WBBSE Madhyamik Mathematics key terms

Money paid for the use of a borrowed sum, calculated only on the original principal for the whole time, without adding earlier interest back into the base.

Interest calculated on the principal plus any interest already earned, so the amount grows each period; the difference between final amount and original principal is the compound interest.

The original sum of money lent, borrowed or invested, on which interest is calculated before any interest is added.

The total sum at the end of a period, equal to the principal together with all interest that has accumulated on it.

The percentage charged or earned per year on a sum of money, usually written as so much per cent per annum.

A comparison of two quantities of the same kind by division, showing how many times one contains the other; written as a fraction or with a colon.

An equality of two ratios; in a proportion the product of the outer terms equals the product of the inner terms.

A relationship in which two quantities increase or decrease together at a constant ratio, so doubling one doubles the other.

A relationship in which one quantity increases as the other decreases so that their product stays constant, such as more workers finishing a job in fewer days.

A solving technique that first finds the value of one unit by division, then multiplies to obtain the value of the required number of units.

A fraction or ratio expressed with denominator 100, used to compare quantities and to express profit, loss, discount and interest as parts of a hundred.

The gain or loss found by comparing selling price with cost price; profit occurs when selling price exceeds cost price, loss when it is less.

The price at which an article is bought or produced, used as the base for calculating profit or loss.

The price at which an article is actually sold to a buyer, after any discount has been allowed.

A reduction allowed on the marked price of an article, usually stated as a percentage of that marked price.

The price written on an article before any discount is given; the selling price is obtained by subtracting the discount from it.

An algebraic expression formed by adding or subtracting terms in which variables have only whole-number non-negative powers, such as 3x squared minus 5x plus 2.

The highest power of the variable appearing in a polynomial with a non-zero coefficient; it fixes the greatest possible number of zeros.

A value of the variable at which the polynomial evaluates to zero; graphically it is where the curve meets the horizontal axis.

The statement that dividing a polynomial by a linear expression x minus a leaves a remainder equal to the value of the polynomial at x equals a.

A linear expression x minus a is a factor of a polynomial exactly when substituting a gives zero, linking factors with zeros.

An equation such as ax plus by plus c equals zero in which each variable appears to the first power only; its graph is a straight line.

Two or more equations that must be satisfied by the same values of the variables; their common solution gives the point where the graphs intersect.

A way of solving simultaneous equations by multiplying one or both equations so a variable has equal coefficients, then adding or subtracting to remove it.

A way of solving simultaneous equations by expressing one variable in terms of the other from one equation and putting that expression into the second.

An equation of the form ax squared plus bx plus c equals zero with a not zero; it has at most two real roots.

The values of the variable that satisfy a quadratic equation, found by factorisation or by the quadratic formula.

The quantity b squared minus 4ac in a quadratic equation; its sign tells whether the roots are real and distinct, real and equal, or not real.

A mathematical statement proved from definitions and earlier established results by logical reasoning, for example the theorem on angles in the same segment.

The statement obtained by interchanging the hypothesis and conclusion of a theorem; it is a new claim and needs its own proof.

Triangles with exactly the same three sides and three angles, so one can be superimposed on the other; tested by side-angle-side, angle-side-angle, side-side-side and right-angle-hypotenuse-side conditions.

Triangles with equal corresponding angles and proportional corresponding sides; their areas are in the ratio of the squares of corresponding sides.

A line drawn parallel to one side of a triangle divides the other two sides in the same ratio; its converse is also used to prove lines parallel.

In a right-angled triangle the square on the hypotenuse equals the sum of the squares on the other two sides; its converse identifies a right angle.

A circle is the set of points at a fixed distance from a centre; chord, diameter, arc, segment, sector and tangent name its standard parts.

A straight line that touches the circle at exactly one point; it is perpendicular to the radius drawn to that point of contact.

A quadrilateral whose four vertices lie on one circle; its opposite angles are supplementary, adding to two right angles.

Half the product of a base and the perpendicular height to it; for a triangle with sides a, b, c and semi-perimeter s, Heron's formula gives the square root of s(s-a)(s-b)(s-c).

A rule giving the area of a triangle from its three side lengths alone, using the semi-perimeter s in the expression s(s-a)(s-b)(s-c) under a square root.

Half the sum of the three sides of a triangle, written s and used inside Heron's formula for area.

The total length of the boundary of a plane figure, found by adding the lengths of all its sides or the circumference of a circle.

The total area of all faces of a three-dimensional object; for a sphere it is four times pi times the square of the radius.

The amount of space enclosed by a three-dimensional object, measured in cubic units; for a cone it is one third of pi times the square of the radius times the height.

Solids with circular bases; a cylinder has two parallel circular faces, while a cone tapers to a point and has a slant height related to radius and height by Pythagoras theorem.

The six ratios sine, cosine, tangent, cosecant, secant and cotangent, defined for an acute angle of a right triangle by pairs of its sides.

An equation true for every angle where both sides are defined, such as sine squared plus cosine squared equals one, used to simplify expressions.

The angle measured upward from the horizontal line of sight to an object above the observer, 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 arithmetic average, found by adding all observations and dividing by their number; it uses every value in the data.

The middle value of observations arranged in order of size; with an even number of observations it is the mean of the two middle values.

The observation that occurs most frequently in a set of data; a data set may have more than one mode or none.

A cumulative frequency curve, drawn by plotting cumulative frequencies against upper class boundaries, from which the median can be read off.

The midpoint of a class interval, obtained by averaging its lower and upper limits and used in computing the mean of grouped data.

The plane fixed by two perpendicular number axes meeting at the origin, allowing every point to be named by an ordered pair of coordinates.

The rule giving the straight-line distance between two points from their coordinates as the square root of the sum of squared differences.

The rule giving the coordinates of the point that divides the segment joining two points in a given ratio, internally or externally.

A measure of the steepness of a line, equal to the change in the vertical coordinate divided by the corresponding change in the horizontal coordinate between two points.

The straight line traced by all points whose coordinates satisfy a linear equation in two variables; two points are enough to draw it.

The matching sides and angles of two congruent or similar figures, which must be named in the same order when the congruence or similarity is stated.

A result that follows directly and easily from an already proved theorem, stated and used without a long separate proof.