# The Mathematical Ninja's C4 Paper

“I stayed in ALL DAY waiting for that delivery of exam papers in Amsterdam,” said the Mathematical Ninja. “I could have been out pillaging, but no, sodding Yodel told me the package was out for delivery and it was only when I called them up for the eighth time they admitted they’d lost it.”

“At which point, you, er, lost it?” asked the student.

“In a manner of speaking, yes. I knew EdExcel were going to need replacement papers pronto, so I knocked a few up.”

“Which were harder than normal?”

“What can I say, I was in a bad mood! Everything was on the syllabus…”

“… Technically…”

“… Although, perhaps, I might concede it was a teensy weensy bit more rigorous than normal. But that’s what Mr Gove wants, right? Rigorous exams? If no-one’s crying at the end, it isn’t rigorous enough.”

“Well… OK. So can you give me any hints about what might come up in C4?”

“I couldn’t possibly do that, it would be an ethical breach of the worst sort!”

“I can offer some chocolate?”

“OK, I can give you an idea of the kind of things I *may* have put on the paper. No promises they won’t have edited, though. And my memory of the whole episode is a bit hazy.”

“Good enough for me.”

### 1. Nasty integration

“You know what?” said the student, “I was kind of expecting that anyway.”

The Mathematical Ninja permitted himself a smile. “Of course. I would be on the lookout for things like $\int 5^x dx$ and $\int \cos(3x)\cos(5x) dx$.”

“The first one is…” the student screwed up his eyes. “$\frac{5^x }{\ln(5)}$?”

“Plus a constant,” said the Mathematical Ninja.

“The other, you use the multiple-angle formulas from C3, the ones you only ever see in Solomon papers.”

The Mathematical Ninja nodded.

### 2. Parametric integration

“On the same topic, I might have slipped in a cheeky find-the-area or find-the-volume question for the parametric question.”

“But that’s easy, you just replace the $dx$ with $\frac{dx}{dt} dt$ as if it’s a substitution!”

“Shh, don’t give away all my secrets!”

### 3. A bastard of a binomial

“I reckon you wouldn’t have given up the chance to do something like $(4 - \frac{x}{2})^{\frac{-7}{2}}$ in the binomial question,” ventured the student.

“You might think that,” said the Ninja. “I couldn’t possibly comment.”

“But again, that’s less difficult than it looks, if I work out the $n$ malarkey separately then fold the numbers in, I might even get some of the signs right!”

### 4. Partial fractions

“See, I don’t really *remember* what I put in there. There might have been an evil partial fractions one, there might not.”

“What do you mean by evil?”

“Well, one with either a bracket squared…”

“… Where you do $A$ over the bracket on its own and $B$ over the bracket squared…”

“… or one with something like $x^2 + 4$ on the bottom…”

“… Where the top needs to be $Ax + B$ instead of just a letter.”

“Maybe it wasn’t so evil.”

### 5. Differential equation

“Again, I can’t be certain, but I’d be surprised if I hadn’t put in a differential equation one that involved a lot of reading.”

“Does it involve marathon runners?”

“Can’t promise. You can decrease the probability of it involving marathon runners if you donate to Colin’s marathon attempt, though. Can’t say fairer than that.”

“Indeed you can’t,” said the student. “Indeed you can’t.”

*Disclaimer: The Mathematical Ninja is not affiliated with EdExcel; he does not embroil himself in fiascos. He has no more knowledge about the content of Tuesday’s paper than you or I.*