Me, Myself & Mathematics..

[Gheld]

Yeah, if your teacher every asks you to show your work and actually grades on it, you're pretty fucked if you just use trial and error.

OP says its for a highschool equivalence, so chances are it will be a standardized multiple-choice stencil graded test, just as simple as the example questions.

[procne]

Am I the only who feels that this math test is not about logical thinking and understanding mathemathics principles, but about putting in random numbers and seeing what comes out?

[tlo]

Hi there.
I've been emo about my worksituation for awhile and yesterday i got a protip from a dude on these forums. He said, "Try to do högskoleprovet" It's like a GED but for swedish people. So i was browsing the "GED" website trying to find some more information about the tests. I found the old tests from 2011 and decided i was gonna try to do it! I read through the testpapers/webpages and was like " Yeeee i can do this!" but soon realised im way to fucking stupid to concieve this type of mathematics.

Stubborn as hell i refused to give up eventhough im in way over my head, i decided to cheat. Pulled out the computers calculator and still,not in a million years could i calculate these numbers, not even with a calculator! Now sitting there bashing random calculator signs i've never seen before hoping i will randomly calculate the numbers.... i eventually realised i need help!

I did 1 year in High school and math was actually something i was good at. But the gap from Highschool math year 1 and University math year 1 is lightyears apart! I will list acouple equations for you to solve and then you can point me in the right direction which kind of mathbook i should pick up and study in !

" Assume that y = x(1+x) where x is a positive integer. Which of the following alternatives is a possible value of Y
A: 10
B: 16
C: 20
D: 24

Which of the following equations is biggest if X is a negative integer?
A: -2x-1
B: -2x
C: x-2
D: 2x "

I see this as a challange so i'd love to learn, i simply just dont know where to start. I dont even know what this kind of math is called !

.

These problems are basic algebra.

Rearranging the equation from the first question yields y = x + x^2. Here there are multiple approaches you could take. If you're familiar with how to solve quadratic equations (that's around grade 10 math here in Canada) you can plug in each value of y into the equation and then find the roots of the equation (solve for x). Whichever y when plugged into the quadratic equation results in a root (value of x) that is a positive integer is a correct value of Y.

Another, easier method is to just qualitatively look at the problem and realize that there are only a few positive integers that when squared and added to themselves could yield values in the range of the possible solutions. So, try x = 1, then x = 2, then x = 3, then when you try x = 4, (4^2 + 4 = 16 + 4 = 20), you see that c) is the only possible answer.

The second question is basically testing your knowledge of negative numbers in algebra. Three properties of elementary algebra that are worth remembering are that the product of (result of multiplying) two positive numbers will always be a positive number, the product of a positive and negative number will always be a negative number, and the product of two negative numbers will always be a positive number. It isn't difficult to derive these properties from the inequality relation, but that's more of a first-year uni level.

So anyways, back to the question, obviously 2x and x - 2 are negative numbers, and obviously -2x and -2x - 1 are positive numbers (using the properties above). -2x and -2x - 1 are identical except -2x - 1 is one less than -2x, so -2x is the equation that will yield the largest number.

These questions are fairly basic, but the good news is there are loads of online resources for learning about math. (http://www.khanacademy.org/) is a great site with lots of tutorials for basic arithmetic, basic algebra (which is around the level you're at) going all the way up to multi-variable calculus and Laplace transformations.

Good luck, it's never too late to learn!

[v2prwsmb45yhuq3wj23vpjk]

OP says its for a highschool equivalence, so chances are it will be a standardized multiple-choice stencil graded test, just as simple as the example questions.

Holy crap I misread his post, I thought it was for a university course. Oh well, still not a good thing to do to yourself IMO.

[Haros]

Am I the only who feels that this math test is not about logical thinking and understanding mathemathics principles, but about putting in random numbers and seeing what comes out?

Nope, that's what it looks like to me. The question is such that you don't need to prove the answer just have a calculator or some scrap paper. Rest can just be trial and error with very basic knowledge of maths and how to work an equation.

[Deleted]

Am I the only who feels that this math test is not about logical thinking and understanding mathemathics principles, but about putting in random numbers and seeing what comes out?

Well you can figure them out by logical thinking without putting in random numbers too. Especially the second question someone with a bit of experience doing basic math will notice the answer by just looking at it.

But we're talking high school math here, not uni level.

[Gheld]

Am I the only who feels that this math test is not about logical thinking and understanding mathemathics principles, but about putting in random numbers and seeing what comes out?

He posted sample questions from a GED primer off of the internet, to help with possibly taking the local equivalent to a GED. The only way to do the said questions without trial and error would require graphing, which I highly doubt is tested on a GED, which aren't even marked based on work shown, single answer single grade multiple choice like every other government standardized test on the planet.

What I would say is that I would not recommend a highschool equivalence because in most cases it isn't the same thing, both for course requirements and employers don't always treat it the same way as an actual highschool diploma. I would recommend checking out an adult education program to get a full diploma, adult ed diplomas usually only require core subjects (language arts and math) so you only need a few hours a week of class time.

[v2prwsmb45yhuq3wj23vpjk]

He posted sample questions from a GED primer off of the internet, to help with possibly taking the local equivalent to a GED. The only way to do the said questions without trial and error would require graphing, which I highly doubt is tested on a GED, which aren't even marked based on work shown, single answer single grade multiple choice like every other government standardized test on the planet.

What I would say is that I would not recommend a highschool equivalence because in most cases it isn't the same thing, both for course requirements and employers don't always treat it the same way as an actual highschool diploma. I would recommend checking out an adult education program to get a full diploma, adult ed diplomas usually only require core subjects (language arts and math) so you only need a few hours a week of class time.

Both questions are done without graphing or trial and error in this thread.

[Haros]

The only way to do the said questions without trial and error would require graphing

20 = x(1+x)

20 = x^2 +x

x^2 +x -20 = 0

(x-4)(x+5) = 0

x -4 =0

x = 4

4 is a positive integer and 20 is a value shown in the answers. Didn't need a graph.

[mittacc]

I'm not 100% on this but i'm pretty sure, i'm in ninth grade atm so i have some understanding anyway.

Which of the following equations is biggest if X is a negative integer?
A: -2x-1
B: -2x
C: x-2
D: 2x "

i would say B on this one because if you have two negative numbers they change into a positive one -(-)=+.

let's say that x=1 that would mean that the problem is like this -(-2)=4 and no the A answer is not bigger -(-2)-1=3.

hope this helped, i didn't understand the first one, maybe i'm not too good on english yet :P

[Deleted]

Thanks alot guys,I got some insight into algebra and know where to further educate myself <3
Feel free to use this as a math discussion thread if you like, Trial and Error vs equations or w/e xD

[Gheld]

Both questions are done without graphing or trial and error in this thread.

First one is super easy. If you look at the equation, it's broken into factors. x and x+1 are factors of y. Therefore, you factor the answers and see which set of factors fits into the equation.

"Solving every possible choice and picking the one that shows a correct result" is the Semantical evil twin of Trial and Error.

Plus immediate logic of the situation solves the first question without calculating anything. If y=x(x+1) then Y can't equal a perfect square or be +/- 1 of a perfect square, which eliminates 10, 16, and 24, leaving only 20. Probably not the intention of the question, but still a terribad example question because of that.

[Haros]

"Solving every possible choice and picking the one that shows a correct result" is the Semantical evil twin of Trial and Error.

If you know your times tables then it would only take a few seconds longer than what you did using logic and in harder questions lets you check yourself or expand on the problem. Maybe it's not perfect but it is decent for problems like this while still showing how you got there.

[Gheld]

If you know your times tables then it would only take a few seconds longer than what you did using logic and in harder questions lets you check yourself or expand on the problem. Maybe it's not perfect but it is decent for problems like this while still showing how you got there.

I'm just saying though, I wouldn't even bother dusting off my math skills because it solves instantly to logic, which is why in this case I didn't even think of quadratics or factors or anything.

That is how I got there though. If y = x(x+n) then y =/= x^2 or x^2 +/-n if you want me to make it look all mathematical. If the grand examiner wants me to do it properly then they'll have to abide to that logic when selecting which answers to have as choices. :P

[Haros]

I'm just saying though, I wouldn't even bother dusting off my math skills because it solves instantly to logic, which is why in this case I didn't even think of quadratics.

That is how I got there though. If y = x(x+n) then y =/= x^2 or x^2 +/-n if you want me to make it look all mathematical. If the grand examiner wants me to do it properly then they'll have to abide to that logic when selecting which answers to have as choices. :P

It's all in the question and how it's phrased. I just like going all out doing things in full even when the answer can be done with a short cut because I've always been taught that doing things in full during maths will pay off and so far it has for me.

[Dendrek]

Several people here are over complicating these problems. Jeavline, I don't know what level of math you're comfortable with. Hopefully this explanation helps. If you need more assistance and think I might be able to provide it, feel free to send me a PM.

These particular questions aren't testing to see if you know "Algebra" (when people say that, they often mean being able to "solve" a problem that contains variables); they're looking to see if you can figure out how the equations work or if you can figure out a logical way to answer them.

Why I know they're not expecting you to use 'solving methods' to find the answer to these problems:

1. The first problem has an infinite number of solutions. What I mean is there are a lot of numbers that you can come up with that are able to satisfy that equation. The only reason there's a single answer to that question is because they narrowed it down to only 4 possible answers and they expect you to figure out which of the 4 is correct. That can be done in a few different ways, but they obviously expect you to plug numbers in, so why not do it the easy way (I'll go into that in a second).

2. The second problem isn't asking for a "solution" at all. (They aren't asking for a number answer, as in "The answer is 3" - they don't want that; they're looking for a comparative answer, as in "The third choice is always the largest one.") This problem definitely doesn't require "Algebra" solving methods to answer. The "easy way" to solve the first problem is the same way you'd solve this one.

So how do you solve problems like these?

It's already been mentioned by others, but I'll break it down more for you. Both problems can be solved by plugging in numbers and comparing the answers. Look at the specific conditions in the problem and let that help you decide what numbers to test.

Assume that y = x(1+x) where x is a positive integer. Which of the following alternatives is a possible value of Y.

Notice the underlined part. It's important because it says something about what X can be. X must be a positive integer. I hope you know what integers are, but in case you don't: Integers are whole numbers (1, 2, 3, 4 and so on) but they can also be negative (-1, -2, -3, -4 and so on) and zero (0) is included. The following numbers are NOT integers: 1.5, -3/4, 2.3333333, pi = 3.14159265..., sqrt(2).

The underlined part tells you what kind of numbers you can plug in. It specifies positive integers, so don't plug in anything that's negative (and don't plug in decimals or fractions either).

Always start with 1 (unless you know you can start with something else):

• y = 1(1+1). y = 1(2) = 2.

Didn't work. Try 2:

• y = 2(1+2). y = 2(3) = 6.

Notice how the answer changed? Plugging in 2 gave us a bigger answer than when we plugged in 1. (Since the available answers we're looking for (10, 16, 20, 24) are bigger than the ones we've gotten so far, it's a good thing our answer are getting bigger. We're on the right track). Try 3:

• y = 3(1+3). y = 3(4) = 12.

Not there yet, but we're getting very close to the possible answers. (We've already passed up the value of 10 (answer a) so we know that's not an answer). Try plugging in 4:

• y = 4(1+4). y = 4(5) = 20!

And we're done. 20 is on the list. No reason to keep going.

Now think about what you just went through (of course I did the work and you were reading, but it's an important lesson): As I plugged in numbers, I noticed what was happening with the answers. I didn't just blindly plug in numbers, and I wasn't randomly choosing numbers either. Let's say the problem was slightly different: they gave you the same equation but much bigger answers: 100, 124, 132, 155. Do you think I would have kept plugging in consecutive numbers: 1, 2, 3, 4, then 5... etc? The answers I was getting were growing, but they weren't growing fast enough. I would have skipped ahead. I'd try plugging in 8 next and see if that got me closer.

Which of the following equations is biggest if X is a negative integer?

Question two asks you to compare the equations, but you can't really compare them just by looking at them, obviously. If you want to compare how big two things are, you need values. So again, you need to plug in numbers.

Notice the underlined part, again. It tells you what kind of numbers you can plug in. So if you read the first explanation, then you should know what a negative integer is. So, what numbers should you plug in? Let's start with the obvious: -1. Now here's the difference between this problem and the previous one: There's not 1 equation to plug in to; there are 4. So logic says you should plug -1 into all 4:

• -2x-1 = -2(-1)-1 = 2-1 = 1
• -2x = -2(-1) = 2
• x-2 = -1-2 = -3
• 2x = 2(-1) = -2

The key to this problem is knowing how to simplify those equations correctly after you plug -1 in. Knowing to plug in -1 shouldn't be to hard for you at this point. The problem made it somewhat obvious that you needed to plug numbers in, and since those numbers had to be negative integers, -1 was the first choice. But if you don't know how to simplify those problems, then you might not have been able to answer that questions.

So looking at the answers I got (and that you should have gotten as well) you should see that the equation that gave the biggest answer was the second. 2 > 1 > -2 > -3.

[Auxis]

I swear, Algebra almost killed me in maths. in my last year, I just passed my maths after the final exams at a 52% for the year. I seriously see situation in life where your going to need algebra skills other than if your maybe doing chemistry or any technical careers. It's not like some woman is going to walk up to you at a checkout and give you some random algebra equation -_-

[Deleted]

I swear, Algebra almost killed me in maths. in my last year, I just passed my maths after the final exams at a 52% for the year. I seriously see situation in life where your going to need algebra skills other than if your maybe doing chemistry or any technical careers. It's not like some woman is going to walk up to you at a checkout and give you some random algebra equation -_-

Economics and Business in general requires alot of algebra.

[Haros]

I swear, Algebra almost killed me in maths. in my last year, I just passed my maths after the final exams at a 52% for the year. I seriously see situation in life where your going to need algebra skills other than if your maybe doing chemistry or any technical careers. It's not like some woman is going to walk up to you at a checkout and give you some random algebra equation -_-

Basic algebra is used a lot in just general life. Make up a bottle of spray to kill weeds in your garden but don't have a large enough container for the instructions on the bottle? Use algebra to get the right amount. Working out quickly how many words are in a hand written essay due in an hour? average a few lines and times that by the amount of lines in the essay. Just because people aren't asking you to rearrange Pythagoras theorem doesn't mean it's not algebra.

[Deleted]

I swear, Algebra almost killed me in maths. in my last year, I just passed my maths after the final exams at a 52% for the year. I seriously see situation in life where your going to need algebra skills other than if your maybe doing chemistry or any technical careers. It's not like some woman is going to walk up to you at a checkout and give you some random algebra equation -_-

Yes i do agree with you, It's most likely not very useful in many career choices. Though personally i would love to be able to understand some equations made by scientist and maybe work on them myself not as a career choice but as a freetime hobby. So many mysteries in numbers yet to be solved