different averages.

A process whose outcome cannot be predicted with certainty before it is performed, although the set of possible outcomes is known. Tossing a coin is a simple example.

The set of all possible outcomes of a random experiment. Every event is a subset of the sample space, and probabilities are assigned to these outcomes.

Two or more events that cannot occur at the same time in a single trial. For such events the probability that either occurs is the sum of their probabilities.

Events in which the occurrence of one does not change the probability of the other. For two independent events, the probability that both occur is the product of their probabilities.

A graph plotting paired observations as points on two axes. The pattern of the points suggests whether two variables are positively related, negatively related or unrelated.

A number between minus one and plus one that measures the strength and direction of the linear relationship between two variables. Values near zero indicate weak linear association.

The line of best fit used to predict one variable from another by minimising the sum of squared vertical deviations. Its slope is called the regression coefficient.