Alfred Ajibola
- 11th February, 2019 @ 11:38 AM
Topics in Mathematics
Angles: Type of angles based on degree measurement Angle Pairs: Types of angle pairs Conversion of Number Bases explained with examples Angles: What are Angles? Categories of Angles Lines and Types in Mathematics Number Base System - Table showing the Number Bases with explanations Mathematics Scheme of Work, SS1, 3rd Term Mathematics Scheme of Work, SS1, 2nd Term Mathematics Scheme of Work, SS1, 1st Term Trigonometry - Sine, Cosine and Tangent explained with worked examples Quadratic Equation - Factorization of Quadratic Equation Algebra - Explanation and Worked Examples on AlgebraAcademic Questions in Mathematics
What type of polygon is shown in the above image?
A. Nonagon
B. Decagon
C. Octagon
D. Hexagon
E. Hepagon
F. Pentagon
Which of the following is not part of a circle?
A. Section
B. Sector
C. Segment
D. Semicircle
E. Secant
F. Center
What angle is shown in the above image?
A. Complementary
B. Supplementary
C. Acute
D. Obtuse
E. Reflex
F. Straight
An angle greater than 90o but less than 180o is termed _____.
A. Complementary
B. Supplementary
C. Acute
D. Obtuse
E. Reflex
F. Straight
Factorize 12a2 - 20a + 3
A. (6a - 1)(2a - 3)
B. (6a - 1)(2a + 3)
C. (6a + 1)(2a - 3)
D. (6a + 1)(2a + 3)
E. (-6a + 1)(2a - 3)
F. (-6a + 1)(2a + 3)
Simplify 10ab + 7ab
A. 17ab2
B. 17a2b2
C. 3ab2
D. 3a2b2
E. 17ab
F 3ab
Which of the following is not a type of angle?
A. Right angle
B. Left Angle
C. Acute Angle
D. Complete Angle
E. Straight Angle
F. Reflex angle
Two lines that can never meet each other are best considered as _____ lines.
Let’s start by explaining the reverse of factorization. Consider the equation below:
(4a + 6)(a – 1)
We can see 4 values from the above equation, they are:
4a, 6, a and -1
If we were to expand the brackets, we will have to:
Multiply +4a by a ….. '+4a x a' = 4a2
Multiply +4a by -1 ….. '+4a x -1' = -4a
Multiply +6a by a ….. '+6 x a' = +6a
Multiply +6a by – 1 ….. '+6 x -1' = -6
Note the followings:
Understand that when there isn't a sign in front of a number or variable, then it is considered to have a plus sign (+) before it.
If there isn’t any number in front of a variable, then it’s considered to have the value '1' before it. For instance ('a' has the same value as '1a').
The result from expanding (4a + 6)(a – 1) will give us:
(+4a x a) (+4a x -1) (+6 x a) (+6 x -1)
4a2 – 4a + 6a - 6
Since -4a and +6a are like terms (–4a + 6a will give us +2a), we will have our answer to be:
4a2 + 2a - 6
If you understood the above example, then factorization will become easier for you.
Factorization is simply the reverse of expanding brackets.
You may have to make some trials and errors when solving certain factorization questions, but following the steps in my examples will make factorization questions easier for you.
Factorize 4b2 – 10b + 4
We have three values from the question. They are:
+ 4b2, -10b, and +4
To factorize the above equation, we will need to split the middle value into 2 numbers whose:
Addition or Subtraction will be equal to -10b
Product will be equal to the 16b2 (that is, the product of 4b2 and 4 (at the right side).
(-8b – 2b) will work for us because:
Their subtraction = -10b
Their multiplication = 16b2
4b2 – 8b – 2b + 4
Notice that 4b2 and 8b are divisible by '4b', (that is, 4b is a factor) while 2b and 4 are divisible by 2, (that is, 2 is a factor). Therefore we can write:
4b(b - 2) -2(b - 2)
Now the brackets are the same, so our answer is:
Answer = (4b - 2)(b - 2)
Factorize 12a² - 20a + 3
To factorize the above equation, we will need to split the middle value into 2 numbers whose:
Addition or Subtraction will be equal to -20a
Product will be equal to 36a² (that is, the product of 12a2 and 3 (at the right side).
-18a – 2a will work for us because:
Their subtraction = -20a
Their multiplication = 36a²
12a2 – 18a – 2a + 3
Notice that 12a2 and 18a are divisible by '6a', (that is, 6a is a factor) while 2 and 3 are not divisible. Therefore we can write:
6a(2a - 3) -1(2a - 3)
Now the brackets are the same, so our answer is:
Answer = (6a - 1)(2a - 3)
Please read on the Number Base System here
Factorize d² + 2d - 8
To factorize the above equation, we will need to split the middle value into 2 numbers whose:
Addition or Subtraction will be equal to +2d
Product will be equal to the 8d² (that is, the product of d2 and 8 (at the right side).
+4d - 2d will work for us because:
Their addition = +2d
Their multiplication = 8d²
d2 + 4d - 2d + 8
Notice that d2 and 4d are divisible by 'd', (that is, d is a factor) while 2d and 8 are divisible by '2', (that is, 2 is a factor), Therefore we can write:
d(d + 4) -2(d + 4)
Now the brackets are the same, so our answer is:
Answer = (d - 2)(d + 4)
Kindly share this article via the links below:
Please click here to contact Alfred if you require any of the following services:
If you need a standard website at an affordable price.
Online training on the academic subjects: biology, chemistry and basic science.
If you require an advanced smart school management system (web application) for your school.
Click here to read on Len Academy Smart School Software.
Please click here to follow Len Academy on Google News.
Amazing facts in Mathematics
The opposite sides of a dice will always give a sum of seven
31,556,926 seconds makes one year
From 0 through 1000, the only number that has the letter 'a' in it is 'one thousand'
÷
The division symbol '÷' is actually called an obelus
Four is the only number in the English language that is spelt with the same number of letters as the number (4) itself
40 is spelt as forty and not 'fourty'. It is the only number that is spelt with letters arranged in alphabetical order
An odd number is a number that cannot be divisible by 2.
Every odd number has an 'e' in its spelling. They include:
555 in Thailand sounds like 'hahaha'. This is because the number '5' means 'ha' in Thailand
In mathematics, 10! means 10 factorial. Below is its calculation:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800
Interestingly, 3628800 seconds is the same as 42 days
42 days is the same as 6 weeks
We can therefore say that 10! equals 6 weeks or 3628800 seconds in mathematics
When you multiply 111,111,111 by 111,111,111; the result equals 12,345,678,987,654,321
Notable points in Mathematics
Let's use algebra to explain the simple statement below:
I am a number. When you subtract 3 from me, the result is 9. what number am I ?
Of course we know the answer is 12. You probably guessed it from your mind because it was that simple. The truth is, We could have a much more complicated statement of such; and that is where algebra comes into play.
Now, to apply algebra in the above statement, we use letters or alphabets to represent the unknown number(s). So using algebra, we can write:
Let the number be y
y - 3 = 9
y = 9 + 3
y = 12
The image above shows a right angled triangle. The angle of the above right triangle is denoted as θ. Below are some points to note:
Hypotenuse is always the longest side of the triangle.
Opposite is the side opposite the angle (θ)
Adjacent is the shorter side next to the angle (θ)
Each of Sin θ, cos θ and tan θ are the ratio of sides of the right triangle. They are calculated by using the formula (margic word) sohcahtoa:
soh
Sin θ = Opposite/Hypotenuse
cah
Cos θ = Adjacent/Hypotenuse
toa
Tan θ = Opposite/Adjacent
Circumference in mathematics means the distance around the edge of a circle (or a another curved surface).
Circumference is to circle or any other curved surface
Perimeter means the distance around a square or rectangle or polygon.
Perimeter is to square or rectangle or polygon