Differential EquationsAn equation involving independent variable x, dependent variable y and the differential coefficients \(\frac { dy }{ dx } ,\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ,…..\) is called differential equation. (1) Order of a differential e…

What is the Foot of a Perpendicular Line? If P be the foot of perpendicular, then P is (lr + x1, mr + y1, nr + z1). Find the direction ratios of AP and apply the condition of perpendicularity of AP and the given line. This will give the value of r and h…

VectorsVectors represent one of the most important mathematical systems, which is used to handle certain types of problems in Geometry, Mechanics and other branches of Applied Mathematics, Physics and Engineering. Scalar and vector quantities: Those quan…

Multiplying Powers Rule: For all numbers x and all integers m and n, xm • xn = xm+n “This simply means when you are multiplying, and the bases are the same, you ADD the exponents.” Consider: Observe this rule at work in the following examples:The bases…

How do you Multiply and Divide Decimals?Multiplication of Decimal NumbersMultiplication of a decimal by 10, 100, 1000 etc.: Method: On multiplying a decimal number by 10, 100, 1000, … the decimal point is shifted to the right by one, two, three, … places…

How Do You Prove Triangles Are Congruenthttps://www.youtube.com/watch?v=GmS-p1S_t5ECongruent FiguresTwo figures/objects are said to be congruent if they are exactly of the same shape and size. The relationship between two congruent figures is called con…

How do you Add and Subtract Rational Numbers?There are four basic operations on rational numbers : AdditionSubtractionMultiplicationDivision.Addition of Rational NumbersIf two rational numbers are to be added, we first express each one of them as ration…

Review of ExponentsExponents are the mathematician’s shorthand.In general, the format for using exponents is: (base)exponent where the exponent tells you how many of the base are being multiplied together.Consider: 2 • 2 • 2 is the same as 23, since the…

Direct VariationExamine the graph at the right:The linear equation graph at the right shows that as the x value increases, so does the y value increase for the coordinates that lie on this line . For instance, if x = 2, y = 4. If x = 6 (multiplied by 3),…

What are the Inverse Trigonometric Functions?The inverse of a function f : A → B exists if f is one-one onto i.e., a bijection and is given by f(x) = y ⇒ f-1(y) = x. Graphs of inverse trigonometric functionsDomain and Range of inverse trigonometric func…