Tag: Calculus
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Can you find the 3 Areas? 🟦🟧🟥
The figure above shows a unit square target for shooting on the rectangular coordinate plane. The target is divided into three regions 1, 2 and 3 by two curves as shown. Find the area of the three regions. Once again, this is a good moment to pause the article and give the problem a go…
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How Would You Tether Your Goat?
A goat is tethered to the edge of a circular paddock, with a lead adjusted so that the goat can eat just half of the field. So can you tell us how long the tether must be? Here’s a smoother paraphrased version that preserves the meaning while reading more naturally: At first glance, it seems…
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Let’s Look At This 2026 Maths Exam For Gifted Students In Iraq
I was scrolling on Reddit today and came across this difficult maths exam from Iraqi High School for gifted students. As someone who has completed a 3-year undergraduate degree in mathematics, I’d say similar problems also appeared on my first year exams in multivariable calculus and differential equations. Somehow it’s more ‘satisfying’ to do calculus-based…
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How To Find The Arc Length And Its Surface Area?
In this article, we will take a deep dive into the derivations of the arc length of a curve and the surface area of the revolution of a curve. Without further ado, let’s dive in! If you have been enjoying the content on our blog, consider checking out our website here. I have made some…
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Student Finds Embarrassing Error in Cambridge Exam
The Cambridge IGCSE is the international equivalent of England’s GCSE, a qualification typically taken by students aged 14 to 16. Recently, a student on Reddit’s AskMath community questioned the official mark scheme for one of the exam’s questions, believing it contained an error. Many other users examined the problem and agreed that the mark scheme…
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What’s the Area between the Curve and the x-axis?
This is the Witch of Agnesi, a bell-shaped mathematical curve named after the Italian mathematician Maria Gaetana Agnesi, famous because its strange name comes from a translation error. If you are brave enough to solve the challenge, read on! Construction and Challenge The figure above shows a circle of radius a centered at the point…
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Calculus Challenge: A Slanted Revolution
In this entry, we will solve the above problem using a rotational matrix. Give this problem a try before jumping into the solution! Solution By rotating the curve C and the line y = x by π/4 radians anticlockwise about the origin, the rotated volume will be given by the rotated curve about the y axis between the points at which…
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Math Genius Mary Adler’s Calculus Problem
The real Math Girl Mary Adler is a fictional character from the movie ‘Gifted’. In the Gifted universe, she is a seven year-old math prodigy. I must say I was also considered a ‘Gifted’ child by many. Gifted not because I was good at mathematics, but because I wielded the exceptional prowess of ‘舉一反三’, which…