VCE Methods Question Thread!

[JieSun92]

Probability that he hits the target exactly five times is nC5 * (0.6)^5*(0.4)^(n-5).
You want this to be more than 0.25...so keep guessing values of n until this probability is greater than 0.25. There's not much you really can do.

yeah i did that but didnt know what to do on my calc. thanks for helping anyways!

[Frozone]

The point (2,-2) implies that


Or if we divide by 2
is our first equation

It has a gradient of 3 at x = 2 so,

Sub in our point of (2,3) because now it's a gradient function

is our second equation

Simultaneously solve for a and b.
You should get and

For part b)

Spoiler

If we know that we can do a bunch of things to find the turning point. We could complete the square, find the two x-ints and take the middle or use calculus.
Since we already found the derivative in terms of a and b we can just use that.


Solve for when


Sub into your original equation to find the y-value

Hopefully that clears some things up (and that my math is correct)

Thanks that helped a lot. I just didn't understand what to do with the gradient they gave me.

[darklight]

For what values of k does 4^x - 5(2^x) = k, have two distinct solutions? This is exam 1 btw.

So what I did was 2^x = a, giving you a quadratic equation. Delta needs to be greater than 0, giving you k> -25/4. However the answer is -25/4<k<0. Without sketching it (which demonstrates why 0 would be the upper limit) how do you work out that 0
Needs to be the upper limit? Thanks!

[SocialRhubarb]

However, before we defined , which means that .

.     If , then will be greater than 0.





you showed in your submission.

There's probably an easier way, that seems a bit long for a methods question. Decent question though, where'd you find it?

[aestheticatar]

Hey everyone

I need help with a binomial distribution question.

Rex is shooting at a target. His probability of hitting the target is 0.6. What is the minimum number of shots needed for the probability of Rex hitting the target exactly five times to be more than 25%?

Pls help.

For the Casio Classpad

We know:
pr(success)=.6
number of successes=5
let number of trials=x

In your main, you can enter this as:
binomialPDf(5,x,.6)
However, we are not trying to solve for anything in main.

Instead, we are going to highlight it all and copy/cut it.
Enter graph&tables.
For your 'y1', paste the 'binomialPDf(5,x,.6)' from before and tick the box.
Instead of pushing the usual graph icon, press the button on the right of it to enter your table.
Your x values will represent the number of trials.
Your y1 values represents the corresponding probability.
In this context, when 'x' number of trials have occurred, your y1 value represents the probability of 'Rex hitting the target exactly five times'.

...
at x=5 y1=.0778
at x=6 y1=.1866
at x =7 y1=.2613
at x=8 y1=.2787
...

When your y1 first exceeds .25, it provides your lowest number of trials, x.
Thus minimum number of trials being x is 7, satisfying the condition that the probability exceeds .25.

Feel free to adjust your starting/ending x values & the size of the steps between your x values.
Once you are in your table, you can easily adjust these values through pushing the icon that lies most right (has x and y in it with arrows pointing up and left).

Hope that helped mate.
Have a great night!

[psyxwar]

Should I bother learning how to find the inverse of a 3 by 3 matrix by hand? Is there any practical application? (Thought it'd be an easy way of doing sim equations but it looks like more effort than just doing them...)

[pi]

Should I bother learning how to find the inverse of a 3 by 3 matrix by hand? Is there any practical application? (Thought it'd be an easy way of doing sim equations but it looks like more effort than just doing them...)

Not really, but if you're keen anyway there's some good stuff in here BORED already? Want to learn a bit of maths? :P

[zhe0001]

how to do?

The height (in cm) that a clock’s pendulum swings above its base can be approximated by the function,
at any time t seconds after being released.

e Find the length of time that the pendulum is below 14 cm travelling from one side to the other.

I get but not what to do next.

thanks!

[Stevensmay]

You have only found when the pendulum will be at 14cm away from whatever. We want all the possible times, so we need a range of t values. To get this we need an inequality.



Solving for t will give us a range of values.

[zhe0001]

You have only found when the pendulum will be at 14cm away from whatever. We want all the possible times, so we need a range of t values. To get this we need an inequality.



Solving for t will give us a range of values.

I know that we need the other t values, but i cant find? how to do

[Stevensmay]

So a quick rearrangement gives us
So we know that is the first time that this will = 0.
We then want to find the second time, which is done by inspection and gives us
Thus, our range of t values is between these two, as this is when it is less than 0.

This might also be a calculator question, making it much easier.

[Frozone]

The curve with the equation y=ax^2 + bx + c has a stationary point at (1,2). When x=0, the slope of the curve is 45 degrees. Find a, b, and c.

[Stevensmay]

Find three equations. Derivative = 1/2 when x = 0 gives us b=1/2.
Solving the derivative 0= 2ax +1/2
We can then sub this into our givenequatigiven equation, leaving us with only an unknown c term. Use the point given and we find our c term.

Or use the stationary point in the derivative.

[Frozone]

Find three equations. Derivative = 1/2 when x = 0 gives us b=1/2.
Solving the derivative 0= 2ax +1/2
We can then sub this into our givenequatigiven equation, leaving us with only an unknown c term. Use the point given and we find our c term.

I don't think I understand you. I can get the b derivative , but not the others.

[Stevensmay]

Sorry the keyboard on my phone and these forums do not work well together. If you don't mind waiting a few hours I will redo it.