VCE Methods Question Thread!

[MNM101]

I'm assuming it's x^4 + (4x^2/2x) not the entire equation over 2x.

Either way, simplify the equation first, obtaining x^4 + 2x from the first equation.

Then we just differentiate it, so using the formula dy/dx x^n becomes nx^(n-1),

We obtain 4x^3 + 2

It's actually all over 2x😓😅

[JHardwickVCE]

(Image removed from quote.)

It's actually all over 2x😓😅

The answer is D. You would need to perform a division first to cancel out the x in the denominator. This will give y=1/2(x^3) + 2x
Through normal calculus techniques (multiply co-efficient by power, then lower power by 1), the answer D is obtained.

[melons]

Could someone help with part d of the attached question? k=1/4 and the mean is 2.

[LiquidPaperz]

if someone can show me full workings for part b and how they got it that would be great, i get where the 225km came from but not the 100 minutes (you'll see once you do it what values im talking about)

Answer is 135km/hour

[IndefatigableLover]

Could someone help with part d of the attached question? k=1/4 and the mean is 2.

If we know that Pr(X>a) = 0.6, then we also know the opposite where Pr(X<=a)=0.4 since all probability must add up to one.

Your answer of the mean which equalled '2' is used (due to the graph of y=f(x) being symmetrical at the mean) thus leads to the conclusion that Pr(X<=2)=0.5
As a result, you know that the domain in which 'a' occurs is from 0<a<2 because if it was any bigger then the probability would be smaller and not reach 0.6.

Here we look at which equation is within this domain. We can see that it's 'kx' where 'k' is 1/4.

Now we just integrate it with our terminals being 'a' and '0'. From f(x), we can see that only one of the values fit inside this domain (that is the first one).



(Skipped a few steps but I'm sure you know how to integrate that and make 0.4 into a fraction).



(reject negative value)

[IndefatigableLover]

if someone can show me full workings for part b and how they got it that would be great, i get where the 225km came from but not the 100 minutes (you'll see once you do it what values im talking about)

Answer is 135km/hour

I had to go back to Q9 (on the other page) but basically you need to finish at the same time (that is 2 hours and 55 minutes or 175 minutes) where you have just passed Checkpoint A at 75 minutes. So basically the time you have to reach Checkpoint B is the difference (that is 175-75=100).

From there just remember to convert your units and use the speed formula and you're all set

[LiquidPaperz]

sorry bout not attaching it.

Yeh i see where the 100 came from, but why do we minus the time it too driver A to do the second part and minus that from what driver b took to do first part

[IndefatigableLover]

sorry bout not attaching it.

Yeh i see where the 100 came from, but why do we minus the time it too driver A to do the second part and minus that from what driver b took to do first part

As I said before, you want the two cars to reach Checkpoint B at the same time. If you look at Car 1 (in Q9), it took 2 hours and 55 minutes to reach Checkpoint B. For the second rally car, it also needs to reach Checkpoint B at this time as well so that it can 'catch the previous driver.' You know that Car 2 has already travelled for 75 minutes and reach Checkpoint A. However, to reach Checkpoint B, it needs to reach there by 2 hours 55 minutes so we subtract the two from each other (to get 100 minutes) which tells us the time for Car 2 to reach Checkpoint B. This makes it so that both cars travelled 2 hours 55 minutes to reach Checkpoint B.

[LiquidPaperz]

ive got the casio classpad, and when trying to draw a graph it only draws a straight line along the x axis, why is it doing this?

i am trying to sketch x = 2t/t^2+1, t is equal to or greater than 1

[keltingmeith]

You should be getting a small curve that asymptotes towards x=0 (just like a quarter of a hyperbola). If you're not, check how you've entered the graph

[LiquidPaperz]

got it, cheers!

how did you know what it looked like? its not a truncus or hyperbola

[keltingmeith]

Exponential laws:

x = 2t/t^2+1 = 2t^(1-2)+1=2/t + 1, which is your standard linear reciprocal (aka hyperbola)

[jessss0407]

hey guys,

I have two questions

1. A normal distribution has mean 8 and standard deviation 3. Give the rule that maps the
curve of the density function to the density function of the standard normal.

2. Suppose that X is normally distributed with a mean of 11.3 and a standard deviation of 2.9.
The values of c1 and c2, such that Pr(c1 < X < c2) = 0.90. Find c1 and c2

Thanks!

[keltingmeith]

hey guys,

I have two questions

1. A normal distribution has mean 8 and standard deviation 3. Give the rule that maps the
curve of the density function to the density function of the standard normal.

2. Suppose that X is normally distributed with a mean of 11.3 and a standard deviation of 2.9.
The values of c1 and c2, such that Pr(c1 < X < c2) = 0.90. Find c1 and c2

Thanks!

The wording of the first question is far beyond what I would expect of a methods students (pretty sure a few of the people in my second year stats class don't know what half of those words mean...). However, it is just the normal rule to find the z-score - if and , then

The second one is a little annoying, and while I wouldn't expect to see it on an exam, it is definitely still in the realm of things you could be asked and what your school might ask.

So, we know that all distributions are symmetrical about the mean. So, if we can find the point where one side is equal to 0.45, we can find one point. We also know that the standard normal is symmetrical about the mean, so each of the values will be the same number, but one will be negative and one will be positive. So, if we can find the answer for the standard normal, we can then convert to the particular distribution we have now. (from this paragraph onwards, you might find it beneficial to draw a bunch of normal distributions and shade in the areas we're trying to find)

So, we define , and then try to find . Now, cutting this in half, what we want to find is . Now, the final step is to turn this around - find the probability that Z is LESS than -d. When we do this, we're looking for 0.5-0.45=0.05 instead. This works in our favour, because now we can use the inverse normal function on our calculator. So, we find . Now, finally we just need to apply some transformations to get to the give normal distribution. So, . Now, remember we need to do this for both a positive d and a negative d. The lower value will be c1, the upper value will be c2. This gives us

[soNasty]

For the first question, I'm pretty sure its referring to the actual function used for the standard normal distribution:
For a standard normal distribution however, the mean is 0 and standard deviation is 1.
In your case the mean is 8 and the standard deviation is 3. So just sub in your given variables into the equation to find the density function.