Odisha BSE Madhyama Mathematics key terms

A number that can be written as a fraction p/q where p and q are integers and q is not zero. Examples include 3, -7/2 and 0.5.

A real number that cannot be expressed as a fraction of two integers. Its decimal form neither ends nor repeats, as with the square root of 2 or pi.

Any number on the number line, whether rational or irrational. The set of real numbers includes whole numbers, fractions, decimals, surds and pi.

An irrational root of a rational number that cannot be simplified to remove the root, such as the square root of 5. Surds obey special rules for multiplication and rationalisation.

The process of removing a surd from the denominator of a fraction by multiplying numerator and denominator by a suitable conjugate or surd.

For a binomial surd such as a plus root b, the conjugate is a minus root b. Multiplying the two gives a rational result and is used in rationalisation.

An algebraic expression made of variables and constants combined using addition, subtraction and non-negative whole-number powers of the variables, for example 3x squared minus 5x plus 2.

The highest power of the variable appearing in a polynomial with a non-zero coefficient. A constant has degree zero and a linear polynomial has degree one.

A value of the variable that makes the polynomial equal to zero. For p(x) equal to x minus 4, the zero is 4.

If a polynomial p(x) is divided by x minus a, the remainder equals p(a). This lets you find remainders without long division.

A polynomial p(x) has x minus a as a factor exactly when p(a) equals zero. It is a special case of the remainder theorem.

An equation of the form ax plus by plus c equals zero, where a and b are not both zero. Its graph is a straight line and it has infinitely many solutions.

Two or more equations that must be satisfied by the same values of the variables. Their common solution is found by elimination, substitution or graphing.

A way of solving simultaneous equations by multiplying equations so that one variable has opposite coefficients, then adding or subtracting to remove that variable.

A method for solving simultaneous equations in which one equation is rearranged to express a variable, and that expression replaces the variable in the other equation.

An equation of the form ax squared plus bx plus c equals zero with a not equal to zero. It has at most two real roots, found by factorisation or the quadratic formula.

The quantity b squared minus 4ac for a quadratic equation ax squared plus bx plus c equals zero. Its sign tells whether the roots are real, equal or imaginary.

The rule giving the roots of ax squared plus bx plus c equals zero as minus b plus or minus the square root of b squared minus 4ac, all divided by 2a.

A sequence in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term.

The constant amount added to each term of an arithmetic progression to get the next term. It may be positive, negative or zero.

The formula for the nth term of an arithmetic progression with first term a and common difference d: a plus n minus 1 times d.

The total of the first n terms of an arithmetic progression, given by n divided by 2 times the sum of the first and last terms, or n over 2 times twice a plus n minus 1 d.

Two triangles are congruent when all corresponding sides and angles are equal. Tests such as SSS, SAS, ASA and RHS are used to prove congruence.

Triangles with equal corresponding angles and proportional corresponding sides. Their side lengths are in a fixed ratio called the scale factor.

Also called Thales theorem: a line drawn parallel to one side of a triangle divides the other 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 is used to test for a right angle.

A ratio of two sides of a right-angled triangle, such as sine, cosine or tangent, defined with respect to one acute angle of the triangle.

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

The angle measured upward from the horizontal line of sight to an object above the observer. It is used in height-and-distance problems.

The angle measured downward from the horizontal line of sight to an object below the observer. It equals the angle of elevation from the object.

The set of all points in a plane at a fixed distance, called the radius, from a fixed point called the centre. A chord, tangent and secant are related lines.

A line that touches a circle at exactly one point. It is perpendicular to the radius drawn to the point of contact.

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

A quadrilateral whose four vertices lie on the same circle. Its opposite angles add up to 180 degrees.

The branch of mathematics dealing with the measurement of lengths, areas, surface areas and volumes of plane and solid figures.

The space occupied by a cylinder, found by multiplying the area of its circular base, pi r squared, by its height h.

The total area covering the outside of a sphere, given by 4 pi r squared, where r is the radius.

The arithmetic average of a set of observations, found by adding all values and dividing the total by the number of values.

The middle value of a data set arranged in order. If the number of values is even, it is the average of the two middle values.

The value that appears most frequently in a data set. A set may have one mode, several modes or no mode.

A number between 0 and 1 measuring how likely an event is, calculated for equally likely outcomes as favourable outcomes divided by total outcomes.