Science subjects made easy.
Mar 16, 2021
Square tricks
66²
666²
6666²
66666²
666666²
What you need to do is to take the square of the last digit writing the result by giving gap in between the two digits and Infront of the first digit, then reduce the last digit of the result by 1 and increase the first digit by 1 and write what you get in the gaps created.
Solutions:
66²= 4356
6662= 443556
66662=44435556
666662=4444355556
6666662=444443555556
Oct 12, 2020
Sep 16, 2020
Finding quadratic equations of given roots.
Find the quadratic equations of the following:
1. -2 and 3
2. 1/2 and 1
3. +√5 and -√5
Solutions:
1. -2 and 3
Let x= -2 and x= 3
X+2=0 and x-3=0
Put the two equations into two different brackets and equate all to 0
(X+2)(X-3)=0
Expand brackets(remove brackets by multiplying every term in the first bracket by each term in the second bracket)
X(X-3)+2(X-3)=0
x² -3x + 2x -6=0
x² - x - 6=0
2. ½ and 1
Let x=½ and x=1
x-½=0 and x-1=0
To eliminate the fraction in the first equation, multiply by 2
2x-1=0 and x-1=0
(2x-1)(x-1)=0
Expand
2x(x-1)-1(x-1)=0
2x² -2x-x+1=0
2x²-3x+1=0
3. +√5 and -√5
Let x=+√5 and x=-√5
x-√5=0 and x+√5=0
(x-√5)(x+√5)=0
Expand
x(x+√5)-√5(x+√5)=0
x²+x√5-x√5-5=0
x²-5=0
Please, feel free to ask your question if any.
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Expect more!
God bless you all.
Jul 4, 2020
Jul 1, 2020
Differentiations.
Do not be scared as I am going to make it so simple for you.
In differentiation, the derivative of any constant is Zero, the derive of X is 1.
There are different rules for finding derivatives in Calculus.
To find the derivative of a number is like finding the square root of a number.
The Rules of derivatives are:
1. Power Rule
2. Quotient Rule
3.Product Rule
4.Chain Rule.
We shall go through them one after the other.
The Power Rule
Find the derivative
f(x)=x⁴+2x³-x²+4x-1
To find the derivative of the above function, find the derivative of each term individually. In doing so, make the power of x the coefficient of x and reduce the power by 1 while, in terms where x has a coefficient, multiply the power of x by its coefficient and reduce the power by 1.Also to remember is that any constant is Zero.
Solution to our problem
Formula is:
f'(x)=4x³+6x²-2x+4
Stay tune for the other rules.
Until I come your way again, stay safe!
Jun 26, 2020
Angles
Angles are formed in different ways.
- Angle can be formed on a straight line. An angle formed on a straight line is 180°,
- When a vertical line is drawn perpendicularly to a horizontal line, a right angle is formed. A Right Angle is simply angle 90°,
- When a transversal line is drawn across two parallel lines, corresponding and alternate angles are formed. Corresponding angles are equal. Alternate angles are also equal. Parallel lines are lines that can never meet even if you draw them from Earth to Heaven. Corresponding angles are otherwise known as F-Shape angles while alternate angles are Z-Shape angles.
- When two transversal lines cut across themselves, vertically opposite angles are formed and vertically opposite angles are equal.
- Complimentary angles are angles that add up to 90°, e.g 60° + 30°, 45° + 45° etc.
- Supplementary angles are angles that add up to 180°, e.g 100°+80°,20°+160°,90°+90°, etc
- Angles formed at a point, add up to 360°,
- In a triangle, the total sum of angles is 180°.
Angles
- Acute Angles: These are angles that are less than 90°, e.g 10°, 20°, 45°, 89°
- Right Angle: This is an angle of 90°
- Obtuse Angle: An angle that is more than 90° but less than 180°, e.g 91°,95°,179°,
- Reflex Angles: They are angles that are greater than 180° but less than 360°,e.g 182°, 185°, 270°, 359°.
Jun 25, 2020
Names of different triangles.
Names of Polygons from 1-20
Jun 2, 2020
Logarithm
Jun 1, 2020
Standard form(Scientific notation)
Standard form is a number of the form, A×10^n
Where A is between 1 and 10, i.e, 1 2 3 4 5 6 7 8 9 while n is the number of places the decimal point is moved to the left or right.When the decimal point is moved to the left, n is positive while it is negative when moved to the right.
When a whole number is written, it has its decimal point at the end.
E.g write in standard form 2567653
Solution:
2567653
To make this number fall between 1 and 10, the decimal point has to be between 2 and 5, therefore, 2567653=2.567653×10^6.
Note that the exponent is positive because the decimal point is moved to the left.
Express in standard form, 0.025
Solution:
When expressing a decimal fraction in standard form, always moved the decimal point to the right such that the whole number is between 1 and 10 and the power must be negative in correspondence to the number of places the decimal point is moved to the right.
So, 0.025=2.5×10^-2
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Please carefully study these for easier understanding of my next lesson. See you soon! When expressing numbers in standard form or scientific notation, always remember that, when the decimal point is moved to the right, the power or index or exponent must be negative while if it is moved to the left, the power or Index or exponent must be positive. See example below:
Class Room
Finding quadratic equations of given roots.
Find the quadratic equations of the following: 1. -2 and 3 2. 1/2 and 1 3. +√5 and -√5 Solutions: 1. -2 and 3 Let x= -2 and x= 3 X+2=0 and...
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This may seem very simple but it is necessary for you to know the types of triangles to avoid embarrassment. An undergraduate in,"Who W...
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For the purpose of those who are preparing for WAEC and UTME, I will like to introduce you to the Mathematics called, "Derivatives"...
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Angles are formed in different ways. Follow me to see the different ways Angles are formed. Angle can be formed on a straight line. An angle...