Table of Properties of Real NumbersLet a, b, and c be real numbers, variables, or algebraic expressions. (These are properties you need to know.)

Continuous FunctionContinuityThe word ‘continuous’ means without any break or gap. If the graph of a function has no break or gap or jump, then it is said to be continuous. A function which is not continuous is called a discontinuous function. While stud…

Area Under a CurveArea of bounded regionsThe area bounded by a cartesian curve y = f(x), x-axis and ordinates x = a and x = b is given by If the curve y = f(x) lies below x-axis, then the area bounded by the curve y = f(x) the x-axis and the ordinates x …

What is Harmonic Progression in Mathematics?Harmonic Progression (H.P.)Definition: A progression is called a harmonic progression (H.P.) if the reciprocals of its terms are in A.P. General term of an H.P.Harmonic meanIf three or more numbers are in H.P…

Circle EquationsA circle is defined as the locus of a point which moves in a plane such that its distance from a fixed point in that plane always remains the same i.e., constant. The fixed point is called the centre of the circle and the fixed distance i…

What is a Geometric Progression?Geometric Progression (G.P.)Definition: A progression is called a G.P. if the ratio of its each term to its previous term is always constant. This constant ratio is called its common ratio and it is generally denoted by r…

Properties of Arithmetic, Geometric, Harmonic Means between Two Given NumbersLet A, G and H be arithmetic, geometric and harmonic means of two numbers a and b. These three means possess the following properties : (1) A ≥ G ≥ H From (i) and (ii), we ge…

Solving Systems of Linear Equations Using MatricesHomogeneous and non-homogeneous systems of linear equationsA system of equations AX = B is called a homogeneous system if B = O. If B ≠ O, it is called a non-homogeneous system of equations. e.g., 2x + 5y…

One-to-one and Onto Functions Remember that a function is a set of ordered pairs in which no two ordered pairs that have the same first component have different second components. This means that given any x, there is only one y that can be paired with t…

Gradient (Slope) of a Straight LineThe straight line is a curve such that every point on the line segment joining any two points on it lies on it. The simplest locus of a point in a plane is a straight line. A line is determined uniquely by any one of t…