The UTMA is the placement test UofT uses to determine whether incoming students are ready for calculus, and it covers a lot more ground than I remembered from high school. I graduated 3 years ago and needed a serious refresher. Spent about 6 weeks preparing, starting at 1 hour a day and increasing to about 2 hours in the final 2 weeks.
Functions and transformations were probably the biggest section — I'd estimate around 30% of the questions touched on function notation, domain and range, composition, and inverse functions. If you're rusty on transformations of parent functions, the questions test those at a conceptual level, not just computation, so formula recall alone won't be enough.
Trigonometry was harder than I expected. Not just SOH-CAH-TOA but unit circle fluency, trig identities, and solving equations with trig functions. I spent about 8 hours specifically on trig because I'd let most of it fade. The unit circle needs to be automatic — you can't afford to derive it during a timed assessment.
Logarithms and exponentials showed up more than I expected, mostly in the form of solving equations and applying log properties. The change of base formula and product/quotient/power rules appeared probably 4–5 times in different forms. Scored well enough to place into MAT137, which was my target. The test felt fair but unforgiving if you have gaps in foundational material.
Unit circle fluency is non-negotiable. I tried to wing it on my first attempt and it slowed me down badly on trig. Two dedicated weeks on the unit circle after that and everything else became significantly faster.
6 weeks is a solid prep window for someone who's been out of school a few years. I came in with only 3 weeks of prep and placed lower than I wanted — had to take a bridging course before MAT137. Give yourself the full time if you can.
Did you find the algebra section straightforward or were there harder factoring and rational expression questions mixed in? I'm writing the UTMA in about 3 weeks and trying to figure out where to focus my remaining time.
Function transformation questions are where I see most people lose time. It's not that the concepts are hard — it's that without practice you end up second-guessing yourself and the time pressure makes it worse.