VCE Methods Question Thread!

[keltingmeith]

The polynomial P(x) has a remainder 2 when divided by x-1 and a remainder of 3 when divided by x-2. The remainder when P(x) is divided by (x-1)(x-2) is ax + b, i.e P(x) = (x-1)(x-2)Q(x) + ax +b

Find the values of a and b

By the remainder theorem, P(1)=2 and P(2)=3. So,

3=2a+b
2=a+b

Solving simultaneously:

1=a
2=1+b <===> b=1

So, a=b=1.

[cosine]

Don't worry, we've all been there - I've even done things like writing a 4 as a 9, or 2/2=2. Hell, once I took the square root of something for absolutely no reason, which lead to a loss in 20 marks.

Nerves does things to you, it's a learning experience - just tell yourself you'll do better next time, and you will.

Omg haha

How can I eliminate these small errors though, like through practice right? Trust me, I practiced more than you think I did for this sac, I actually think excessive over-preparing lead to my miserable mark?

[keltingmeith]

Omg haha

How can I eliminate these small errors though, like through practice right? Trust me, I practiced more than you think I did for this sac, I actually think excessive over-preparing lead to my miserable mark?

Nope, that's going to make it worse, tbh. Something can be "over-practised", and the worst part is, the more you practice, the more you're likely to spiral and fall if you make a mistake.

The best way to not make mistakes is to just be calm through everything, and don't rush. You're more likely to not make a mistake if you're calm about something, than if you rush through and check your paper at the end. If you've made a small mistake, you will probably miss it on a second read-through, so it's better to just not make them to begin with than to have time at the end to check.

[dankfrank420]

Nope, that's going to make it worse, tbh. Something can be "over-practised", and the worst part is, the more you practice, the more you're likely to spiral and fall if you make a mistake.

The best way to not make mistakes is to just be calm through everything, and don't rush. You're more likely to not make a mistake if you're calm about something, than if you rush through and check your paper at the end. If you've made a small mistake, you will probably miss it on a second read-through, so it's better to just not make them to begin with than to have time at the end to check.

This is the polar opposite to my technique.

I rush through the exam in half the allotted time and spend the rest checking answers. I tried a similar technique to you once, but I panicked because I thought I was going too slow.

[warya]

This is the polar opposite to my technique.

I rush through the exam in half the allotted time and spend the rest checking answers. I tried a similar technique to you once, but I panicked because I thought I was going too slow.

I'm exactly the same, I end up doing the test start to finish like 3 times. Its bad though especially in multiple choice, because it leads to second guessing yourself. Maybe slow and steady wins the race? 

[keltingmeith]

There's no proper hard and fast way to do a test, SAC or exam. I simply assessed cosine's issue at hand, and then offered an alternative method which could help to reduce stress. If triple checking works for you, go ahead and do it - in fact, I'd suggest doing it.

[Caesius]

How would I eliminate y from these equations to form a quadratic equation?
x^2 + y^2 = 4a^2  and  2x + 2y = b

Thanks in advance!

[keltingmeith]

How would I eliminate y from these equations to form a quadratic equation?
x^2 + y^2 = 4a^2  and  2x + 2y = b

Thanks in advance!

Why do you want to eliminate y and "form a quadratic equation"? What's the actual question you're trying to answer?

[Caesius]

Why do you want to eliminate y and "form a quadratic equation"? What's the actual question you're trying to answer?

Never mind, I've solved it now! Its from an extension question involving a rectangle in a circle with pronumerals for the dimensions. I don't know why it wants me to eliminate y, but the answer was needed in the next part of the question.

[keltingmeith]

Never mind, I've solved it now! Its from an extension question involving a rectangle in a circle with pronumerals for the dimensions. I don't know why it wants me to eliminate y, but the answer was needed in the next part of the question.

Mind sending me a picture of the question or something? It seems so odd that I just want to see it...

[cosine]

When we perform transformations using martices, what does the mean?
Also what does the mean?

[keltingmeith]

When we perform transformations using martices, what does the mean?
Also what does the mean?

It just means your making a map from the Cartesian Plane, to another Cartesian Plane.

And the x' and y' are just used because the transformation makes a new relationship, so you can't keep up with the same x and y - you need a new one. (personally, I use x_t and y_t, because we normally use the dashes to signify derivatives)

[lzxnl]

This is the polar opposite to my technique.

I rush through the exam in half the allotted time and spend the rest checking answers. I tried a similar technique to you once, but I panicked because I thought I was going too slow.

I maintain, to this day, that I got a 49 in spesh precisely because I took too long in the exam. I didn't get enough time to check through exam 2 completely and I ended up dropping a mark on a question that I hadn't checked because I didn't read the question properly the first time through.
Of course, the difference between a 49 and a 50 at the end of the day is 0.1 aggregate points so it's only an issue of pride for me. But you can see my point. You need to strike a balance between working quickly to get checking time and being careful.

When we perform transformations using martices, what does the mean?
Also what does the mean?

So the R^2 => R^2 means you're starting in two dimensions and you end on two dimensions.
An example of R^2 => R^1 would be
x = cos t, y = sin t, which parametrises the unit circle. See how I start with two variables and end with one? Hence the R^2 => R^1

x' and y' mean transformed x, y variables. So if I move my function 3 up, I write y' = y + 3

[I_I]

Hello guys,
It's an early morning but I have a question I need to ask 
can't ((x+1)²)^1/2+1 be simplified to x+2 since the square root and the power cancel each other out?
Also, the answer can also be abs(x+1)+1 according to the practice exam paper, how is this possible?
Thanks!
Catherine

[cosine]

Hello guys,
It's an early morning but I have a question I need to ask 
can't ((x+1)²)^1/2+1 be simplified to x+2 since the square root and the power cancel each other out?
Also, the answer can also be abs(x+1)+1 according to the practice exam paper, how is this possible?
Thanks!
Catherine

  , so yes, it can be written like that.

It can also be the absolute of (x+1) +1 because if you plug any number in x - it will always produce a positive value - try it!