Month: September 2018

No, You Don’t Need Quadratic Formula

On the MANSW Facebook page, a fellow teacher from another school threw this question to the brain’s trust. All the answers provided to the problem by others used the Quadratic Formula, but the Algebra from those solutions was not exactly clean. Personally, I don’t think getting the answer in...
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Trigonometric Tricks in Geometry

I was digging through some old notes of questions I had done in the past and came across this one. I don’t remember who gave me this question but it was a fascinating one that combined both geometrical reasoning and the sine rule. Question In the triangle \(ABC\), \(AB...
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Geometry Induction

My boss at work gave me this interesting question to work out. It’s unusual as most induction questions are algebraic but this one was related to geometry and counting techniques. Not many of these around. I thought it was pretty cool. Question Prove that an \(n\)-sided convex polygon has...
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The Perfect View

I don’t remember where I got this question from (probably a textbook somewhere) but I remember it specifically for the different kind of way I went about solving it. Most people like to make a single variable the subject before differentiating, and this is usually the only way they...
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Special Integral: \(\int_0^\frac{\pi}{2}\ln(\sin x)\;dx\)

I remember when I was in Year 12, we were given this question on an integration worksheet that challenged my friend, Parth, and I so much so that we stayed back after school to use the large whiteboard to solve this problem even after all our friends had left...
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