VCE Methods Question Thread!

[knightrider]

How would you do these questions?

Find an antiderivative of

[keltingmeith]

How would you do these questions?

Find an antiderivative of

Linear expressions like this you can do without expanding.

Step 1: Treat the brackets as a normal polynomial, and anti-derive:


Step 2: Divide by the gradient of the linear expression:


Step 3: Simplify.

Just to check we have done it all right, let's derive this, and see if we get the original expression:


So, we're all good. You could, of course, expand the brackets out and anti-derive each term, but that will be very difficult for binomials power 4 and beyond.

[knightrider]

Linear expressions like this you can do without expanding.

Step 1: Treat the brackets as a normal polynomial, and anti-derive:


Step 2: Divide by the gradient of the linear expression:


Step 3: Simplify.

Just to check we have done it all right, let's derive this, and see if we get the original expression:


So, we're all good. You could, of course, expand the brackets out and anti-derive each term, but that will be very difficult for binomials power 4 and beyond.

Thanks euler fan
when you differentiate this dont you get 
How did you get back to

[theBRENDAN97]

Much better - slightly wrong use of brackets, but I'm pretty sure I know what you're talking about here:

Okay, the first graph doesn't even require a derivative. You can derive it if you want, and check for when f'(x)>0, but it's so much easier to just graph it: https://www.google.com.au/webhp?sourceid=chrome-instant&rlz=1CASMAE_enAU568AU568&ion=1&espv=2&es_th=1&ie=UTF-8#q=4%2B(4)%2F(2%20-%20x)
Look at the graph from left-to-right - if the curve moves up, the f'(x)>0 (as this means it's increasing). You should see that the graph increases for all x - EXCEPT when it jumps from positive infinity to negative infinity. The graph actually isn't defined at this point - it's our asymptote, the one point not defined in the domain they give you.

Second question, just flip the x using exponents:


For the last one, it's tempting to do something like the quotient rule - instead, split up the fraction and go from there:

Thanks so much.

[keltingmeith]

Thanks euler fan
when you differentiate this dont you get 
How did you get back to

The chain rule - you're forgetting to multiply by the diff of the bracket.

[ETTH96]

Hey guys, how do you ANTI-differentiate xcos(x)?

[Phenomenol]

Hey guys, how do you ANTI-differentiate xcos(x)?

You won't need to know how to do this in Methods without some prior guidance.

They might ask you to differentiate xsin(x) and "hence" find the antiderivative of xcos(x).

[knightrider]

For this question related to picture attached i was wondering is if they gave us the x coordinate of the maximum turning point would you have to include that as well as a value of x where the gradient is zero

For the gradient function sketched at right, state all values of x where the
gradient is:
a zero

[LiquidPaperz]

just a quick question.

if a question says what is the average slop between the lookout and the point f, i had 1/70 = 0.01429. however the answer says 1/70. when it says average other then y2-y1... are we meant to express it in a fraction form?

[silverpixeli]

just a quick question.

if a question says what is the average slop between the lookout and the point f, i had 1/70 = 0.01429. however the answer says 1/70. when it says average other then y2-y1... are we meant to express it in a fraction form?

Always express answers in exact form for methods unless they specifically ask for a certain number of decimal places. 1/70 is definitely preferred. If it was a terminating decimal (like 1/4 = 0.25) then the decimal form would be okay as well, but for something like 1/70 which has a decimal part that continues forever it's considered incorrect to provide a decimal answer (unless they asked you for it)

[silverpixeli]

How would you do these questions

For each gradient function graph below, give:
i the value of x where the gradient is 0
ii the sign of the gradient (positive or negative) left of this point
iii the sign of the gradient right of this point.

the graphs are y (gradient of function) vs x

the values of x where the gradient is 0 is asking for the values of x where y is zero,
(because the gradient function, y, is the value of the gradient at whatever x value)

in this case, gradient=0 at x=3 because this is where y=0


to the left of this point, the y value of the graph is positive (all the points of the line are above the x axis, or y>0) and since y IS the gradient, that means the gradient's sign is positive

likewise, to the right of x=3, the y values are all negative --> gradient is negative everywhere right of x=3

make sure you try the rest of the questions to practice this concept of what the graph actually represents

For this question related to picture attached i was wondering is there gave us the x coordinate of the maximum turning point would you have to include that as well as a value of x where the gradient is zero

For the gradient function sketched at right, state all values of x where the
gradient is:
a zero

so like before, since y is the gradient function, when we want the places where the gradient is zero we looks for the places where y=0 which is just x=-6 and x=2

The turning point of this parabola, y is a positive and since y is the gradient in a gradient function, the answer is no, you don't include it because here, y is not zero so the gradient is not zero


the confusion arises from the fact that the gradient of the parabola (the gradient function) is zero here, but notice the difference:

• the turning point is a place where the gradient of the gradient function is zero (but the gradient function is not necessarily zero)
  
• the intercepts are places where the gradient function is zero

that's a confusing concept so make sure you spend some time trying to understand

[LiquidPaperz]

Always express answers in exact form for methods unless they specifically ask for a certain number of decimal places. 1/70 is definitely preferred. If it was a terminating decimal (like 1/4 = 0.25) then the decimal form would be okay as well, but for something like 1/70 which has a decimal part that continues forever it's considered incorrect to provide a decimal answer (unless they asked you for it)

what about in further? if the question didnt ask we should leave in standard?

also, a container the shape of a cone, with its circular face on the ground, is filled to a third of its depth. what fraction of the total volume is filled with water?

ando. A cylinder of Radius R and Height H has volume V. the volume of a cylinder with radius 3R and heigh H is.... answer is 27V but i get 9V?

[knightrider]

the graphs are y (gradient of function) vs x

the values of x where the gradient is 0 is asking for the values of x where y is zero,
(because the gradient function, y, is the value of the gradient at whatever x value)

in this case, gradient=0 at x=3 because this is where y=0


to the left of this point, the y value of the graph is positive (all the points of the line are above the x axis, or y>0) and since y IS the gradient, that means the gradient's sign is positive

likewise, to the right of x=3, the y values are all negative --> gradient is negative everywhere right of x=3

make sure you try the rest of the questions to practice this concept of what the graph actually represents

so like before, since y is the gradient function, when we want the places where the gradient is zero we looks for the places where y=0 which is just x=-6 and x=2

The turning point of this parabola, y is a positive and since y is the gradient in a gradient function, the answer is no, you don't include it because here, y is not zero so the gradient is not zero


the confusion arises from the fact that the gradient of the parabola (the gradient function) is zero here, but notice the difference:

• the turning point is a place where the gradient of the gradient function is zero (but the gradient function is not necessarily zero)
  
• the intercepts are places where the gradient function is zero

that's a confusing concept so make sure you spend some time trying to understand

Thanks so much silverpixeli what you said is what i thought but i just satrted questioning my self so i asked to make sure

[M_BONG]

Hey guys,

I have two multiple choice question that needs assistance.

No idea how to do Q3 (finding the minimum value of f)

What I did was taking the negative parts of all of the modulus.
Thus, f(x)= (-2x)-(2x-a)-(2x+a)
= -6x

Which wasn't one of the options provided.

I chose A out of a frenzy but answer is B. Anyone explain please?


The other question Q13 MC,

I chose D. Doesn't the left rectangle method understimate the area because the rectangles are below the curve? Answer says it is nan overestimate, which I find makes no sense because the rectangles are below the curve.. But I checked with the CAS and it is indeed an overestimation? How do you overestimate when rectangles are below curve?

Thanks


 

[AirLandBus]

Hi can I please have help with this question:

Question 10 - Answer is C
11 - Answer is B (I believe - someone might want ot confirm this).