VCE Methods Question Thread!

[snowisawesome]

A = (10,22.5)
B = (23,9)

An island lies on the perpendicular bisector of line segment AB. Its port is denoted by C. It is known that the x-coordinate of C is 52. Find the y coordinate of C.

Mid point of AB = (16.5, 15.75)
M = (9-22.5)/(23-10)
M = -13.5/13
For perpendicular lines, m1 * m2 = -1
(-13.5/13)*m2 = -1
m2 = 13/13.5

y = mx + c
15.75 = (13/13.5)(16.5) + c
15.75 = (214.5/13.5) + c
c = -0.13888889
y = (13/13.5)x - 0.13888889
x = 52
y = (13/13.5)(52) - 0.13888889
y = 49.78111

Is this correct?

[keltingmeith]

A = (10,22.5)
B = (23,9)

An island lies on the perpendicular bisector of line segment AB. Its port is denoted by C. It is known that the x-coordinate of C is 52. Find the y coordinate of C.

Mid point of AB = (16.5, 15.75)
M = (9-22.5)/(23-10)
M = -13.5/13
For perpendicular lines, m1 * m2 = -1
(-13.5/13)*m2 = -1
m2 = 13/13.5

y = mx + c
15.75 = (13/13.5)(16.5) + c
15.75 = (214.5/13.5) + c
c = -0.13888889
y = (13/13.5)x - 0.13888889
x = 52
y = (13/13.5)(52) - 0.13888889
y = 49.78111

Is this correct?

Change your answer to a fraction, and probably.

[snowisawesome]

Change your answer to a fraction, and probably.

What do you mean by "probably"?

[Yertle the Turtle]

What do you mean by "probably"?

In other words, he hasn't checked your working, but the steps appear to be correct. I would agree, without having checked the answer, but the VCAA markers want you to keep things in fraction form rather than decimals.

[exit]

In other words, he hasn't checked your working, but the steps appear to be correct. I would agree, without having checked the answer, but the VCAA markers want you to keep things in fraction form rather than decimals.

Yep. Always keep in fraction form unless asked for decimal places or the fraction is ridiculous like 3424/729 because VCAA will accept decimal in that scenario .

[snowisawesome]

Thanks for the above help guys

[Bri MT]

Just to reinforce what everyone else has said. ALWAYS use exact form rather than a decimal approximation unless specifically told

[snowisawesome]

If i'm average at best for methods can i get a still get a 35 raw with just a lot of effort? My main areas of weakness are application questions, so if i spend a lot of time for application questions, will that help?
Thanks

[domjamriska]

If i'm average at best for methods can i get a still get a 35 raw with just a lot of effort? My main areas of weakness are application questions, so if i spend a lot of time for application questions, will that help?
Thanks

Undoubtedly, 35 is very achievable. The main thing with methods is consistent and sustained effort, i was able to cram and achieve excellent SAC scores but was ultimately punished in the exam; the course involves a wide array of sections and after you finish one I would highly encourage spending 15-20minutes a night (or every second night) practicing the key skills before transitioning into more complex application questions.
Based off your message it sounds like you have a firm grasp of the basic mechanics of mathematical methods but maybe struggle sometimes to interpret questions when they require you to extrapolate equations etc .. I think practice exams and checkpoints may help, possibly with a teacher/tutor looking over your shoulder to explain their thinking and reasoning for the early stages.

[Yertle the Turtle]

If i'm average at best for methods can i get a still get a 35 raw with just a lot of effort? My main areas of weakness are application questions, so if i spend a lot of time for application questions, will that help?
Thanks

It is important, as domjamriska says, to put in consistent and sustained effort. Similar to all subjects, except maybe folio subjects, "hard work beats talent when talent does not work hard". The work put in will be where you get your score from. Cramming is not going to help in the end, but if you start now, you can improve.

With application questions, the thing to remember is to think about what they want you to find out, and then think what formulae fit your knowns and unknowns, etc. You must answer the question! You will not receive the marks for working or answer if you were not finding out quite what the question asked for, so make sure you understand what it is really looking for.

[snowisawesome]

Thanks guys for the help above

[snowisawesome]

A = (-4,6)
B = (6,-7)
a. Find the coordinates of the point P on the line segment AB such that AP:PB = 3:1
stuck on this question
my working out so far
√((x+4)^2 + (y-6)^2 = 3)   (everything's inside the square root)
(x+4)^2 + (y-6)^2 = 9
(x+4)(x+4) + (y-6)(y-6) = 9
x^2 + 8x + 16 + y^2 - 12y + 36 = 9
x^2 + 8x + y^2 - 12y = -43
got stuck here, since the working out doesn't look right
since it said AP:PB = 3:1, i assumed that the distance of AP is 3 times the distance of PB

[jazzycab]

It can certainly be done by looking at the distance between points, however, the first distance is not necessarily 3 (you could call it 3z for instance, and the other one would be z)

You'd also need to use the fact that the point P is on the line segment AB (i.e. find the equation of the line and substitute it in).
This, however, could be an algebraic nightmare.
A much simpler solution would be to consider the problem geometrically (there is a formula that we could generate for the coordinates of a point split in an arbitrary ratio internally on a line segment, but isn't required for methods).
The ratio AP:PB=3:1 suggests that the line segment is split into 4 equal length segments (and P is closer to B than to A).
If we let M be the midpoint of the line segment AB, then P is simply the midpoint of MB.

[snowisawesome]

Thanks
Do you know what's the best way to prepare for methods 3/4 in the holidays?

[jazzycab]

Thanks
Do you know what's the best way to prepare for methods 3/4 in the holidays?

If you have a fairly good grasp of the content from Units 1 and 2, then you probably don't need to spend too much time revising the content itself. The best thing you could do would be to develop your mathematical analysis and interpretation of complex problems.
This is the area that most people have the most difficulty with.
A task I quite like to work on these areas is to take a set of problem-solving questions (exam-style would be best) and rewrite them as a sequence of textbook-style questions (because, ultimately, that's all application questions are, but packaged in a complex, often convoluted way).
This gets you formalising the thinking required to successfully complete questions of this type and if you dig a bit deeper, should give you some insight into solution strategies that are more efficient than others.