Math Formulas

When we talk about formulas, we expect complex expressions and numbers and exponents! Formulas actually make it easier for students to solve and understand the concepts of mathematics usually introduced to them from lower. Here is a list of a few important formulas that students from different grades apply in the classroom.

1. Volume of Sphere \( =\frac{4}{3}\pi r^3 \), r is the radius – A formula that is applied to calculate the volume of a sphere, a three dimensional, circular solid.
2. Area of a Circle \( =\pi r^2 \), r is the radius – If we cut a sphere in exactly two halves, we get a circle at the surface of one of the halves, and the area of the circle is calculated with the given formula.
3. Perimeter of a Rectangle \( =2(l+b) \), l is the length and b is the breadth. – Now that we see the area of a circle, the perimeter is a different concept in relation to geometric shapes. The perimeter of a rectangle introduces us to the length of the boundary of a geometric shape.
4. Pythagoras Theorem, \( c^2=a^2+b^2 \) where c is the length of the hypotenuse, a and b are the lengths of the other two sides of the right triangle. – Created by the great Pythagoras, a Greek mathematician, this formula mentions the relationship between the hypotenuse, the longest side of a right angled triangle, and the lengths of the other two sides.
5. Sum of interior angles of a polygon \( :(n-2)\times 180^{\circ} \), where n is the number of sides. – The previous formula spoke of a right angled triangle, which is a polygon. In fact all closed shapes with three or more than three sides are polygons. And the sum of the interior angles of a polygon is calculated with the formula given.
6. Point slope form: \( y-y_1=m(x-x_1) \), where m is the slope and \( (x_1,~y_1) \) are the coordinates of the point passing through the line. – Polygons are made up of straight lines and when we speak of lines, there is a way to represent a straight line in the form of one of mainly four types of equations, and this equation represents the slope, and one point on the line.
7. Exponents: \( a\times a\times a\times a\ldots(n~times)=a^n \) – Moving away from geometry we have a formula that prevents us from repeated multiplication. Representing an expression that indicates repeated multiplication makes life easier for a lot of students.
8. Simple Interest: \( I=Prt \) where P is the principal amount, r is the rate of interest (in decimal form), and t is the time period. – While on the topic of increasing a number exponentially, we can also look at making money grow with the application of simple interest.
9. \( \text{Mean}=\frac{\text{Sum of all data values}}{\text{Number of data values}} \) – And when we need to calculate the mean of a set of numbers or values, we just need the sum of all the values and divide it by the number of values. This formula is definitely of statistical significance!
10. Dilation: On dilation, the coordinates of the figure \( (x,~y) \) become \( (kx,~ky) \), where k is the scale factor. – Of importance in coordinate geometry the concept of dilation is to either increase or decrease the size of a geometric shape by a given scale factor.