VCE Methods Question Thread!

[tennis1]

\(\frac{d}{dx}(log_ax)=\frac{1}{xln(a)}\)

\(\frac{d}{dx}(log_7x)=\frac{1}{xln(7)}\)

cheers

[lzxnl]

Remember that there is a change of base law in use there.

[MB_]

So there's this pdf graph (triangular)
with f(x)= x/24 from 0 <x< 4
            =  -1/48(x-12) from 4<x<12

Find w such that P(w<x<12)=0.25

nb. sorry if it doesn't make sense because I can't attach graph

\(\int_{w}^{12} \frac{-1}{48}(x-12)dx = 0.25\)

Solve for w and you get \(w=-2\sqrt{6}+12,w=2\sqrt{6}+12\)

\(w=-2\sqrt{6}+12\) (w=7.1) because it fits within the domain

[wyzard]

Thanks! However, I'm a bit stuck on the step straight after unfortunately...

So I have (tanx+1)/(tanx-1), the answer then converted this to (tanx-1)/(tanx-1) + 2/(tanx-1), I'm not sure how though.

Here's a neat trick:
Substitute u = tan x and then you'll have (u + 1)/(u - 1). You can then perform a long division to obtain 1 + 2/u, then all that's left is just substitute tan x back in

[sayy11]

In the VCAA answers, how do you know what the terminals should be, which equation to use and what you're suppose to make it equal to in order to solve for a? 

[StupidProdigy]

In the VCAA answers, how do you know what the terminals should be, which equation to use and what you're suppose to make it equal to in order to solve for a? 

You need to check yourself whether the area under the curve from 0 to 4 for y is less than, greater than or equal to 0.7. If it's less than 0.7, the rest of the probability is given by the other curve defined for y>4. If it's greater than 0.7 than we could simply evaluate the integral of y/16 from 0 to 'a' since the other curve will not contribute any area (if it does we will go over the 0.7 value. In this case, it is less than, so we need the sum of the probability given by the first curve y/16 from 0 to 4 plus the probability given by the second curve from 4 to 'a' and equating this sum to 0.7 since that is the probability we require

[Guideme]

2. The function given by f(x)= a^3x^2-a^2x^3, where a is not equal to 0, has a turning point at the point T(b,c), where b is not equal to 0
a. find f'(x)
b. Show that b=(2/3)a
c. Express c in terms of a, and hence state the coordinates of T.
d. If a=3/2, fint the coordinates of the turning point and explain why it is a local maximum.

Thank you

[Muchos Help]

Could someone help me with a)ii) and b)i) here http://m.imgur.com/a/2ad1d

Is my working correct? For ii) I'm not sure if I've interpreted this correctly but since it is displacement from A, then when t=0 -> x=-4?

Is bi) correct? The answer looks pretty dodgy so I'm doubting myself..

[solution]

This is a very specific question, but I do not have an example. Say we have a sin graph, which models the height of a tide. The "x-values" represent hours after 9AM, while "y-values" represent height in m. If the question asks between what times is the height below 2m, we would solve y=2 for the x values. If we get 2 answers like x=2.88912331 and x=5.491821902, would we always round the time to the nearest minute, or would we have to check whether or not the rounded times are below 2m?

(I hope this post makes sense. Essentially, "for modelling questions, is rounding supposed to be to the nearest number, or the number which satisfies the question")

[MightyBeh]

2. The function given by f(x)= a^3x^2-a^2x^3, where a is not equal to 0, has a turning point at the point T(b,c), where b is not equal to 0
a. find f'(x)
b. Show that b=(2/3)a
c. Express c in terms of a, and hence state the coordinates of T.
d. If a=3/2, fint the coordinates of the turning point and explain why it is a local maximum.

Thank you

Solutions here, sorry about the large image and messy handwriting.

The key to remember with part a is that a is a constant. The rest is just regular rearranging, lmk if something's still unclear.

Could someone help me with a)ii) and b)i) here http://m.imgur.com/a/2ad1d

Is my working correct? For ii) I'm not sure if I've interpreted this correctly but since it is displacement from A, then when t=0 -> x=-4?

Is bi) correct? The answer looks pretty dodgy so I'm doubting myself..

Seems reasonable to me but I didn't do the question for myself, I just read over your answer. Should be good tho

This is a very specific question, but I do not have an example. Say we have a sin graph, which models the height of a tide. The "x-values" represent hours after 9AM, while "y-values" represent height in m. If the question asks between what times is the height below 2m, we would solve y=2 for the x values. If we get 2 answers like x=2.88912331 and x=5.491821902, would we always round the time to the nearest minute, or would we have to check whether or not the rounded times are below 2m?

(I hope this post makes sense. Essentially, "for modelling questions, is rounding supposed to be to the nearest number, or the number which satisfies the question")

If it asks for the time you give it as (9 + 2.89...)AM, if it asks for an x-value then you state the x-value. Generally with those sorts of questions your answer will actually be a set of numbers, say {x: 2.89 <= x <= 5.49}. Most of the time the question will tell you how to present your answer, but if it doesn't use exact answers unless you're told otherwise, approximate answers are not technically correct. If you come up with an example question I could p[robably be more specific.

[solution]

Solutions here, sorry about the large image and messy handwriting.

The key to remember with part a is that a is a constant. The rest is just regular rearranging, lmk if something's still unclear.
Seems reasonable to me but I didn't do the question for myself, I just read over your answer. Should be good tho
If it asks for the time you give it as (9 + 2.89...)AM, if it asks for an x-value then you state the x-value. Generally with those sorts of questions your answer will actually be a set of numbers, say {x: 2.89 <= x <= 5.49}. Most of the time the question will tell you how to present your answer, but if it doesn't use exact answers unless you're told otherwise, approximate answers are not technically correct. If you come up with an example question I could p[robably be more specific.

The distance, d metres, of water from a fixed point O on the sand at any time t hours after 9.00am is modelled by the equation:
d(t) = 4 + 2sin((pi(t+2))/6)

Children are allowed to play on the sand when the water is 2.5m or less from the fixed point O.

At what time(s) between 9am and 6pm are the children likely to play?

The answer says 2:37PM to 5:23PM (I got this as well), but at 2:37PM and 5:23PM the water is actually above 2.5m. So wouldn't the answer be 2:36PM to 5:22PM?

[MightyBeh]

The distance, d metres, of water from a fixed point O on the sand at any time t hours after 9.00am is modelled by the equation:
d(t) = 4 + 2sin((pi(t+2))/6)

Children are allowed to play on the sand when the water is 2.5m or less from the fixed point O.

At what time(s) between 9am and 6pm are the children likely to play?

The answer says 2:37PM to 5:23PM (I got this as well), but at 2:37PM and 5:23PM the water is actually above 2.5m. So wouldn't the answer be 2:36PM to 5:22PM?

This is just a case of rounding to the nearlest minute, which is pretty standard. In reality the answer is actually 2:37 and 12ish seconds but the seconds aren't really relevant to the question because it's unreasonable for a lifeguard to count to exactly 12 before allowing some kids to swim and in the grand scheme of things it wouldn't change very much. It is more correct to say 2:38pm to 5:22pm (note that you round inwards; 2:36pm and the water is still higher than 2.5m). A VCAA question would specify exactly what they want your answer as though, so don't worry about it too much.

[aestheticatar]

11. A sample of 100 first-year university science students were asked if they study physics or chemistry. It was found that 63 study physics, 57 study chemistry and 4 study neither. A student is then selected at random. What is the probability that the student studies:
a. either physics or chemistry but not both
b. both physics and chemistry? In total, there are 1200 first-year university science students.
c. Estimate the number of students who are likely to study both physics and chemistry. Two students are chosen at random from the total number of students. Find the probability that:
d. both students study physics and chemistry
e. each student studies just one of the two subjects
f. one of the two students studies neither physics nor chemistry.

11. a. 18/25 b. 625 c. 288 students d. 0.0576 e. 0.2304 f. 0.0784

Can someone please help with 11e and f? Thank you!

[Dem16]

Is it better to use pencil or pen on the exam?
I'd rather use pencil, but my teacher always said it was better for the assessors to use pen....??

[tennis1]

My CAS  calc keeps giving me answers in weird consn(1) for trig,  and I don't know how to change it back to just normal decimals :/

Anyone know how?

My teacher said to just convert it to radians... but that doesn't work.

Btw the calc is Cas Claspad fx-CP400