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 90^{o} but less than 180^{o} is termed _____.
A. Complementary
B. Supplementary
C. Acute
D. Obtuse
E. Reflex
F. Straight
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.
Angles are generally considered as a part of geometry. It is formed at a place where two line intersects or meet each other; and is measured in degrees.
An angle is defined as a figure formed by two sides of a line (called rays) meeting at a common endpoint (called vertex).
Angles are classified into various types based on the following criterias:
Based on their degree measurement
Based on their pairs (angle pairs)
Please on angle pairs here.
Based on their direction of rotation
Angles can be determined based on their measurement in degree. To this end, an angle with zero degree (0^{o}) is called a zero angle; and it's formed when the arms of the angle are at the same position.
If we increased the size of the angle to a certain degree, the name of the angle changes automatically. For instance, an angle between 0^{o} through 90^{o} is termed an acute angle but as soon as we increase the size of the angle to 90^{o}, its name changes to a right angle.
You can read on lines and type of lines in mathematics here.
Generally, we are seven types of angles based on their degree measurement. The image below shows six of these:
Below are explanations on the types of angle based on degree measurement:
Zero Angle: This is an angle that has a measurement of 0^{o}. It is formed when both arms of the angle are at the same position. Below is an image that shows a zero angle.
From the above image, the points P, Q and R are on the same position. As a result, the angle PQR equals zero degree (∠ RPQ = 0^{o})
Acute Angle: This is an angle whose degree measurement is greater than 0^{o} but less than 90^{o}. Instances of acute angles include 1^{o}, 15^{o}, 30^{o}, 45^{o}, 60^{o} 89^{o}, etc. The image below shows a 60^{o} angle.
Right Angle: An angle that is exactly 90^{o} is termed a right angle. For this reason, it's also called a 90^{o} angle (90 degree angle). They are represented by drawing a small box between the vertical and horizontal arms of the angle. See the image below:
Obtuse Angle: An obtuse angle is always greater than 90^{o} but less than 180^{o}. Examples of obtuse angles are 91^{o}, 110^{o}, 130^{o}, 150^{o}, etc. It is shown in the image below:
You can read on trigonometry (sine, cosine and tangents) here.
Straight Angle: This is an angle that is exactly 180^{o}. Straight angle may also be termed as an angle on a straight line. See the image below:
Reflex Angle: This is an angle whose degree measurement is greater than 180^{o} but less than 360^{o}. Angles that fall within this range includes 181^{o}, 200^{o}, 250^{o}, 359^{o}, etc.
You can attempt various questions and answers for students here.
Complete Angle: This is an angle whose measurement is exactly 360^{o}. Complete angle are also known as full rotation angle:
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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