Assam HS Class 11-12 Business Mathematics & Statistics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Union rule for two sets

For finite sets A and B, the number of elements in either set is n(A) + n(B) minus n(A∩B), so overlapping elements are not counted twice.

Equivalence relation

A relation on a set that is reflexive, symmetric and transitive. It splits the set into disjoint equivalence classes whose members are related to each other.

Composite function

For functions f and g, the composite f∘g maps x to f(g(x)). It exists only where g(x) falls inside the domain of f.

Inverse function condition

A function has an inverse only if it is both one-one and onto. The inverse reverses each ordered pair, so f⁻¹(y) = x exactly when f(x) = y.

Singular matrix

A square matrix whose determinant equals zero. It has no inverse, and the corresponding linear system has either no solution or infinitely many solutions.

Cramer's rule

Solves a square linear system by replacing one column of the coefficient matrix with the constants column. Each variable equals that determinant divided by the main determinant.

Matrix multiplication condition

The product AB exists only when the number of columns of A equals the number of rows of B. The result has rows of A and columns of B.

Arithmetic progression nth term

In an AP with first term a and common difference d, the nth term is a + (n−1)d, and the sum of n terms is (n/2) times the first plus last term.

Sum of infinite geometric series

For a geometric series with first term a and ratio r, the infinite sum equals a/(1−r), provided the absolute value of r is less than one.

Geometric mean relation

For positive numbers a and b the geometric mean is the square root of ab. Three numbers are in geometric progression exactly when the middle one squared equals the product of the other two.

Combination formula

The number of ways to choose r objects from n distinct objects, ignoring order, is n!/[r!(n−r)!], written as nCr and equal to nC(n−r).

Circular permutation count

Arrangements of n distinct objects around a circle number (n−1)!, because rotations are treated as identical. When mirror images also count as the same, halve this value.

At least one counting rule

To count selections satisfying at least one condition, subtract the number satisfying none from the total number of selections. This avoids case-by-case addition.

Compound interest formula

An amount P invested at rate i per period for n periods grows to P(1+i)ⁿ. Interest earned is that amount minus the original principal P.

Present value of annuity

The present value of n equal end-of-period payments R at rate i is R[1−(1+i)⁻ⁿ]/i. It gives the loan amount such payments can repay.

Effective annual rate

When nominal rate i is compounded m times a year, the effective annual rate is (1+i/m)ᵐ − 1, allowing comparison of loans with different compounding frequencies.

Marginal revenue and marginal cost

Marginal revenue is the derivative of total revenue and marginal cost the derivative of total cost. Profit is maximised where they are equal and profit's second derivative is negative.

Price elasticity of demand

Elasticity measures responsiveness of quantity to price, computed as −(p/x)(dx/dp). Demand is elastic when its absolute value exceeds one and inelastic below one.

Limit of (sin x)/x

As x approaches zero in radians, sin x divided by x approaches one. This standard limit underlies derivatives of trigonometric functions and appears in business growth models.

Definite integral as area

The definite integral of a function between two limits equals the signed area under its curve over that interval, found by evaluating an antiderivative at both limits and subtracting.

Primary versus secondary data

Primary data are collected first-hand by the investigator through surveys, observation or experiment. Secondary data were gathered earlier by someone else and are reused.

Exclusive and inclusive classes

Exclusive classes have no gap, such as 0–10 and 10–20. Inclusive classes like 10–19 and 20–29 need half the gap added and subtracted to convert them.

Ogive curve

A cumulative frequency curve plotted against class boundaries. It estimates the median, quartiles and percentiles by reading the value at the corresponding cumulative frequency.

Median of grouped data

Median equals L plus [(N/2 − cf)/f] times h, where L is the lower limit of the median class, cf the preceding cumulative frequency and h the class width.

Coefficient of variation

The standard deviation divided by the arithmetic mean, usually expressed as a percentage. It compares variability of series measured in different units or with different averages.

Empirical mode relation

For moderately skewed distributions, mode approximately equals three times the median minus twice the mean. It estimates the mode when only the mean and median are known.

Karl Pearson correlation coefficient

A measure of linear association between two variables, ranging from minus one to plus one. It is computed from the sum of products of deviations divided by the product of standard deviations.

Regression coefficient interpretation

The slope of the regression line gives the average change in the dependent variable for a one-unit increase in the independent variable, with sign matching the correlation.

Spearman rank correlation

A correlation measure for ranked or qualitative data, computed as one minus six times the sum of squared rank differences divided by n(n²−1).

Time series components

A time series is analysed as trend, seasonal variation, cyclical variation and irregular variation. In the multiplicative model these four are multiplied together.

Laspeyres price index

A weighted price index using base-year quantities in both the numerator and denominator. It tends to overstate price rise because it ignores substitution toward cheaper goods.

Binomial distribution mean

For n independent trials each with success probability p, the number of successes has mean np and variance npq, where q is one minus p.