It seems to me that the most common reason students give for not taking “advanced” math classes (when they have a choice) is that they’ll never have to use it in the “real world.” I had to use a lot of math in my former careers in computer science and electrical engineering, but there are plenty of other examples out there.
Where have you had to use real math in everyday life?
I will start with an example. I used to have a gas tank when I had my ranch. It was a cylinder on its side, 6 feet long and 3 feet in diameter. When I sold the tank it had diesel fuel in it, and I obviously wanted to charge for the fuel, too. There was a hole on the top where I could insert a stick and see that there was 14 inches of fuel. How many gallons was that?
Heh. I think I would’ve figured out its maximum capacity, figured that 14" is between 1/3 and 1/2 of 36", and figured that given how cylinders work, I’d charge the buyer for gas equal to somewhere around 1/4 of the total capacity. Figuring it out more accurately would be beyond my powers, but I’d also figure it’d be beyond the powers of the buyer, and if it wasn’t and they could explain their answer, I’d accept it.
Or I’d go here and then here to get an approximate answer of 114 gallons. Is that close enough? (If so, I believe I would’ve ripped myself off–it looks like, full, the volume would be 317 gallons, and by charging them for 1/4 of the capacity, I’d give about 37 gallons away for free.
It’s extremely rare for me to use any math above elementary school math, unless you count spreadsheet design as math.
A whole host of other examples. People that say they don’t use math in their everyday lives are ridiculous.
I see someone else listens to Car Talk. 
OP asks whether you have ever used “advanced” math, decried by the youth as useless, not any math, ever. None of this is “advanced” math as per the OP. Mostly simple arithmatic. Furthermore instant calculators are avilable for things like exchange rates and compounded interest. I have my doubts anyone actually sat down with pen and paper to figure these things. And if they did, they are silly.
One time (I was actually still in high school) I did use the Law of Sines to calculate the angles needed to be cut on two boards to bring them together in a mitered join less than 90 degrees.
The shop teacher didn’t believe me, but when we did it his way, by overlapping the boards, drawing lines, and lining them up with the angled table saw, the answer came out the same. I was the talk of the entire school for an hour or two (did you hear? Hello Again applied the law of sines! What, really!? etc. Helps to go to high school with 2,000 nerds). I would point out that there was a practical way of solving the problem that didn’t involve any math. So it was not “needed,” strictly speaking.
Other than that, never. My major careers have been as a copywriter and an attorney.
When I was a kid, I asked my dad how much water our backyard above-ground pool held. He challenged me to figure it out myself. So I did.
10,300 gallons.
I was a math major, my roommate was an art major who would “never need math.” But, he took an algebra class anyway.
At one of his first jobs, some kind of large scale photo reproduction, he had to adjust the big device by hand using a trial and error method, to get things laid out correctly. He figured out that a simple equation would tell him the settings he needed, without the trial and error, worked out the equation and used it every day. To the other employees who still used the old method, it was like magic, or maybe voodoo. Anway, I was so proud. He not only figured out that math would solve such a problem, he actually solved it himself and understood how to use the solution in a practical manner. I don’t think he ever convinced the other employees to try this radical new method.
By “advanced” math, I mean what you learn when you go past the required basics. It would include trig, functions, complex algebra, probability, statistical analysis, integrals, differentials…
Another example: I used to teach a woodworking class. One of our projects was a hexagonal clock. The students had to start with the height they wanted, and then calculate what size board they’d need to buy and what angles to use on the saw for the cuts. That seems like pretty basic middle-school math to me, but only one of the kids figured it out on her own.
Frankly, most of the math I do in managing my business seems like every 8th-grader in the country should be able to do it, but it’s beyond most of the adults. Just problems like: On average, I sell one a month of a certain item. Over the course of a year, do I get a better return on investment buying one at a time at a 40% discount or five at a time at a 45% discount? Then factor in the odds that I’ll be out of stock and miss a sale if it takes three days to restock and I only have one on the shelf. Is it worth keeping two instead of one even if the discount is the same?
I didn’t remember the total capacity of the tank, so I had to calculate the area of the portion of the cross-sectional circle that lies below the chord line, multiply by 6 feet to get volume, and then convert to gallons.
Actually, I’ve heard of Car Talk (it’s a radio program, right?), but I’ve never listened to it. Did they discuss a similar problem?
Yup. Every week they have a puzzler that’s only tangentially related to cars, if at all. They had this a few months ago, and generated a lot of interest and creative solutions (none of which were correct). Lots of near-misses - but you really do need to use higher math to solve.
That guy has way too much time on his hands.
And multiplying a whole number by a single digit decimal for a dinner party, and converting between currencies (simple fractions) is not advanced math, or even-non basic math, or even above what a 5th grader knows — even if you needed to do it by hand, which you don’t. That’s all I was saying, it was in regards to Omar Little’s list, which I found non-responsive to the OP.
Most recently?
-Knowing that the new HDTVs are in the 16:9 format but are sold giving the diagonal measurement as the screen size I was able to calculate aproximate heights and widths of various sets so I could tell my parents what would fit inside their cabinet and if a 4:3 picture on a new 32" LCD would be bigger or smaller than on their old 27" CRT.
-Used a lot of formulas to figure out how many 4x8 vs. 4x10 sheets of drywall I needed to finish off our back room.
Take it to the pit, if you’ve got such a hard-on for me. 
Um, what? I don’t have a hard on for you. Those just aren’t examples of advanced math that involves “trig, functions, complex algebra, probability, statistical analysis, integrals, differentials…”.
Why didn’t you just look it up, or look at the packaging if in-store? Without accounting for the bezel and stand, you could be off by a lot.
I used math this morning to take a table of demographic data points and plot the probability of this thread’s title putting a Neil Young tune into the head of any given member of a set of more-or-less random individuals.
I really enjoy taking jewelry (fabrication) classes. Every so often I want to design a piece, and then my knowledge of geometry is useful. Once I even did a construction with compass and straightedge! I believe (it was a while ago) it was because I needed a perpendicular bisector and didn’t have a ruler or right angle around.
Not advanced math, but I once took a wax casting class where you had to multiply the weight of the wax by the relative densities of silver-to-wax to find the weight of silver you need to use. The relative density of silver to wax turns out to be around 10. …You would not believe the number of people in that class who had problems with that, and were all “Oh no, math!! I can’t do that!” Or maybe you would.
ETA: Larry Mudd’s post reminds me that almost every day, when I read the news, my rudimentary knowledge of statistics comes in handy (usually to raise my skepticism as to the article’s claims).
The Street-Fighting Mathematics book/course is for ‘educated guessing’. It seems to be very good, although I have not read it yet.
One of my most triumphant instances of mundane math is when I calculated the number of coffee beans in a container for a contest. I got it to within two dozen out of a few thousand beans.
Edit: For somewhat advanced math, I think I’ve used mental calculus to estimate volumes. And, of course, basic probability and statistics.
I guess I use functions in nursing, although I don’t think of them that way.
If a drug is prescribed as 0.2 milligrams per kilogram per hour, it’s delivered by pharmacy in a 500mL bag with 100mg of drug in it and I’ve got drip tubing that breaks 1mL of fluid into 10 drops, I need to figure out how many drops per minute the 83 pound patient should get. So that’s functions, right? But I’d set it up with Dimensional Analysis:
gtt(drops) 10gtt 500 mL 0.2mg 1 kg 83 lbs 1 hour
__________ = ______ X ____ X _____ X______ X _____ X ______ = 6.29= 6 gtt/min
minute 1 mL 100 mg kg/hr 2.2 lbs patient 60 minutes
So I set up my tubing and med and make sure that I’m giving only 1 drop every 10 seconds.
It can get even more complicated, especially in pediatrics, where a patient must get a set amount - no more, no less - of fluid every hour. In that case, I have to figure out how many mLs of medicine they’re getting and subtract that from their maintenance fluid and reset it accordingly, too.
Even if I’m not working with a gravity drip, I’ve got to set the pump for the right number of milliliters per hour. More annoyingly, even if the drug is given over 20 minutes, I’ve got to figure out how much would be given over an hour, because pumps are only programed in hours, not minutes. Seems silly and error prone to me - there’s no reason the pump couldn’t be made to program it to deliver, say, 30mL over 20 minutes, but no, you’ve got to program it for 90mL over 1 hour and then tell it there’s only 30mL to deliver. Again, I think that’s a very simple “function”.
That’s about as advanced as it gets. Nothing you couldn’t do with high school algebra.