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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An angle is a figure formed when the two sides of a line (termed rays) meet at the vertex. Recall that the vertex is a common endpoint where the two sides of a line (rays or arms) meet.
Please read more on the introduction to angles here.
In geometry, we have a category of angles known as angle pairs (or pairs of angles). Such angles are described as angle pairs because they always occur in twos. Their occurrence in pair will also show a specific property in the respective angles.
Note: Recall that angles can also be classified based on their degree measurement.
Please read on classification of angles based on degree measurement here.
Below are types or classifications of angles based on their occurrence in pairs:
Complementary Angles: These are two angles (or pair angles) that sum exactly to 90^{o}. Understand that a 90^{o} angle is also termed a right angle. For this reason, the 30^{o} and 60^{o} angles (sharing a common endpoint) will be considered as complementary angles because they sum up to a right angle (90^{o}). They are shown in the image below:
Supplementary Angles: These are pair angles whose sum equals 180^{o}. In the image below, notice that the angles (120^{o} and 60^{o}) are supplementary because they sum up to 180^{o}.
Recall that the 180^{o} angle is also termed a straight angle or angle on a straight line.
Adjacent Angles: Two angles are said to be adjacent when they share the same arm and vertex which does not overlap. In the image below, notice that the three arms (or rays) of the angle do not overlap and they also meet at a common endpoint called the vertex.
You can read on factorization of quadratic equation here.
Corresponding Angles: These are pair angles present on the same side of the vertex when a line intersects a pair of parallel lines. It is noteworthy to state that corresponding angles are always on the same side. See the image below:
Corresponding angles are always equal to each other when the lines are parallel. However, the line that intersects both parallel lines is called the transversal.
Alternate Interior Angles: They are pair angles formed when a line intersects or cuts two parallel lines. The intersecting line is called the transversal. Alternate interior angles are in opposition to each other. Also, both alternating angles are always equal when the lines are parallel.
The Alternate Interior Angles Theorem states that if two lines are parallel, then the pairs of alternate interior angles are congruent.
Note: The term congruent in the above theorem implies that both angles are equal, identical in form and coincides exactly when superimposed.
Alternate Exterior Angles: In simple terms, the alternate exterior angles are the vertical angles of the alternate interior angles. They are always equivalent or the same when the transversal intersects two parallel lines. They are shown in the image below:
Vertically Opposite Angle: These are angles formed at a point where two opposite lines cross or intersects each other centrally. The term vertical (in vertically opposite angles) implies that both angles share the same vertex; and not necessarily the common up-down meaning often ascribed to vertical.
The image below shows two pairs of vertically opposite angles. Notice that the sum of degree measurement in vertically opposite angles is always lesser than 360^{o} with both angles having equal degree measurements.
Vertically opposite angles may simple be referred to as vertical angles.
Instances where vertically opposite angles are present in real-life include a pair of open scissors, railroad crossing signs, open pliers, etc.
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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
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