mental ability questions with answers

Let us learn about mental ability questions with answers

If student take interest to find solution of math given problems, they can improve their mental ability.

1. Write five prime numbers between 50 and 75.

Solution: 53, 59, 61, 67, 71

2. Every prime number is odd except

Solution: 2

3. What should be added to 40.09 to make it 51 dollars?

Solution: 10.91 dollars

Math is the ability to perform arithmetic calculations without the help or aid of external computing tools. Math test require more & more background knowledge & ability in math basic skills.

In our next blog we shall learn about help math I hope the above explanation was useful.Keep reading and leave your comments.

equation of a line from two points

Let us learn about equation of a line from two points

If Students are given 2 points, how can they find the equation of the line passing through the 2 points? If student know the slope & a point (x₁, y₁) student have that

rise y - y₁
m = =
run x - x₁

Now multiplying by

x - x₁

equation of a line from two points Point Slope Formula for the Equation of a Line

y - y₁ = m (x - x₁)

Find the equation of line from the point (1,2) with slope 4.

Solution:

We use the formula:

y - 2 = 4(x - 1) = 4x - 4 Therefore y = 4x - 4 + 2 = 4x - 2.

In our next blog we shall learn about how to calculate ratios I hope the above explanation was useful.Keep reading and leave your comments.

inverse log

Let us learn about inverse log

If 2 functions g(x) & f(x) are defined so that (f ο g) (x) = x and (g ο f) (x) = x we say

that g(x) & f(x) are inverse functions of each other.

Functions f(x) & g(x) are inverses of each other in case the operations of g(x) reverse all the operations of f(x) in the reverse order & the operations of f(x) reverse all the operations of g(x) in the reverse order

The Best Example: Determine the inverse log function of f(x) = log(x + 5).

Solution: f(x) = log(x + 5)

We know that, f(f^-1(x)) = x.

So, f(f^-1(x + 5)) = log(f^-1(x) + 5) = x

i.e., 10^x = f^-1(x) + 5 ( log₁₀y = x => 10^x = y )

f^-1(x) = 10^x - 5

This is the required inverse log function.

In our next blog we shall learn about about the author examples I hope the above explanation was useful.Keep reading and leave your comments.

square root of 45

Let us find out square root of 45

Square root property of 45: Square root of45 (√45)

General property of square root

Method 1: square root of 45 (√45)

Solution:√45 = √5 x √9

= √5 x √3x3

= √5 x √3^2

= 3√5

√45 = √(9 x 5) = 3√5

In our next blog we shall learn about velocity time graph I hope the above explanation was useful.Keep reading and leave your comments.

increasing and decreasing functions

Let us learn about increasing and decreasing functions

A function is called increasing when it increases as the variable increases & decreases as the variable decreases. A function is called decreasing when it decreases as the variable increases & increases as the variable decreases.

The graph of a function specifies plainly whether it is increasing or decreasing.

The derivative of a function can be used to determine whether the function is decreasing or increasing on any intervals in its domain. Incase f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) <>decreasing on I. Because the derivative is 0 or does not exist only at critical points of the function, it must be negative or positive at all other points where the function exists.

Theorem on Decreasing or Increasing of Functions:

Let letter “f” be continuous on [a, b] & differentiable on the open interval (a, b).

(a) “f” is decreasing on [a, b] if f '(x) <> ε(a, b)

(b) “f” is increasing on [a, b] if f '(x) > 0 for each x ε(a, b)

Theorem on Decreasing or Increasing of Functions can be proved by using Mean Value Theorem.

Theorem on Decreasing or Increasing of Functions can be used in various problems to check whether a function is increasing or decreasing.

In our next blog we shall learn about structure of nephron I hope the above explanation was useful.Keep reading and leave your comments.

definite integral calculator

Let us learn about definite integral calculator

definite integral calculator is mainly for finding the indefinite integral of the given expression by getting an input value.

Find the definite integral of the function f=x⁶ within the limit (0,1).

Solution:

Function f=x⁶ has a limit (0,1)

Now the definite integral can be calculated as,

=1/7-0

= 1/7

Definite integral calculator is same as the integral calculus calculator but it is mostly for finding the integral which is covered by a specific intervals. That is definite integral calculator has upper limit value & lower limit value.

For this definite integral calculator 1st the given expression should be integrated as integral calculator & then the limits should be applied. The final output can be derived by substituting the lower limit - upper limit

In our next blog we shall learn about quadrants of a graph I hope the above explanation was useful.Keep reading and leave your comments.

number line to 20

Let us learn about number line to 20

A number line is a line of real numbers can be arranged, according to their value. Each point on a number line corresponds to a real number& each real number has a distinctive (unique) point which corresponds to it. The best example, the number 1.5 (1 1/2) corresponds with the point on a number line which is halfway between 1 & 2.

The points on a number line are said to be as coordinates. The point zero is called the origin. & the numbers to the left side of the origin are negative numbers & the numbers to the right side of the origin are positive numbers. The counting numbers are starting from 1.These numbers are also said to be as natural numbers. Natural numbers are numbers that was a base of the number system. The number line to 20 will help student to understand the basic things in number theory. This type of number line will includes of numbers from 1 to 20.

That is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20.

So totally 20 numbers...

In our next blog we shall learn about unit circle diagram I hope the above explanation was useful.Keep reading and leave your comments.