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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Trigonometry is an aspect of mathematics that deals with triangles and the relationship between the 'three sides' and 'three angles' of triangles.
In Trigonometry, the right triangle is of interest to us because sine 'sin (θ)' and cosine 'cos (θ)' and tangent 'tan (θ)' are the three functions that reveal their shapes.
Please read on Angles and Types of Angles here.
Before exploring these functions, let’s understand the names given to the three sides of a right triangle:
Note: 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 below:
To get the ratio of the angle, make sure to always remember the magic word SOHCAHTOA
Sin = Opposite/Hypotenuse
CAH
Cos = Adjacent/Hypotenuse
TOA
Toa = Opposite/Adjacent
Note: The functions sine, cosine and tangent helps us to easily calculate the sides of the triangle (
Similarly, it also aid us to calculate the angle (sine, cosine and tangent) when we know the sides of the triangle.
Please read on Lines in Mathematics here.
Below are some worked Examples:
Find the sine, cosine and tangent of 30° whose hypotenuse has a value of 2, opposite has a value of 1 and adjacent has a value of √3.
The image below illustrates the question.
Since we already know the length of each side of the triangle, the angles for sine, cosine and tangent can easily be calculated by implementing the keyword SOH-CAH-TOA
Sine = Opposite/Hypotenuse
Sin(30°) = 1 / 2 = 0.5
Answer: Sin(30°) is 0.5
Cosine = Adjacent/Hypotnuse
Cos(30°) = 1.732 / 2 = 0.866
Answer: Cos(30°) is 0.866
Tangent
Tan(30°) = 1 / 1.732 = 0.577
Answer: Tan(30°) is 0.577
Note: You may confirm the answers from a scientific calculator if you wish.
Please read on Algebra explained with some worked examples.
Find “d” from the diagram below using the sine function.
Image Credit: Maths is Fun
From the figure above, we can conclude that:
The angle is 39^{o}
The hypotenuse is 30m (Longest side of the triangle)
“d” is the opposite side of the triangle (side opposite the angle)
Applying the SOH-CAH-TOA formula, we will get:
Sin 39° = Opposite/Hypotenuse
Sin 39° = d/30
d = Sin 39° x 30
d = 0.6293 x 30
Answer: d = 18.9cm
Note: Once we know the value of sine, cosine and tangent in a right triangle, we will be able to calculate the less common functions (Secant, Cosecant and Cotangent) using the formula below:
Secant Function:
sec(θ) = 1/cos
Cosecant Function:
csc(θ) = 1/sin
Cotangent Function:
cot(θ) = 1/tan
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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