VCE Methods Question Thread!

[TheCommando]

12. If you're finding the probability you don't pick a black ball 3 times (ie you get 0 black balls), it's (6/10)³ ie probability you pick a red ball every time. If you're finding the probability you get 3/3 black balls, it would be (4/10)³. If it's replaced that means you put it back in after you take it out. Not replaced means it's taken out and not put in, therefore decreasing the total number of balls by 1 each time

15. It is a bit ambiguous, it didn't say the sum of the numbers was noted. In the exam they would be more specific though, so don't worry

PS you didn't link Q16 and 17. What exactly got you stuck though?

Also how do u get pr(x) =1, 2 and 3
I have no idea

[Shadowxo]

Also how do u get pr(x) =1, 2 and 3
I have no idea

Bit rusty but there should be a formula for it- basically the probability of a certain outcome happening times number of ways to get the outcome
So for 1 black ball, you'd need 1 black and 2 red. Probability of getting black red red is 4/10 * 6/10 * 6/10. Number of ways of getting one black and two red is 3C1 = 3
So we end up with 3* 4*6*6/1000 or just multiplying these values.

[Andyling]

Hey Guys, I'm currently doing methods 1-2 (in year 10) and will do 3-4 next year. Does anybody know what sort of exam mark and average sac mark I need to get a SS of 40?

[Shadowxo]

Hey Guys, I'm currently doing methods 1-2 (in year 10) and will do 3-4 next year. Does anybody know what sort of exam mark and average sac mark I need to get a SS of 40?

Hi!
I'd recommend you check this out Methods Grade Distributions for Assessments
To get a 40+ you'd be wanting a minimum of A/A/A but that would probably get you just below 40. If you get A+/A/A (any way around), you'd probably be looking at around 40.
For some context, the subject I got A/A/A in I received 38, and the subjects I got A+/A+/A and A+/A+/A+ I received 42

Hope this helps a bit I'm sure others can be more specific

[Andyling]

Ah thanks, and around what sac average (%) did you need to get for an A/A+

[Shadowxo]

Ah thanks, and around what sac average (%) did you need to get for an A/A+

I got 90-95% and got A+ (second in school for SAC marks, equal first overall)
I'd probably say for A+ you'd need 90-95 depending on your cohort and school, 85+ for A, again depending on cohort and school

[Andyling]

Cheers, was very helpful.

[LPadlan]

Hey, if anyone could show full working out with the following questions that would be great.

1.Given that the function f has rule of the form f(x)=ax^2+bx and f(1)=6 and f '(1)=0, find the values of a and b.
2.The gradient of the curve with equation y=a/x +bx^2 at the point with coordinates (3,6) is 7. Calculate the values of a and b
3. The tangent to the function y=ax+b/x^2 has a stationary point at (-1,-6) write two simultaneous equations in terms of a and b and then find the equation for the function

[Shadowxo]

Hey, if anyone could show full working out with the following questions that would be great.

1.Given that the function f has rule of the form f(x)=ax^2+bx and f(1)=6 and f '(1)=0, find the values of a and b.
2.The gradient of the curve with equation y=a/x +bx^2 at the point with coordinates (3,6) is 7. Calculate the values of a and b
3. The tangent to the function y=ax+b/x^2 has a stationary point at (-1,-6) write two simultaneous equations in terms of a and b and then find the equation for the function

Most of these are pretty standard, I'd recommend going over how to differentiate etc.
I'll do 1) as an example, you should be able to do the rest
We know f(1)=6, so if x=1, y=6
So 6=a*1+b*1
f'(x)=2ax+b using standard derivatives
f'(1)=0 so when x=1,y=0
So 0=2a+b so b= -2a
Substituting into the earlier equation:
6=a-2a = -a
a=-6
b= -2a = 12

[LPadlan]

This is probably common sense to a lot of you, but please help
How do you find the antiderivative of sin(Theta-pi/3)

[syubi]

When you are given the margin of error (say 2%) and are asked to find the sample size, do you round n to an integer? I'm confused because if you round n up or down to an integer, the margin of error would not be exactly 2%?

[Shadowxo]

When you are given the margin of error (say 2%) and are asked to find the sample size, do you round n to an integer? I'm confused because if you round n up or down to an integer, the margin of error would not be exactly 2%?

Yes you need to round n. You want the margin of error to be less than or equal to 2%, (ie not bigger than 2%) so you'd round n up so it's both a whole number and results in a margin of error of less than or equal to 2%

This is probably common sense to a lot of you, but please help
How do you find the antiderivative of sin(Theta-pi/3)

The antiderivative of sin is -cos (as d/dx (cosx) = -sin(x) ) so you change the sin to -cos and divide by the derivative of the inside (as with differentiation you multiply it by the inside, you want to do the opposite). Since the derivative of a constant is 0 and the derivative of theta is just 1, you divide by 1
So you end up with -cos(theta-π/3)

[LPadlan]

Yes you need to round n. You want the margin of error to be less than or equal to 2%, (ie not bigger than 2%) so you'd round n up so it's both a whole number and results in a margin of error of less than or equal to 2%
The antiderivative of sin is -cos (as d/dx (cosx) = -sin(x) ) so you change the sin to -cos and divide by the derivative of the inside (as with differentiation you multiply it by the inside, you want to do the opposite). Since the derivative of a constant is 0 and the derivative of theta is just 1, you divide by 1
So you end up with -cos(theta-π/3)

Hey, thanks for the reply! But, on my calculator it says the antiderivative of sin(theta-pi/3) is -cos(theta+pi/6)x

[Sine]

Hey, thanks for the reply! But, on my calculator it says the antiderivative of sin(theta-pi/3) is -cos(theta+pi/6)x

One thing to keep in mind about antiderivitives (especially trig) is that the you will have "different answers" that are equivalent.

To check your answer simply input this into the graphing screen "your answer" - "calculator answer" since the difference between these antiderivitives will be a constant you will see that you recieve a horizontal line (not always y = 0) since the difference could be 2.5 which would yield a line at y=2.5

[Shadowxo]

Hey, thanks for the reply! But, on my calculator it says the antiderivative of sin(theta-pi/3) is -cos(theta+pi/6)x

If you're doing this on your calculator make sure you type in x instead of theta for the function, or find the integral with respect to theta instead of x.
If you integrate with respect to x it will treat everything else, even theta, as a constant.
I think your calculator treated (theta-π/3) as a constant as it didn't have x in it, and hence just added x onto the end and rewrote it. (integral of a constant is the constant * x)