Posted in ask uncle colin, calculus, core 4.

Dear Uncle Colin, I have a pair of parametric equations giving $x$ and $y$ each as a function of $t$. I'm happy with the first derivative being $\diff{y}{t} \div \diff{x}{t}$, but I struggle to find the second derivative. How would I do that? - Can't Handle An Infinitesimal Nuance Hi,

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Posted in ask uncle colin, core 4, integration.

Dear Uncle Colin, Why can't I work out $\int \left( \ln(x) \right)^2 \dx$ using the reverse chain rule? -- Previously Acceptable, Reasonable Technique Stumbles Hello, PARTS, There are two answers to this: the first is, you can't use the reverse chain rule -- which I learned as 'function-derivative' when I

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Posted in calculus, circles, core 4, ninja maths, pirate maths.

"Let me see that!" commanded the Mathematical Ninja, looking at one of the Mathematical Pirate's blog posts. "That's... but that's..." "It's not wrong!" said the Mathematical Pirate, smugly. "It just works!" "But you're presenting it as magic, not as maths." The Mathematical Pirate nodded eagerly. "Lovely magic! How does it

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Posted in ask uncle colin, calculus, core 4, integration.

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I've been trying to integrate $\int \frac{x^2}{x-1}

Read More →At granny's house, it always seems to go the same way after lunch: Bill and his cousin chase each other around the dining room, while the adults try to make head or tail of their toys. This Sunday was no different: the toy in question comprised a large number of

Read More →A reader (not, in fact, a Core 4 student) wrote in to ask: I have an ellipse in my spreadsheet program, using the formula $y = \frac ba \sqrt{a^2 - x^2}$, and I want to know the angle the normal to the ellipse makes with the horizontal at any value

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Posted in core 4, integration.

A student asks: How do you integrate $\int_{0}^{\frac{\pi}{4}} \sec^4(x) \d x$? Yuk. Let me say that again for good measure: yuk. That's going to need a trigonometric identity and, I think, a substitution. But that's ok: we can do that. Let's roll up our sleeves. Step 1: get rid of

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Posted in core 4, integration.

A student asks: I've got to work out: $\int \cosec^2(x) \cot(x) \d x$. I did it letting $u = \cosec(x)$ and got an answer -- but when I did it with $u = \cot(x)$, I got something else. What gives? Ah! A substitution question! My favourite -- and it sounds

Read More →"Where's the Mathematical Ninja?" asked the student. "He's... unavoidably detained," I said. In fact, he was playing Candy Crush Saga. But sh. "What can I help you with today?" "Well, you know the binomial expansion...?" "Intimately," I said. "Well, I got it pretty well at C2... but now we're doing

Read More →A few months ago, I wrote a post about replacing long division with a coefficient-matching process. That's brilliant for C2, but what happens if you're looking at a C4 question that wants a quotient and a remainder? Well, it gets a bit more complicated, that's what happens. But it's not

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