Mainly Maths Here

  Infinity---------------------------------------------------- What is infinity? Have you ever wondered how many times can one go around a circle? How many points there are on a line? How many circles are there in a sphere? The answer is infinity! Many refer to infinity as if it was a gigantic number; it's not. In fact, infinity is just never ending. Something that keeps going on. Infinity isn't a real value, it isn't measurable or quantifiable, one cannot actually reach infinity. Infinity plus one is still infinity! There are numerous paradoxes to explain the concept of infinity, one example is pi. Pi is a never ending number. It starts like 3.141592653 ...... The decimals here 'lead to infinity'! Practically, infinity doesn't hold a lot of value, but it is frequently used in concepts like geometry, cosmology, logic and computing, and it helps in the development of mathematical theories as well.  Working with infinity While working with infinity, interesting th...

  You must have come across 'e' in many calculators, it's not just any other alphabet but actually a number! Just like pi! The Euler's number is one of the most popular numbers in math. It is an irrational number, it never ends and 'e' is a common way of denoting it's value of 2.182818284590.....   Question Suppose you have a box of chocolates and you drop them all on the floor, the probability of each chocolate going back in the wrong spot is 1/e! The more the chocolates, the closer the answer to 1/e! Uses 'e' is used a lot in logarithms, it also has something to do with the 'ln' on your calculator. Practically, 'e' is used in data science, growth and population models, and physics amongst other concepts. The Graph When you differentiate a curve, you get an equation stating the gradient of every point on the curve, but when you differentiate a y=e^x curve, the gradient at any point will always be e^x! The  f(x)=e^x graph never actual...

  Trigonometry revolves around finding the length/ angle of a part of a triangle using various methods. One can use the basic formulas to find the values of a right angled triangle but we can use other formulas for non-right angled triangles. Important Formulas:  This formula is used to find the area of any triangle  ↑ In all of these formulas, the uppercase letters represent the angle and the lowercase letters represent the side opposite to the corresponding angle. Now let's work with a question! We can first use the cosine rule to find one the angles. Let us start by finding out the value of the angle opposite 6.5cm.  So we use the cosine rule, and substitute the values: a=6.5 b=4.3 c=5.2 and cosA is unknown.  We make cosA the subject of the formula and solve. Then we find A using the inverse cos. A= 85.8 Now we have an angle and a side. We can use the sin rule to find the rest of the angles: sin85.8/6.5= sinB/4.3= sinC/5.2 We get the values of the angles as A...

  In a graph, there are numerous points which join to form various polygons. These polygons may be irregular in shape, with any number of sides. The area of these polygons can be found using different methods! If we have a regular polygon, we can use that polygon's formula to find the area. So if we have a hexagon, we can just use the formula :                                              a^2(3√3)/2 This is the formula to find the area of a regular hexagon. 'a' represents the length of a side. There is a different formula for different regular polygons.  The side length of a polygon can be found using the distance formula, where we calculate the distance between two points. But, what if the polygons are not regular? If they have different side lengths and different angles on each side? The formula generally used here is commonly known as the sh...

   Differentiation Differentiation is a method of finding the gradient of any point in a polynomial graph. Polynomial graphs are graphs of quadratic, cubic, quartic, etc. equations. By differentiating the polynomial equation, we create another general equation that gives us the gradient of any point on the graph.  To find the gradient of a specific point on a graph, we usually take the point and draw a tangent from that point. Then we make a right angled triangle of that tangent and use Pythagoras Theorem to find the gradient( the hypotenuse). This method is too long and drawing tangents make it susceptible to human error. This is why we use differentiation!  How to differentiate: We do it in parts. We take the power of the value and multiply it to the coefficient. Then we subtract the power by one. For example: If y = x 4 , dy/dx = 4x 3 If y = 2x 4 , dy/dx = 8x 3 If y = x 5  + 2x -3 , dy/dx = 5x 4  - 6x -4 dy/dx is the 'symbol' of differentiation. Question...

  SIMULTANEOUS EQUATIONS:-   Often, solving a problem requires an equation. Sometimes there is more than one unknown variable in an equation.  For example: 3x + 6y = 15 Here, there can be multiple combinations of answers of x and y, and trial and error is not an efficient way of solving the equation. This is when other equations are given to help find the unknown variables algebrically. Let us take another equation and calculate 'simultaneously'. 2x - 2y = -4 Now let us write the equations together: 3x + 6y = 15______________equation 1 2x - 2y = -2_______________equation 2 Now, we multiply both the equations in such a way that the coefficient of one variable becomes equal: 6x + 12y = 30 we multiplied the first equation by 2. 6x - 6y = -6 we multiplied the second equation by 3. The coeeficient of 'x' becomes 6 in both! Now we can subtract the equations to get rid of the 'x'. All we do in this step is change the sign of every corresponding variable: (6x-6x) + (12y...