<p>I’m taking an algebra class, and I’m doing fine in it (98%). Everything seems to be super easy. I practice a lot, though, and I was wondering what type of problems I should focus my practice on. Obviously, I’ll do some of both, but which deserves more attention; the applied problems or the given statements? I’ll give some examples so that you’ll see what I mean:</p>
<p>Let’s say I’m studying Systems of Linear Equations;</p>
<p>Should I practice more given math problems like the following:</p>
<p>Ax + By + Cz = D
Ex + Fy - Gz = H
Jx - Ky + Lz = M</p>
<p>Where the capital letters are applicable constants and the lower case letters are variables that you must figure out through one of the various methods.</p>
<p>OR</p>
<p>Should I spend more time on solving applied problems like:</p>
<p>A small isolated farm uses a windmill and a gas generator for power. During a 10 day period, they produced 3010kW h of power, with the windmill operating at 45% capacity and the generator operating at capacity. During the following 10 day period, they produced 2900 kW h with the windmill operating at 72% capacity and the generator down for 60 h for repairs (operating at capacity otherwise). What is the capacity (in kW) of each?</p>
<p>Thanks.</p>
<p>*Asking to see which will help more in the future courses studying engineering.</p>
<p>Practice the first until you can do it in your sleep (shows what a boring person you are - just kidding). The latter is much more applicable in the real world - being able to interpret problems into a form that you can solve.</p>
<p>A lot of math competitions are taking what they give you, and figuring out what you can do with it. Solving for the sake of solving, until you find a variable that you can use to solve for the answer they want.</p>
<p>Solve this questions:</p>
<p>The airport is 10 miles away. You have to average 60 mph in order to get there in time. For the first 5 miles, you averaged 30 mph. What do you have to average for the next 5 miles in order to get there in time?</p>
<p>Yes, practice the first until you know like the back of your hand.</p>
<p>Now here is the thing about learning higher math…you learn newer techniques that build on earlier techniques.</p>
<p>To be honest, I have forgotten how to use algebra for the first problem. All I see is linear algebra and putting that left side in echelon form and solving. :-)</p>
<p>Well, I would first figure out how much time you had to get there.</p>
<p>10miles/60mph = 1/6 h = 10 minutes to get there in time.</p>
<p>First 5 miles, you drive 30mph. 5miles/30mph = 1/6 h = 10 minutes spent driving for the first 5 miles. You just wasted the entire 10 minutes driving slow, so I guess you’ll have to park and watch the plane fly over you.</p>
<p>I guess in a competition I would lose because I didn’t take note right off the bat that 10/60 and 5/30 were equivalent.</p>
<p>Some occasions I can’t figure out how to solve the ones in my book, but my class is online, and my teacher is an *** so I guess I’m on my own. I typically figure it out eventually. Practice makes perfect, I suppose.</p>
<p>I do pretty well at learning how to solve the equations. Usually after one problem I’ve got it. I’ll do maybe 30 more after that to engrave it and then I’ll try to pull an equation from those applied word problems and do at least 20 if not thirty of those. That’s for each section, while there are typically 6 sections per chapter,</p>
<p>Is solving linear equations using 3x3 determinants algebra or linear algebra?</p>
<p>Just wondering, because that’s what I’m doing right now in my algebra class. I usually watch a few Khan videos before doing practice problems, and these problems were grouped under the “Linear Algebra” section on Khan instead of “Algebra”.</p>
<p>**Nevermind. I just checked blackboard and he said we are supposed to skip the sections involving 2x2 and 3x3 determinants. I wasted hours of my day learning and practicing this stuff over and over again. Lol. I guess I should read the instructions more carefully next time.</p>
<p>It’s used in both. Depends on what other aspects of it you’re considering.</p>