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.
I'm in a similar boat — full-time job, studying in whatever gaps I could find. Honestly the biggest thing for me was just being consistent with short sessions rather than cramming. I'd do 30-45 minutes on my lunch break and maybe another 20 at night before bed. It wasn't glamorous but it added up. The trig identities caught me off guard because I hadn't touched them since grade 12, so I'd focus there early if you've been out of school for a while.
The practice tests were what actually got me ready. I didn't trust my comfort level until I'd done a few full runs under time pressure. Once I started hitting the scores I needed consistently, I felt a lot calmer going in. You've got this if you keep showing up for it.
Honestly the thing that clicked for me was stopping trying to memorize formulas and actually working through the logic of why limits behave the way they do. I'd been grinding practice problems for weeks and still blanking on the test, but once I slowed down and really understood what a limit is asking, everything else started to fall into place. It wasn't about doing more problems, it was about doing fewer problems but actually thinking them through.
If you're prepping right now, don't skip the trig review even if you think you remember it. I thought I was fine there and I wasn't. That caught me off guard more than anything else on the actual test. Give yourself a week just on trig identities and unit circle stuff and you'll feel way more confident walking in.
I actually failed my first attempt, which was embarrassing but also kind of a wake-up call. I'd been doing broad review — a little bit of everything — and honestly I wasn't focused enough on the areas where the test actually hammers you. Second time around I spent most of my prep on utma/questions/functions and graphing because that's where I kept losing points, and it made a huge difference. Once I understood how those concepts connected to the rest of the material it just clicked.
The other thing I changed was timing. First attempt I ran out of time on the back half because I didn't practice under any pressure. Second time I timed every practice session and forced myself to move on if I got stuck. If you've already failed once, don't panic — you probably know more than you think, you just need to find the gaps and actually close them before you go back in.
I was in almost the exact same boat. Working full-time means you can't just marathon-study on weeknights, so I broke it into 30-minute chunks during my lunch break and maybe another 30 before bed. It's not glamorous but it adds up. The trig identities caught me off guard because I genuinely hadn't touched them in years, and that took up a solid week of review on its own.
Honestly the hardest part was staying consistent when work got busy. Some weeks I only got three sessions in instead of five, and I had to be okay with that. If you're short on time, prioritize functions and limits over the algebra stuff since you'll likely remember more of that than you think. Just keep showing up and you'll get there.