A level H2 maths question spotting thoughts for AY2014

Yes this year's H2 Maths papers will be happening slightly earlier than usual, on two consecutive days 6 and 7 November 2014. Not that it would make any meaningful difference, because you the conscientious student (okay I am presuming that's the case) by now should be close to a hundred percent ready to do battle, otherwise ......... I don't really have to spell it out here do I?

Before I begin things proper, allow me to draw your attention to the ever so excessively cherished and erroneously worshipped mathematical formula booklet issued during every instance of a major assessment of one's junior college life - the MF15. It is neither your good friend nor trusted sidekick. It is only there to serve as an affirmation of sorts regarding recollection of things if your over tensed-up state of mind somewhat loses grip on some details of a particular math expression. It is not there to hold your hand every single step of the way.

Yet too many a time I have seen ineffective individuals desperately turning pages of the MF15 the minute he/she encounters an unfriendly looking trigonometry question. Or an intimidating integral screaming to be evaluated. Salvation, you say? More like utter confusion as eyes scan lines and lines of printed formulas. Confused as to whether to use a double angle manipulation, or the factor formulae. Or a common trigonometric identity. Or whatever. In the end, time slips by unforgivingly, and he/she is probably nowhere or perhaps just a wee bit somewhere closer to solving the problem. Sounds familiar? Are you one of these people described? Why can't you expend some effort to store all core formulas within your grey matter to avoid having to endure this agony time and again? It is not fatal to do a spot of memorization work, you have my assurance.

Okie dokes, let's now head over to the highlights of my (definitely not quite accurate) forecasts regarding what might possibly happen in this year's edition of the H2 A level Maths examination.

Applications of Differentiation

Call it a hunch if you so desire, aside from the rather commonplace parametric differentiation to obtain dy/dx, the question might also task a student to develop the underlying Cartesian equation from a set of parametric descriptions. And it isn't all too difficult. For example, if

Also, are you well versed in connected rates of change? I never fail to train my students to crack the following template problem (see immediate below) at top speed, do give it a try if you haven't chanced upon it thus far:

Applications of Integration

If you can perform parametric differentiation properly, please ensure you can do the same for parametric integration, which typically arises in area-under-curve and volumes of solids of revolution problems. A quick refresher:

Complex Numbers

Reconciling vectors with complex numbers? Yes it can happen, though I pray it doesn't, because it will almost certainly pummel the confidence of many. I for one have been thoroughly exhausted trying to explain to my charges the geometrical (and vector) implications of a polygon with none of its vertices being hinged at the origin when produced in an Argand digram, but somehow majority of them refuse to accept that the concept of vector addition/subtraction can be deployed in the topic of complex numbers. In their minds, vectors are vectors, while complex numbers are, well, just complex numbers. It is a "crime" to mix them both.

I have written a short piece detailing the process of computing various vertices of the above polygon-you can access it here. (see no.15 under supplements on the page)

Statistics

I have said it before: many embrace this section more than Pure Mathematics, and it isn't hard to see why. The GC (Graphic Calculator) does almost all the heavy lifting here, so the most likely reason behind you sinking (hopefully it doesn't happen though) is because you were less than meticulous in keying in the various commands. That said, I have noticed some struggling with using table constructs on the GC to capture the mode of a Binomial or Poisson distribution, so make sure you are adequately skilled in that department.

Oh, and consider an approximate distribution ONLY when the question explicitly requires you to do so. Discrete distributions (such as Binomial and Poisson) when approximated to that of continuous ones (such as the Normal distribution) require continuity correction, whilst that of a Non-normal to a Normal distribution via Central Limit Theorem (CLT) needs NO such modifications. Even at the present moment, I still see a small handful who absentmindedly pen in an unnecessary +/- 0.5 adjustment during the course of invoking CLT.

Lastly, as a friendly reminder, you don't want to be penalized over various definitions, so make sure you can provide a coherent explanation of the level of significance within a hypothesis testing story context, or what a p-value rendered by the GC truly means. Because however small the amount of marks being lost (unwittingly if you wish to argue), it could see you sliding from an A to a B grade.

I still have a couple more predictions floating in my head, that said this is as much as I can offer in a single post. Next stop: a very long, long holiday break. But before that, make sure you remain all sharp and alert for the most important set of written examinations of your 18 years of existence on planet Earth.

Good luck kids. Peace.

### Exclusive Interview With The Founder of Open Curriculum

Exclusive Interview With The Founder of Open Curriculum

THIS INTERVIEW WAS FIRST PUBLISHED ON WHITE GROUP MATHEMATICS ON 5 OCTOBER 2014

I first came to learn of Open Curriculum which curates and collates CCSS aligned K-12 lesson materials from all over the internet into a single giant learning depository), when its founder Mr Varun Arora e-mailed me a while ago for a sneak preview of his creation. As a non-profit entity without the receipt of any significant measure of help from others, Open Curriculum's efforts look rather impressive considering it has aggregated almost 5000+ pieces of learning materials till date (mostly Mathematics related though at the current moment) in a relatively short period of time. In our correspondences, I suggested conducting an interview with him as to bring about greater public awareness about his portal, to which he readily agreed. And so here we are.

Hi Varun, it's really nice to have you today for this dialogue session. How and what inspired you to come up with this idea of setting up Open Curriculum? Is it turning out the way you envisioned it to be?

Nice to be here for this! I don't know if was one moment or idea that inspired me to do OpenCurriculum. It was a large number of things that accumulated over time to caring about the larger problem. Obviously influenced by my experiences with poverty, education, and building technologies early in my life - all things I most care about. I think I started working on about a year after I first conceived its barebones.

Its definitely not turning out to be how I envisioned it to be! I was a little further from reality at the point of envisioning it. Its a lot more modest today, I guess. Its not a bad thing - its very much grounded now.

Any notable difficulties encountered along the way whilst prepping the beta version of Open Curriculum for release?

Far too many to count! I can tell you this though: technology was not one of them. I think our biggest challenges even today, as is true of the time before releasing the beta, are understanding what the teacher community wants. Its a hard hard problem, as they often don't know the answer to that themselves, and the market is highly segmented.

Are you running Open Curriculum full time all by yourself? Or do you also hold down a job elsewhere?

It's my full-time job :) I don't earn a living out of it, but I get by with support of generous people. Joshua Siktar works part-time on some authentic content and community, but the product is all me.

I cannot imagine doing this AND having another job! that would drive me completely nuts haha. Its important to realize that the content library on the website, which mostly people see, is actually only the tip of the large iceberg that OC is and is only a very recent development. The majority of the iceberg is exposed to a much smaller audience - but where the bulk of complexity lies.

Interestingly, while you emphasized on your website you are pretty much a non-profit establishment, I see a whole collection of investors prominently cited on the ABOUT page of yours. How should audiences react, since they might be inclined to think you are receiving considerable financial backing possibly in exchange for revenue sharing?

Ha - that can be a little misleading, I guess. Okay, so there is no revenue sharing. The investments are all structured as donations. And haha, even though they are so pretty prominent top tier names, these donations are fractions of the size true "investments" they make in traditional for-profits. We barely scrape by.

How exactly does Open Curriculum plan to sustain itself financially in the long run?

Marketplace. marketplace. marketplace. We want to be what the appstore did for apps. YouTube did for videos. Amazon did for books. We want to be the fundamental backbone / infrastructure / distribution channel on which all curriculum is discovered, bought and sold. We'd take % commission on sales.

That said, there is no plan in immediate future to turn on the revenue engine. Right now the sole focus is growing demand.

There are already numerous other vendors running Massive Open Online Courses (MOOCs) on the world wide web, Coursera and Udacity amongst them. What sets Open Curriculum apart from these course providers?

That we are not a MOOC website?! One doesn't come to OpenCurriculum and learn anything haha. We strictly cater only to teachers and curriculum people - students are not quite welcome yet.

As far as I observe, OpenCurriculum gathers and harvests lesson materials from reputable sources such as Khan Academy and the MARS Initiative. Do you also create your own original content to share with learners?

Not yet. We tried it, but it doesn't reap the benefits that organizing existing great curriculum does. You see, you've got to be large enough like Netflix before you start making 'House of Cards'. We are laying the foundations of what will be the most powerful distribution channel in the years to come, and becoming a producer of content might hurt our focus.

At the moment, only the Mathematics section is directly accessible by the public. According to the announcement on your homepage, the English section is still under lock and key, made only available to those who have received invites. Why the secrecy? When do you plan to officially share it with the world?

Well English is much harder than math, and we are building it out slowly and steadily (a lot more minds on it than we put in on math). Its not as universal as math. And putting out something garbage (at least something below our bar for high quality) lowers our users' trust in our product. Quality is way more important than quantity or immediate access of materials for our users. So it takes a while until we can meet our own expectations.

We don't have an official date for English planned yet - because the more we dive into it - the more complex it gets. I hope we can release it within the next two months :) Fingers crossed!

Open Curriculum is getting bigger and better with time, undeniably. Do you have any concrete plans to further develop the site in the foreseeable future, such as implementing new learning features and themes ?

Oh there is so much magical stuff going on under the hood - I can't wait till we bring those things out to the public one day! In our obsession to only release very intuitive and thoroughly tested and privately used things, we end up seeming slow. But beautiful and usable product experiences only emerge as a result of orientation to detail and thoughtful iteration.

It's been most delightful talking to you and gaining valuable insights about your pet project. Thanks once again for agreeing to this interview, and may Open Curriculum blossom into the next big thing on the internet. God bless.

Thank you - its been an honor!