VCE Methods Question Thread!

[^^^111^^^]

Thank you so much!

This seems like a really simple question, but how do I go about solving this?

e^x=3

I have a inkling I have to convert to natural log, but I don’t know what do after i do this:
loge(x)=loge(3)

I second this:

No need for the two natural logs, simply create a log keeping e as the base and 3 as the number. Keep in mind that you're solving for x, so x must be on its own on one side. This becomes x = loge(3)

In case u are still confused, think this will help you out:

a^x = b
==>> then x = loga(b)
This is because you will be taking log of base a in both sides.
So:
loga(a^x)=loga(b)
x=loga(b)

Thus applying this to your question:
e^x=3
x=loge(3).

Does that help?

[IThinkIFailed]

I second this:In case u are still confused, think this will help you out:

a^x = b
==>> then x = loga(b)
This is because you will be taking log of base a in both sides.
So:
loga(a^x)=loga(b)
x=loga(b)

Thus applying this to your question:
e^x=3
x=loge(3).

Does that help?

Thanks, I get it now

[rubymat]

Hey! I'm not sure if this is where I am supposed to post this, as it is my first post - so please let me know if I'm doing anything wrong.

I'm doing some holiday HW for 1/2 Methods and have come across a question I can't do, and I can't find any useful resources elsewhere. This is the question:

ABCD is a quadrilateral with angle ABC a right angle. D lies on the perpendicular bisector of AB. The coordinates of A and B and (7,2) ad (2,5) respectively. The equation of line AD is y = 4x-26.
a) Find the equation of the perpendicular bisector of the line segment AB.
b) Find the coordinates of point D.
c) Find the gradient of the line BC.
d) Find the value of the second coordinate, c, of point C(8,c).
e) Find the area of quadrilateral ABCD.

So far, my answers are:
a) y=5/3x-4
b) (66/7,82/7)
c) 5/3
d) C(8,15)

But part e has me stumped! How can I work out the area when I only know the vertices, and it is an irregular shape?

I was thinking of finding the area of triangle ABC (a right angled triangle) and then using perpendicular lines and simultaneous equations to find the height of ACD to find the area of that triangle, but I'm not sure if that would work or if there is an easier way.

Thanks in advance!

[TheEagle]

Hint: split the shape into 2 and see the familiar angle

[TheEagle]

Hey! I'm not sure if this is where I am supposed to post this, as it is my first post - so please let me know if I'm doing anything wrong.

I'm doing some holiday HW for 1/2 Methods and have come across a question I can't do, and I can't find any useful resources elsewhere. This is the question:

ABCD is a quadrilateral with angle ABC a right angle. D lies on the perpendicular bisector of AB. The coordinates of A and B and (7,2) ad (2,5) respectively. The equation of line AD is y = 4x-26.
a) Find the equation of the perpendicular bisector of the line segment AB.
b) Find the coordinates of point D.
c) Find the gradient of the line BC.
d) Find the value of the second coordinate, c, of point C(8,c).
e) Find the area of quadrilateral ABCD.

So far, my answers are:
a) y=5/3x-4
b) (66/7,82/7)
c) 5/3
d) C(8,15)

But part e has me stumped! How can I work out the area when I only know the vertices, and it is an irregular shape?

I was thinking of finding the area of triangle ABC (a right angled triangle) and then using perpendicular lines and simultaneous equations to find the height of ACD to find the area of that triangle, but I'm not sure if that would work or if there is an easier way.

Thanks in advance!

I may be wrong but I don't even think you are expected to know how to figure out the area in unit 1/2 methods. I learnt how to find the area of a non right angled triangle in spesh 3/4 (1/2 * a*b*sin c). If you're still curious, watch this video: https://www.youtube.com/watch?v=DzhsiuIiKCg

Which textbook are you using?

[angrybiscuit]

Greetings!
I'm not sure if this is the right place to put this but it was on a methods sac.
If a question asks, what is the rate at which x is decreasing, will the answer be positive or negative?
The question is above the rate at which water is flowing out, hence the gradient is negative. But if it asks, the rate at which it is decreasing, will the answer be positive or negative?

[rubymat]

I may be wrong but I don't even think you are expected to know how to figure out the area in unit 1/2 methods. I learnt how to find the area of a non right angled triangle in spesh 3/4 (1/2 * a*b*sin c). If you're still curious, watch this video: https://www.youtube.com/watch?v=DzhsiuIiKCg

Which textbook are you using?

Hi,
We're using Cambridge Senior Maths for our textbook.
Thanks so much for the link - I'll check it out now. I feel a lot better knowing I'm not necessarily supposed to know how to do this!
Thanks again

[cotangent]

Greetings!
I'm not sure if this is the right place to put this but it was on a methods sac.
If a question asks, what is the rate at which x is decreasing, will the answer be positive or negative?
The question is above the rate at which water is flowing out, hence the gradient is negative. But if it asks, the rate at which it is decreasing, will the answer be positive or negative?

I would say positive since they have already defined in the question that it is decreasing and now, I am assuming that they are just wanting the numerical figure of the rate at which its decreasing. But just in case, I would write a sentence explaining "the water level is decreasing at a rate of "x" litres per hour. (where x>0).

[Sine]

I would say positive since they have already defined in the question that it is decreasing and now, I am assuming that they are just wanting the numerical figure of the rate at which its decreasing. But just in case, I would write a sentence explaining "the water level is decreasing at a rate of "x" litres per hour. (where x>0).

+1 Would definitely recommend this for any instance you are not sure whether your answer is clearly answering the question.

[IThinkIFailed]

So let’s say my equation is this:
Ln(1/3x)

When expressing the transformations in a matrix, is this correct?

[  5     0] 
[  0    1]

[^^^111^^^]

So let’s say my equation is this:
Ln(1/3x)

When expressing the transformations in a matrix, is this correct?

[  5     0] 
[  0    1]

Sorry this might just be me, but can you tell me the resulting image of the graph for your curve,  f(x)=ln(1/3x)?

[jnlfs2010]

Any tips in producing a bound reference? What would you put in the bound reference and what can you put into a bound reference?

(bringing a textbook is kinda stupid since it is not compiled or condensed)

[Sine]

Any tips in producing a bound reference? What would you put in the bound reference and what can you put into a bound reference?

(bringing a textbook is kinda stupid since it is not compiled or condensed)

There are plenty of threads answering this so I would advise you to look for those and have a look at those responses.

Personally I think a bound reference should include; difficult questions, common mistakes (that you make personally), broad overview summary of the course (e.g. notes).

[colline]

Any tips in producing a bound reference? What would you put in the bound reference and what can you put into a bound reference?

(bringing a textbook is kinda stupid since it is not compiled or condensed)

Just adding onto what Sine said, you can also consider putting in more obscure CAS commands or reminders if you've written any UDFs.

You're absolutely right that bringing in a textbook is useless. Ideally your bound reference should be incredibly short  (a few pages at most) because you shouldn't NEED to actually consult it during exam time.

[TheEagle]

Just adding onto what Sine said, you can also consider putting in more obscure CAS commands or reminders if you've written any UDFs.

You're absolutely right that bringing in a textbook is useless. Ideally your bound reference should be incredibly short  (a few pages at most) because you shouldn't NEED to actually consult it during exam time.

Would you happen to know where to get UDF's?