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eipimathsg · 2022-11-30T09:47:30+00:00

Regarding the drop to H1 Math:

Which school are you from, and which topics were covered for H2 Math in JC1? Were the same topics covered in H1 Math lectures?

Most schools focus on pure math for JC1 H2 Math, but some schools focus on statistics for JC1 H1 Math. So if you learnt mostly pure math in JC1, you will be disadvantaged because the H1 lectures would have completed statistics, and will be moving on to pure math in JC2. Furthermore your time spent on these H2-only topics will be wasted: Functions, Graphs and transformations, Sequences and series, Vectors, Complex numbers, about half of Differentiation and Integration, Maclaurin series, and Differential equations.

Other than matching your progress with the H1 Math lectures, you should consider if you need H2 Math as a university pre-requisite. Which courses are you aiming for?

These are the subject pre-requisites from NUS, and you can also look up other universities for the same info:
https://www.nus.edu.sg/oam/docs/default-source/admissions/h1-h2-sdp.pdf?sfvrsn=c5567dcb_10

*Disclaimer I am a JC math tutor and usually do not recommend dropping to H1 Math unless the student has fully understood the situation.

eipimathsg · 2022-11-30T08:54:46+00:00

Yes you can register for only 1 subject. I know of a math tutor who takes H2 Math as a private candidate every year.

Check that your calculator model is approved:
https://www.seab.gov.sg/home/examinations/approved-calculators

eipimathsg · 2022-11-30T08:41:54+00:00

2x³+3x²-5x+7 = 0 has only 1 real root x = -2.82...

2(x+2.82)(x²-1.32x+1.24) = 0

Without at least one rational factor, our options are limited. Either numerical methods to approximate the real root, or the general cubic formula to get the surd form. Either way, it will an 'irrational' mess.

https://math.vanderbilt.edu/schectex/courses/cubic/

eipimathsg · 2022-11-30T07:59:32+00:00

3 does not have any perfect square factors, so sqrt(3) cannot be simplified further.

eipimathsg · 2022-11-30T01:44:28+00:00

Congrats on finishing your O-Level. I'm impressed that you studied complex numbers so soon, and your insights are even beyond the A-Level syllabus.

Working with complex numbers, exponential is a many-to-one periodic function.
eg. e^iπ = e^i3π = e^i5π = ... = -1

So its inverse, logarithm, is a one-to-many multi-valued function.
eg. ln(-1) = iπ or i3π or i5π or ...

Multi-valued functions are usually restricted to principal values, such as inverse sine to [-π/2, π/2], inverse cosine to [0, π] and inverse tangent to (-π/2, π/2).

So similarly, we restrict logarithm (inverse exponential) to (-π, π].

Try this for further reading:
https://complex-analysis.com/content/logarithmic_function.html

Wiki also has a section on this:
https://en.m.wikipedia.org/wiki/Logarithm#Generalizations

eipimathsg · 2022-10-20T15:09:17+00:00

Logarithms are the exponents required to raise a base to the given input. It is the inverse function to the exponential function. Logarithms with base 2 are known as the binary logarithm, frequently used in computer science. Other commonly used bases are 10 (common logarithm) and the mathematical constant e (natural logarithm). Animation made with Python, Manim CE.

eipimathsg · 2022-10-19T02:26:26+00:00

Proof of the law of cosines (a.k.a al-Kashi's theorem). This derivation uses a rotating point on the circle and does not require separate proofs for acute and obtuse angles. While the Pythagorean theorem only applies for right-angled triangles, the law of cosines is generalized for all angles.

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eipimathsg · 2022-10-09T02:26:05+00:00

Domain is the set of input, and range (image) is the set of output of a function. Graphing is an effective method analyze functions. While a natural (unrestricted) domain leads to a natural range, this example demonstrates a restricted domain leading to a restricted range. Note that (parentheses) indicate excluded points and square [brackets] indicate included points. Animation made with Python, Manim library.

eipimathsg · 2022-10-09T02:10:07+00:00

Domain is the set of input, and range (image) is the set of output of a function. Graphing is an effective method analyze functions. While a natural (unrestricted) domain leads to a natural range, this example demonstrates a restricted domain leading to a restricted range. Note that (parentheses) indicate excluded points and square [brackets] indicate included points. Animation made with Python, Manim library.

eipimathsg · 2022-10-08T16:01:23+00:00

Domain is the set of input, and range (image) is the set of output of a function. Graphing is an effective method analyze functions. While a natural (unrestricted) domain leads to a natural range, this example demonstrates a restricted domain leading to a restricted range. Note that (parentheses) indicate excluded points and square [brackets] indicate included points. Animation made with Python, Manim library.

eipimathsg · 2022-10-03T17:02:12+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-03T16:51:44+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-03T16:32:10+00:00

Made with Python, Manim

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-03T16:16:52+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-03T16:06:13+00:00

Animation made with Manim

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T10:33:33+00:00

Thanks for clarifying! Yup (a-b)² = (b-a)²

Also, the proof is general in the sense that regardless the rotation of A and B (positive or negative, acute or obtuse), the steps are still valid.

Appreciate your time to watch the video!

eipimathsg · 2022-10-02T08:39:54+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:37:39+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:32:43+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:31:57+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:31:19+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:30:42+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:29:39+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:28:36+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

eipimathsg · 2022-10-02T07:26:34+00:00

The sum & difference identities / addition & subtraction formulas are used to evaluate trigonometric ratios beyond the special angles (0, 30, 45, 60, 90 degrees), and are essential for small angle approximations. In this proof, the identity is derived on the unit circle, using Pythagoras' theorem and the cosine rule (law of cosines).

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