Vivian Moate Mathematics Tutoring

For AI HL and SL, a bare minimum outline of the key things you need to know about the main hypothesis tests. Generally, the idea is that the tests give you a value (chi-squared or t-value) where the higher it is, the less likely your null hypothesis is true. Unfortunately, most of the time we use the p-values and the significance levels, so LEARN the inequalities for how to draw conclusions!

You also need to know where to put the data/statistics in and where to find the tests on your GDC, and watch out for how to phrase the hypotheses and your conclusions - this is a good one to read the Mark Schemes carefully to see what phrases the examiners need to see to award the final marks. When practicing, make sure to find a few questions on using the Goodness of Fit test on Normal or Binomial Distributions, as well as practice all 4 types of t-tests.

HL students, you'll also need to know things like the z-test (and when to use z or t-tests), Type I and Type II errors, critical regions, and generally making hypotheses for tests you've not seen before and drawing the right conclusions based on the values given. Let me know if you'd like a summary sheet on these!

I've had a few requests for a summary sheet about the different forms of Quadratics, so here's the basic information about the three and how to change between them. You'll probably want to add examples or more information as you revise!

On the most part, unless the question says "write in the form of a(x-p)(x-q)" or "write in the form of a(x-h)^2+k", you stick with the form you're given and work with that as all three forms will give you the roots and vertex.

Rational functions - how to find the key points and sketch (all courses), including a shortcut that you should only use for straight forward questions. Watch out for questions where you get the graph and you have to work backwards for the values in the equation - you can use the same methods shown here, just backwards.

AA HL: for oblique asymptotes (when the power in the numerator is higher than the denominator), use polynomial division to rewrite the function as y = Ax+B + {fraction with no x in numerator}, and then the oblique asymptote is Ax+B

AI HL: for logistical models, the numerator L gives you the asymptote y=L and remember it's known as the "carrying capacity" (aka limit of the growth being modeled)

It's the summer holidays! Everyone is now released from the weekly slots, but remember this means your usual time is not reserved for you for September.
You've all worked super hard and deserve a nice break, but please don't stop working over the summer on your IAs and general practice/revision. Email me sooner rather than later if you need to see me (>24 hours notice), I'll be available all summer except the week of July 3 to 10.

Availability for a typical week (email me to check):
Mondays: mornings before 12:30, evenings after 5:30
Tuesdays: evenings after 5:30
Wednesdays: all day
Friday: mornings before 12:30

The IA ideas with the most potential come from the oddest places - if this (not quite a cylinder) bucket has holes at the bottom and the toddler is scooping water with the (kinda hemisphere) spade, how fast does she need to scoop water to fill the bucket? Bit of geometry to demonstrate ownership of the problem, bit of calculus (rate of water in and out) for additional math methods, maybe a bit of related rates for the HL students, and results you can really talk about (no, you cannot borrow the toddler to scoop water to test your answer).

Something everyone forgets is that you can always find d by subtracting any two consecutive (one after the other) terms and r by dividing any two consecutive terms!

Sequences and series is a topic that is almost guaranteed (as much as you can guarantee anything on an IB paper) to come up on your exams, but the questions could be anything from really straightforward to super tricky so be clear on the facts and how you can use the formulae (good advice for just about the whole course!).

A lot of teachers ask students to choose two different methods/topics from class to use in their IAs, but that's not always necessary. You can choose just one that's then applied and understood really well, or you can choose two that have nothing to do with each other and you'll be struggling to use either.

Some teachers suggest their students find a topic that's not on the syllabus (and often beyond the course), like famous math problems or complicated algebraic methods, which could turn into an excellent exploration with a lot of work, or (more often) sound a bit like you're quoting from websites Maths Is Fun or Statistics For Dummies.

This example would be more an AI HL exploration, though AA SL or HL could address a similar aim of finding a model but doing so using algebra rather than regression.

Choosing your research question for your IA is possibly the hardest part of the whole coursework! There is also nothing wrong with finalizing your aim AFTER you've started doing some calculations to see what the situation is. These examples are more an AI exploration than AA (more statistics than algebra), but the marking criteria is the same for both.

If you choose something vague, then you'll be working hard through the whole exploration to get further than the bottom of all 5 criteria, as your work won't have purpose or direction.

If you choose something simple but with purpose, then your math will probably easily address your aim, but you don't give yourself much room to show independent thinking (vital for C and E).

If you choose something meaningful with a specific question to answer, then you will be able to explain what math you choose to use, what the results mean, and then take those results to go onto further exploration (e.g. finding that the linear regression correlation coefficient is low so therefore doing a logarithmic regression, or trying a polynomial and an exponential model and comparing the two using a Chi Square goodness of fit).

I'm back! Between exam revision, Covid, and marking, I'm afraid this page has been neglected for a while. But hopefully the revision sheets already here have been useful and keep an eye out for more coming soon (open to requests if there's a topic you need) - including some info sheets about the IA!

Happy Easter holidays! All students are released from your usual weekly slots, so email me sooner rather than later if you'd like to keep your normal time and/or book a different time.

Remember it's important to have a break over the holidays, but it's also a good time to get ahead on anything time consuming, like revision notes for the next exams or IA prep.

Now you'll know why if I use psi in every example from now on.

Greek Letters

If you ever see someone using a capital xi in an equation, just observe them quietly to learn as much as you can before they return to their home planet.

Term time schedule: green means available, red means unavailable - but even if the time you prefer looks unavailable, email me anyways and I'll see what I can do!