VCE Methods Question Thread!

[brightsky]

Complete the square.

x = y^2 + 2y = (y^2 + 2y + 1) - 1 = (y+1)^2 - 1
y = +-sqrt(x + 1) - 1

Note that the equation of the INVERSE of the given function contains both the plus and the negative square root. If you require the INVERSE FUNCTION, then you would have to restrict the domain of the original function and take either the positive or the negative square root.

[T-Infinite]

Complete the square.

x = y^2 + 2y = (y^2 + 2y + 1) - 1 = (y+1)^2 - 1
y = +-sqrt(x + 1) - 1

Note that the equation of the INVERSE of the given function contains both the plus and the negative square root. If you require the INVERSE FUNCTION, then you would have to restrict the domain of the original function and take either the positive or the negative square root.

OH YEAHHH! I totally forgot about the complete the square method! Thank you for refreshing my memory

[Only Cheating Yourself]

I think I'm getting  little better with my maths, i looked over linear equations and wasn't able to do questions like
(4x-3)^2=16 now i'm able to them and most importantly why I'm doing it like when rearranging things you use reverse operations to get rid ^2 as we want to make the x linear which is easier to solve you you square root the bracket which eliminates the ^2 and what ever you do to one side you do to the other.

[hobbitle]

Exactly right :-)

[M_BONG]

Hey guys, how would you interpret the following question?

Question: "A sand timer consists of two cones joined at the apex. When the timer is turned over, the sand starts pouring from the top cone into the bottom one at a constant rate of . Find the rate of change of the depth of the sand in the top cone when the depth is 0.8cm"

I interpreted to be , whereas the textbook solutions manual interpreted to be . What do you guys think? Shouldn't the rate be negative since volume is decreasing from the top cone (as sand is pouring to bottom cone?)

Thanks in advance!!

[lzxnl]

You're correct, but I think in this question only the magnitude really is what they're getting after. Most questions say "how much is it decreasing" anyway.

[Toki]

you went wrong there!
it should be
NO BRACKETS for -y+1




and for the y



subbing it in,



rearrange,


[edit]
Brightsky's method is way more efficient & is definitely my favourite when approaching transformations
[/edit]

Our school hasn't taught us this method for translating and reflecting graphs. Where can I learn this from?

[psyxwar]

Sine and cosines are cofunctions right, not complementary functions?

[Nato]

Our school hasn't taught us this method for translating and reflecting graphs. Where can I learn this from?

The essentials textbook has theory on the use of this method.

[brightsky]

Sine and cosines are cofunctions right, not complementary functions?

I don't think there is such a thing as 'complementary functions'. Sine and cosine are cofunctions of each other because sin(pi/2 - x) = cos(x) and cos(pi/2 - x) = sin(x). Hence the 'co' in front of cosine. Tangent and cotangent are also cofunctions of each other, as are secant and cosecant.

[psyxwar]

I don't think there is such a thing as 'complementary functions'. Sine and cosine are cofunctions of each other because sin(pi/2 - x) = cos(x) and cos(pi/2 - x) = sin(x). Hence the 'co' in front of cosine. Tangent and cotangent are also cofunctions of each other, as are secant and cosecant.

Yeah thanks. Maths quest refers to them as "complementary functions"...

[lzxnl]

I think they call them that because the sine of the complement of x is the cosine of x and vice versa.

[M_BONG]

Just a quick clarification:

Would I be correct in saying that the left rectangle method is used to approximate area under the graph and right rectangle method is used to approximate area above the graph?

If the above is not right, can I please get a clarification on when the two methods are used? Also, do these kind of questions (of approximating areas using rectangles) often come up in VCAA exams or are they only used in my textbook (Quest) as an introduction to finding areas using integration?

[T-Infinite]

Please help me with this question.

So I've done part a) and I found to be . I'm kinda confused on part b) , I don't remember how to find the suitable domain.

[b^3]

Just a quick clarification:

Would I be correct in saying that the left rectangle method is used to approximate area under the graph and right rectangle method is used to approximate area above the graph?

If the above is not right, can I please get a clarification on when the two methods are used? Also, do these kind of questions (of approximating areas using rectangles) often come up in VCAA exams or are they only used in my textbook (Quest) as an introduction to finding areas using integration?

What exactly do you mean by under and over the graph?

The left endpoint estimate will under-approximate the area if the curve is increasing over that domain, and over-approximate if the curve is decreasing over that domain. The right endpoint estimate is the opposite, it will over-approximate the area if the curve is increasing over that domain and under-approximate the area if the curve is decreasing over that domain.

Normally you might get a MC question where it'll give you an image with the rectangles drawn on it and then find the approximation. It's still good to know how to apply both too. There was also a SA or ER question a few years ago which related the tangent line and the area under that to over and under approximating the area depending on whether the curve was decreasing or increasing.