Peppy Square

Archive for the ‘square root’ Category

1. Hypothesis testing:

The following is a test of whether intrinsic mean value is greater than extrinsic mean value, given that the sample size is n

Higher Mathematics – The Straight Line

/ = divided by

Gradient:

“Gradient is a number that measures the slope of a line. Divide the vertical distance by the horizontal distance.

D (up/down) / D (along)

The notation for the gradient is ‘m’ -> Mab = the gradient of line ab!

The basic formula for the gradient is;

Y1-y2 / x2-x1

Example:

Find the gradient of line AB, where A = (2,4) and B = (5,9)

M = b1-b2 / a1-a2

= 4-9 / 2-5

=-5 / -3

= 1.66

Any two lines which share a common gradient are parallel.

Any two lines which have a value of -1 when their respective gradients are multiplied, are perpendicular.

A straight line has the equation; y = m x + c

Y = the ‘y’ value

M = the gradient

X = the ‘x’ value

C = the ‘y’ intercept

If you know the equation of a line, then you can find the x or y value by setting the x or y value to 0 respectively.

I.e. to find y, set x = 0 (and vice versa)

To find the distance of a straight line when we know any two points on the line, we can use the ‘distance formula’:

AB = the square root of; (a2-a1)^2 + (b2-b1)^2 – where ^2 = squared

If we know two points on a straight line then we can work out the midpoint between those two points;

= (a1 – a2 / 2 , b1 – b2 / 2)

In simpler form, the midpoint is (difference between the two a values, difference between the two b values)

Special Lines in a Triangle:

Median: joins a vertex to a midpoint on the opposite side

Altitude: is a line through a vertex perpendicular to the opposite side

The 3 medians of a triangle meet it ‘G’, the centroid of the triangle.

It is a common sentiment among humans, with a wee bit of emphasis on kids, that mathematics at its lowest and most raw form is simply hard. There are, however, different aspects of mathematics that we have to learn about more for they can be useful in developing strategies in dealing with real life situations. Vedic arithmetic is one of these less known mathematical concepts.

Basically, vedic arithmetic is a subset of vedic mathematics. This concept involves an algorithm operation which focuses on the algorithmic and correctness issues concerning numerals. There are questions concerning the label for this concept as critics continue to demand evidence supporting the concept’s right to be referred to as vedic as well as mathematics. The lack of evidence is specific on the aspect concerning the connection of the whole system with that of the verdict sutras.

In its simplest form, verdict arithmetic involves numbers and numbers along with the other different basic concepts in mathematics such as the four major operations, square and square root, cubes, fractions and decimals. With the use of the equations, we can easily get to the answers to any numerical problems. Men of science usually make use of such equations to provide scientific calculations involving theories and methodologies in physical sciences. The use of the vedic formulas are helpful in making the calculation as fast as lightning and in order to end up with one liners for the answers.

The history of vedic arithmetic dates back a long time ago. Sri Bharati Krsna Tirthaji gave this name to refer to this mathematical concept as this is described as a form of ancient system rediscovered from the Vedas. There was a time when this concept was used to make sense of the way the mind works. It was a great help in getting the students directed towards the most appropriate way of solving the equation.

In our modern age of computers and calculators, a lot of people have shied away from developing skills of mental math, in particular, the basic methods of mental arithmetic. School children have asked why there is a need to learn about it when a calculator is readily available. This is a valid reason and can really catch the teacher off guard. This is however, a challenge left on the hands of our educators.