MATHEMATICS
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Mathematics 10 Major Units
In this and the next article, I am going to introduce major topics/ units in Foundations of Mathematics and Pre-calculus 10. For example, Algebra, Factoring, Trigonometry, and Polynomials.
Algebra
Algebra is one of the main element make out most of the units in Math 10 (Foundations of Mathematics and Pre- calculus 10). If you don't know how to use it or you never heard of what is Algebra, then you are failing for the course, so you to do more practice before you attend the course. Algebra is a branch of mathematics that uses symbols, such as letters, to represent numbers and unknown quantities in equations and formulas. You need to figure out some missing information, and put it in a equation, such as 2x+1 = 5 Find x, x is the missing information from question You can find the answer by going backwards like a detective to find x. For example, 2x+1= 5. Step 1 -1 each side of the =, the equation will become, 2x+1-1=5-1. Step 2: Cancel out the +1 and the -1 on the left side of the = and -1 on the right side of the =. 2x=4. Step 3: Divide both side by 2 and you will get the answer is 2.
Here are the step in the equation:
2x+1= 5
2x-1+1= 5+1
2x=4
2x/2 =4/2
x=2
This question is a easier version of the question in Math 10, teachers will teach harder topics like polynomials and more advanced algebra questions.
Trigonmetry
Trigonometry is focused entirely on the fundamental relationships between the angles and side lengths of triangles, primarily using the right-angled triangle as its basis. The core functions—sine, cosine, and tangent (remembered by the acronym SOH CAH TOA)—express the trigonometry ratios of the opposite (O), adjacent(A), and hypotenuse (H) sides. During this unit, teachers will allow students use calculators to calculate the questions that is about sine, cosine, and tangent, because it is the only way to find answers in those kind of equations.
Here is a example of how to use trigonometry in a question:
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You are standing on the ground 20 meters away from the base of a tall tree. You look up to the very top of the tree with an angle of elevation (the angle from the ground up to your line of sight) of 35 degrees. How tall is the tree? Use the acronym SOH CAH TOA)
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Draw a Diagram: Imagine a right-angled triangle.
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The height of the tree is the Opposite side (let's call it
ℎ).
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The distance you are standing from the base is the Adjacent side (20 meters).
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The angle you are looking up at is the angle
θ
=𝜃 (35 degrees).
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Choose the Right Ratio: You know the Adjacent side and the angle, and you want to find the Opposite side. The trigonometric ratio that relates Opposite and Adjacent is Tangent (TOA):
tan(θ)=Opposite over Adjacent
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Plug in the Values:
tan(35 degrees)=H over 20
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Solve for the Unknown: ℎ by itself, multiply both sides of the equation by 20:
ℎ=20 x TAN 35 degrees
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Calculate (using a calculator):
ℎ≈20×0.7002
ℎ≈14.0 meters
Answer: The tree is around 14 meters tall.
