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For the same reason that calculus is required for many Bachelors degrees; it's a course in symbolic logic.
If they wanted a course in symbolic logic, it can be found without having to teach stuff that nobody will use. Very few bachelor's degrees require calculus... only degrees in the mathematics, engineering, technology and science disciplines.
Given the roots 2+-3i, determine the quadratic equation. From this, determine the constants on comparing with the characteristic form of a quadratic equation. Additionally, find the global maxima or minima of this function.
This should be done in 10 minutes without a formula sheet if you have learned algebra & basic calculus well. It was the easiest question in my 12th grade final exam (I studied high school in India, where math exams are ridiculously hard).
Other "fun questions" (according to my teacher) from that exam:
Determine the area bound between sin (2x) and cos(x) in the interval [0 pi]
Find the points of inflection for e^(5*sin(x)) and comment upon the concavity and convexity of this function.
Find the maximum dimensions and area of a rectangle possible inside a unit circle.
Derive the formula for volume of a cone from a line using integration.
Water is pumped into a spherical tank having a 4.5 m radius. The flow rate is 1.2 gpm and increases by 0.25 gpm every second for 1 minute. How much of the tank is filled in 45 seconds.
and 10 other questions of similar difficulty level .
The average on this exam was a 48. I, by gods grace got a 74 after studying for 2 sleepless nights. I thought I failed. WHOO !!!! .
Last edited by Adi from the Brunswicks; 12-30-2013 at 01:43 PM..
One is the one about only having 20 dollars and gasoline costing $3.50 per gallon. How many gallons will $20 buy? Of course, the unknown is how many gallons, but, it's so easy to know the unknown, it's pointless to write an equation including an x. It's trying to make it more complicated than necessary.
It does not make it any more complicated. I would argue that it makes the equation much simpler as "x" can be anything and, therefore, simplifies the equation. "x" is simply a variable term. Whether it be gallons of gasoline, pounds of cheese, bushels of grain, hours of labor, etc., "x" is what represents the quantity (in this case) that you are solving for. You even said it yourself: "Of course, the unknown is how many gallons." The "unknown" in this case is "how many gallons" or, quite simply, the term "x."
Any functioning human being "solves for x" nearly every day of their lives.
If they wanted a course in symbolic logic, it can be found without having to teach stuff that nobody will use. Very few bachelor's degrees require calculus... only degrees in the mathematics, engineering, technology and science disciplines.
BofS in marketing and finite math with a heavy dose of calculus was required.
I laugh when my 8th graders question when we will use algebra. I tell them that question might be relevant in trig, or in parts of geometry, but they have brought a knife to a nuclear fight asking that in algebra.
THE ENTIRE ECONOMIC ENGINE RUNS ON y = mx + b. Every business in the universe. b is your start up cost, m is how much you are selling your product for, and x is the number you sell.
If mx + b does not get positive, pretty soon, you are out of business.
THIS SIMPLE ALGEBRAIC equation is the basis for EVERYTHING commercial. Maybe the WALMART greeter does not need to know that, but the paperboy does. As does the guy that cuts the grass.
I don't want to hurt anyone's feelings, but if you don't recognize this basic use of algebra, you are in the lower tier. Don't fret too much, you have lots of company!
A great many of you guys had problems in math, algebra in particular due to frontal lobe development issues. Frontal lobe development has NOTHING to do with intelligence or ability, but it does provide one the ability to think abstractly, and to reason farther along the decision matrix.
Too much math is taught too soon for many. Those that don't get an abstract concept in math, say in the 8th grade probably wont, no matter how many times they are taught, until , the development of the frontal lobe reaches a point where their ability for abstract thought is developed.
I teach 8th graders and we generally work on slope after Christmas, that is the rise over run, or how fast the y value is changing in respect to the x value. This leads to rate of change, which is what slope is all about. Rate of change!
I have only done this for 12 years, many would not acknowledge my expertise. Having said that, with few, and I mean very few exceptions, those that flunk the first slope quiz in Jan, flunk the last one in March.
THey just are not ready to cross the abstract divide. It is sooooo obvious to one that a) has taught and b) has any ability at metacognition. I have so many kids stop me in town, when they are in high school, and the conversation almost always gets around to, "oh yeah, I finally get algebra...it really isn't that hard." Yep, their frontal lobe finally developed.
It does not make it any more complicated. I would argue that it makes the equation much simpler as "x" can be anything and, therefore, simplifies the equation. "x" is simply a variable term. Whether it be gallons of gasoline, pounds of cheese, bushels of grain, hours of labor, etc., "x" is what represents the quantity (in this case) that you are solving for. You even said it yourself: "Of course, the unknown is how many gallons." The "unknown" in this case is "how many gallons" or, quite simply, the term "x."
Any functioning human being "solves for x" nearly every day of their lives.
Feel free to say whatever you wish to say. I say it makes it appear to be more complicated and mysterious. That's what I say. Making a post about how simple it is just to call the unknown x does not suddenly part the Red Sea creating an epiphany in my mind. At this stage of my functioning human being life, it goes into my very active file 13.......
You have to solve for X all the time, whether you consider your real-life computations "algebra" or not. However, as a math tutor, I don't understand why people need to know "college algebra". For example, who cares if you can factor or solve quadratic equations? I've known since 7th grade that x = -b +/- the square root of (b squared - 4ac) all divided by 2a, but in over 20 years I have never once encountered a practical real-world application of that. I cannot support teaching people things just to teach them things. Make it practical and kids will want to learn. Throw useless stuff at them and they'll check out.
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