VCE Methods Question Thread!

[cosine]

Hi

Can anyone explain to me the trick where you convert 2x-3/5-2x to    -2/(2x-5) -1 in like 2 steps or something?
Thanks! 

Okay, so

Step 1:
Assure that the denominator is in the form of (x-a), that is, the x is positive and there is no coefficient infront:






Step 2: Now, what we have is . We have to do something about the - but lets leave it out for now and continue. Now do your normal synthetic division, or whatever you use to divide polynomials. After doing so, you should yield 2 and 2.

Step 3: Take the second number and that is your remainder, so the factor always goes under the remainder as:

- ()

Step 4: Now, get rid of the - by multiplying the whole term by it. This should get you

-1

Hope it helped, and credit goes to EulerFan and Brightsky for teaching me this method

[Zues]

can someone show me how to use long division using x + 3 as a factor. because i know p(-3) gets 0

im not getting the same answer here.

[brightsky]

           3x^2 - 6x
         --------------------------
x + 3 | 3x^3 + 3x^2 - 18x
           3x^3 + 9x^2
          ------------------
                        -6x^2 - 18x
                        -6x^2 - 18x
                        ---------------
                                       0

Hence, 3x^3 + 3x^2 - 18x = (x+3)(3x^2 - 6x) = (x+3)[3x(x - 2)] = 3x(x-2)(x+3).

[keltingmeith]

I feel I should note you should only use polynomial division when you absolutely have to, as it's very time consuming. Always venture to take x out as a common factor when you can immediately, because it will simplify things:



So now, all we have to do is factorise the quadratic - something we can do by inspection:



(factors of -6: (-2,3), (-3,2), (-1,6), (-6,1) ===> 3-2=+1, therefore (x-2)(x+3))

[AirLandBus]

When completing questions from the textbook related to find the domain and range, is says we are allowed to use the CAS to graph it. Now, is it expected in the exams that every questions we will have to hand graph it? Or are we fine to graph it on the CAS during the exercises, but still know how to graph them by hand? As it would be very time consuming to do it by hand during the exercises.

[keltingmeith]

When completing questions from the textbook related to find the domain and range, is says we are allowed to use the CAS to graph it. Now, is it expected in the exams that every questions we will have to hand graph it? Or are we fine to graph it on the CAS during the exercises, but still know how to graph them by hand? As it would be very time consuming to do it by hand during the exercises.

As long as you know you can do them by hand, you'll be fine.

If you do the exercises via CAS because you don't know how to do them by hand, though, you're just sabotaging yourself.

[AirLandBus]

Yeah, sweet. Im planning to do a bunch of exercises practicing all the graphs from quads to the absolute values and the square root functions again to refresh the memory. Thanks buddy

[AirLandBus]

As long as you know you can do them by hand, you'll be fine.

If you do the exercises via CAS because you don't know how to do them by hand, though, you're just sabotaging yourself.

Sorry, another question. When writing out the domain and range, do the examiners prefer set or interval notation? Which is better?

[Zues]

i see my book do it like y < 3 but id usually go (-infinity, 3)

[cosine]

It doest really matter, I think. As long as they are all correct, they have the same meaning but different notation

[keltingmeith]

It doest really matter, I think. As long as they are all correct, they have the same meaning but different notation

^this. Use the one you're more confident with.

[AirLandBus]

Is this also the right notation for set?

For say, y=square root of (3+x)

Then the domain would be {x:x>_ -3}
Range would be {y:y>_ 0}

[keltingmeith]

Yes, that looks fine.

[SE_JM]

I really need HELP!!!

It's a logarithmic/exponential question

solve for x:

1.4^(x+2) = 25(0.9)^x

I keep getting the wrong answer. Please answer in much detail as possible (otherwise I won't understand )

Thanks!!

[keltingmeith]

I really need HELP!!!

It's a logarithmic/exponential question

solve for x:

1.4^(x+2) = 25(0.9)^x

I keep getting the wrong answer. Please answer in much detail as possible (otherwise I won't understand )

Thanks!!

This was a doozy, and definitely wouldn't expect it from a VCE exam (not to say you shouldn't know how to do it anyway. ):

So, first we look at our equation and say, "I don't like those powers. Let's log it all to get rid of them":



Note the use of log rules to separate the 25 and 0.9, because otherwise I would not have been able to pull the x out the front with the logarithms magical "turn an exponent into a multiple" power.

Now you do this as normal - collect like terms, factorise, simplify:



You can then get a numerical answer via calculator.