Assam ASSEB Higher Secondary Mathematics key terms

A relation from set A to set B is any subset of the Cartesian product A × B, so it is a set of ordered pairs (a, b) linking elements of the two sets.

A relation from A to B in which every element of A appears in exactly one ordered pair, so each input value produces exactly one output value.

For a function f from A to B, the domain is the whole set A, that is, the complete collection of input values for which the function is defined.

The range of a function is the set of all actual output values it takes; it is a subset of the codomain and may be strictly smaller than it.

A function f is one-one, or injective, when different inputs always give different outputs, that is, f(a) = f(b) forces a = b.

A function f from A to B is onto, or surjective, when every element of the codomain B is the image of at least one element of A.

When f is both one-one and onto, its inverse sends each output back to the unique input that produced it, so that f inverse of f(x) equals x.

A number of the form a + bi, where a and b are real numbers and i squared equals minus one; a is the real part and b the imaginary part.

The conjugate of a + bi is a minus bi, obtained by reversing the sign of the imaginary part; a number multiplied by its conjugate gives the real number a squared plus b squared.

The modulus of a + bi is the distance of the point (a, b) from the origin in the Argand plane, equal to the square root of a squared plus b squared.

A coordinate plane in which the complex number a + bi is plotted as the point (a, b), with the real part measured horizontally and the imaginary part vertically.

A single number associated with a square matrix, found by expanding along a row or column using cofactors; it is nonzero exactly when the matrix has an inverse.

The transpose of the cofactor matrix of a square matrix; dividing the adjoint by the determinant gives the inverse of the matrix.

A square matrix whose determinant equals zero; such a matrix has no inverse and its rows or columns are linearly dependent.

The value that the output of a function approaches as the input approaches a stated point; the function need not actually be defined at that point.

A function is continuous at a point when its limit there exists, the function is defined there, and that limit equals the value of the function.

The instantaneous rate of change of a function, defined as the limit of the difference quotient as the change in the input tends to zero.

A rule for differentiating a composite function: differentiate the outer function at the inner function and multiply by the derivative of the inner function.

A point where the value of the function is at least as large as at all nearby points; at such an interior point the first derivative is zero or does not exist.

A function whose value does not fall as the input rises; on an interval where the derivative is positive, the function is strictly increasing there.

The family of all antiderivatives of a function, written with an arbitrary constant, because differentiating any member of the family returns the original function.

The integral of a function between two limits a and b, read as a signed area and evaluated as F(b) minus F(a) using any antiderivative F.

The theorem connecting the two branches of calculus: for a continuous function, the accumulated area function differentiates back to the original function, and the definite integral is found from any antiderivative.

The vector drawn from a chosen origin to a point P, written as vector OP; it fixes the location of the point relative to that origin.

For vectors a and b, the scalar a dot b equals the product of their magnitudes and the cosine of the angle between them; it is zero when they are perpendicular.

The vector a cross b has magnitude equal to the product of the magnitudes and the sine of the angle between them, and points perpendicular to both by the right-hand rule.

The cosines of the angles that a line makes with the positive x, y and z axes; their squares add to one, and together they describe the orientation of the line.

The number obtained as a dot (b cross c); its absolute value is the volume of the parallelepiped built on the three vectors, and it is zero when they are coplanar.

Two lines in space that are neither parallel nor intersecting, so they lie in different planes; their shortest distance is measured along a common perpendicular.

The linear expression in the decision variables whose value is to be maximised or minimised in a linear programming problem, for example total profit or total cost.

The linear inequalities or equations that restrict the decision variables in a linear programming problem, reflecting limits on resources, demand or capacity.

The set of all points that satisfy every constraint of a linear programming problem at the same time; it is the intersection of half-planes and is usually a polygon.

A feasible point at which the objective function reaches its required maximum or minimum value over the feasible region of the problem.

A way of solving a linear programming problem by evaluating the objective function at every vertex of the feasible region and selecting the best value obtained.

The probability of event A given that event B has already occurred, equal to the probability of both events divided by the probability of B, provided that is not zero.

Two events are independent when the occurrence of one does not change the probability of the other, so the probability of both equals the product of their probabilities.

A formula that reverses a conditional probability: the probability of A given B equals the probability of B given A times the probability of A, divided by the probability of B.

A real-valued function defined on the sample space of an experiment, which assigns a numerical value to each possible outcome.

A table, formula or graph listing every value of a discrete random variable together with its probability; the probabilities are non-negative and add up to one.

The distribution of the number of successes in n independent trials each with the same success probability p; the probability of exactly r successes is nCr p^r (1-p)^(n-r).