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
Factorize 12a^{2}  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. 17ab^{2}
B. 17a^{2}b^{2}
C. 3ab^{2}
D. 3a^{2}b^{2}
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.
An angle at exactly 90^{o} is a/an _____ angle.
Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____.
The two sides that forms an angle are referred to as the _____.
The point where the two sides of an angle meet is termed the _____.
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Numbering begins with 0 (zero). Also, numbers are expressed in bases (sometimes called radix). A base 10 number for instance will comprise of 10 digits ranging from 0 – 9.
Note: We generally use base 10 in our numbering system.
Base 10 digits will comprise of: 0 1 2 3 4 5 6 7 8 9
Since the above numbers are composed of 10 digits, Base 10 may be referred to as decimals or denary digits.
The table below illustrates base 10 digits:
Unary or Base 1 
Base 10 
Sumary 

0 
All base digits starts at 0 
1 
1 
Next digit is 1 
11 
2 
Next digit is 2 
111 
3 
Next digit is 3 
1111 
4 
Next digit is 4 
11111 
5 
Next digit is 5 
111111 
6 
Next digit is 6 
1111111 
7 
Next digit is 7 
11111111 
8 
Next digit is 8 
111111111 
9 
Next digit is 9. Base 10 digit ends with 9 
1111111111 
10 
After the last digit which is 9 above, we will start at zero again, but add 1 to the left 
11111111111 
11 
We will add 1 digit to the right 
111111111111 
12 
We will add 1 digit to the right 
1111111111111 
13 
We will add 1 digit to the right 
11111111111111 
14 
We will add 1 digit to the right 
111111111111111 
15 
We will add 1 digit to the right 
1111111111111111 
16 
We will add 1 digit to the right 
11111111111111111 
17 
We will add 1 digit to the right 
111111111111111111 
18 
We will add 1 digit to the right 
1111111111111111111 
19 
We will add 1 digit to the right 
11111111111111111111 
20 
After the last digit which is 9 above, we will start at zero again, but add 1 to the left 
111111111111111111111 
21 
We follow the same procedure all through 
Apart from base 10 (Decimal), we also have other bases like:
Note: When we have a base number greater than 10; for instance base 11 or base 12 or base 13 and so on, the next digit will be an alphabet in its ascending order.
Let's see the examples below:
Note: Base 16 is also known as hexadecimal digits.
Hexadecimal digits prove useful in Internet Protocol Address (IP Address) and Media Access Control Address (MAC Address) in computer networking.
Please read on the OSI Model of Networking here.
The digits for base 16 (Hexadecimal digits) are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
With regards to base 2, it will comprise of only 2 digits which are 0 and 1.
Since we have just 2 digits here, base 2 is often referred to a binary digit.
Binary digits are fundamental to how computers work. This is why you may see stuffs like "01001100101011011" in a programming or computer language. Remember, we have just two digits in binary and that’s 0 and 1.
The table below shows what base 2 would look like:
Base 1 
Base 2 
Summary 

0 
All base digits starts at 0 
1 
1 
Next digit is 1. Base 2 digit ends with 1 
11 
10 
We start at zero again, but add 1 to the left 
111 
11 
We will add 1 digit to the right 
1111 
100 
Since the above digits is all 1’s and base 2 ends with digit 1, we will change all the 1’s to 0’s and add 1 to the left 
11111 
101 
We will add one to the farthest 0 at the right 
Note: Understanding base 2 is very vital for Internet Protocol address (IP Address) in computer networking.
Please read on Computer Networks here.
Ternary or Base 3 comprise of 3 digits which are 0, 1 and 2.
The table below shows what base 3 would look like:
Unary/Base 1 
Base 3 
Summary 

0 
All base digits starts at 0 
1 
1 
Next digit is 1. 
11 
2 
Next digit is 2. Base 3 digit ends with 2 
111 
10 
We will start back at 0 and add 1 to the left 
1111 
11 
Next digit is 1 from the right 
11111 
12 
Next digit is 2 from the right 
111111 
20 
We will start back at zero and add one to the left 
1111111 
21 
We will add 1 to the right 
11111111 
22 
We will add 1 to the right 
111111111 
100 
Since the above digits is all 2’s, we will change all the 2’s to 0’s and add 1 to the left 
1111111111 
101 
We will add 1 to the farthest right 
The table below shows a summary of base 10, base 2, base 6, base 11 and base 16 respectively.
Unary 
Base 10 
Base 2 
Base 6 
Base 11 
Base 16 
1 
1 
1 
1 
1 
1 
11 
2 
10 
2 
2 
2 
111 
3 
11 
3 
3 
3 
1111 
4 
100 
4 
4 
4 
11111 
5 
101 
5 
5 
5 
111111 
6 
110 
10 
6 
6 
1111111 
7 
111 
11 
7 
7 
11111111 
8 
1000 
12 
8 
8 
111111111 
9 
1001 
13 
9 
9 
1111111111 
10 
1010 
14 
A 
A 
11111111111 
11 
1011 
15 
10 
B 
111111111111 
12 
1100 
20 
11 
C 
1111111111111 
13 
1101 
21 
12 
D 
11111111111111 
14 
1110 
22 
13 
E 
111111111111111 
15 
1111 
23 
14 
F 
1111111111111111 
16 
10000 
24 
15 
10 
Notice that we skipped the zero (0) value in the above table.
Please read on the Conversion of Number Bases explained with worked examples here.
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Amazing facts in Mathematics
The opposite sides of a ðŸŽ² dice ðŸŽ² 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 ðŸ™„
An odd number is a number that cannot be divisible by 2.
Every odd number has an 'e' in its spelling. They include:
 One
 Three
 Five
 Seven
 Nine
555 in Thailand should sound like 'hahaha'. This is because the word '5' means 'ha' in Thailand
10! Actually means 10 factorial in mathematics. 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
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
The image above shows a right angled triangle. The angle of the above right triangle is denoted as θ
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 curverd surface).
Perimeter means the distance around a square or rectangle or polygon.
Circumference is to circle or any other curved surface
Perimeter is to square or rectangle or polygon