VCE Methods Question Thread!

[captkirk]

Hey everyone, I'm having trouble with this question.

http://imgur.com/a/5H3KC

The wording has gotten to me :s
Thanks in advanced -

[Shadowxo]

Hey everyone, I'm having trouble with this question.

http://imgur.com/a/5H3KC

The wording has gotten to me :s
Thanks in advanced -

For this, you just have to remember your formulas. E(aX+b)=aE(X)+b    and     Var(aX+b)=a²Var(X)
We know E(Y) = Var(Y) so
E(aX+6) = Var(aX+6)
a*E(X)+6=a²*Var(X)
Subbing in the values provided for E(X) and Var(X),
a+6=a²
a²-a-6=0
(a-3)(a+2)=0
a=3 or a=-2, a is positive so
a=3

b) is just subbing in

[captkirk]

For this, you just have to remember your formulas. E(aX+b)=aE(X)+b    and     Var(aX+b)=a²Var(X)
We know E(Y) = Var(Y) so
E(aX+6) = Var(aX+6)
a*E(X)+6=a²*Var(X)
Subbing in the values provided for E(X) and Var(X),
a+6=a²
a²-a-6=0
(a-3)(a+2)=0
a=3 or a=-2, a is positive so
a=3

b) is just subbing in

Thank you for the quick response

[Lil_Coccinellidae]

Hey, I was wondering how together my Casio to answer in fractions? Model fx-CP400. I've tried changing the button to standard, and it's still answering in decimals. The answer provided by VCAA says 16/81 which is 0.1975308642, which is what I got on my calculator, but the problem is that the decimal once typed into the cas does not equate to the fraction (not enough decimal places). This is for a probability question on the 2016 exam 1, Question 4, and it's not the first time this has happened for a VCAA examination paper.

[Shadowxo]

Hey, I was wondering how together my Casio to answer in fractions? Model fx-CP400. I've tried changing the button to standard, and it's still answering in decimals. The answer provided by VCAA says 16/81 which is 0.1975308642, which is what I got on my calculator, but the problem is that the decimal once typed into the cas does not equate to the fraction (not enough decimal places). This is for a probability question on the 2016 exam 1, Question 4, and it's not the first time this has happened for a VCAA examination paper.

Exam 1 is calculator free so you'd need to do it by hand and hence get the answer as a fraction.
Usually in calculator sections like exam 2, the answer will be in decimals so you don't have to worry about converting it to a fraction
If it's a calculator section I'd expect they'd accept answers in decimals even if it's written as a fraction on the solutions

[A TART]

How would I do this question without a calculator?
If sin x=0.3, co α=0.6 and tan θ=0.7, find the values of:

tan(π/2−θ)

[Opengangs]

How would I do this question without a calculator?
If sin x=0.3, co α=0.6 and tan θ=0.7, find the values of:

tan(π/2−θ)

[VanillaRice]

How would I do this question without a calculator?
If sin x=0.3, co α=0.6 and tan θ=0.7, find the values of:

tan(π/2−θ)

Nice answer by Opengangs 

Since the cotangent function isn't covered in Methods, I'd like to add the following to derive the property which Opengangs used (especially for those who don't do Specialist):

Recall the definition of tan

Now, use your complementary properties for sin(π/2−θ) and cos(π/2−θ) to rewrite the expression in terms of tan(θ).


Hope this helps

[TheCommando]

http://imgur.com/a/DwVSl
For. 3b why is my working out wrong
And how do i do 5a

[evandowsett]

Hey Commando,

For 3b: You don't need to -- the 0.1875. It just needs to stay as -0.5 - 0.1875 you don't subtract the negative because it's still in the first stage of the integration. We would subtract the negative when subbing in 0 for x, but because it's 0 we just 'ignore' it. The answer should be -0.6875.

For 5a: It's a parabola. You could expand it out and sketch it from there, or simply sketch it straight away. Figuring out your t-intercepts by letting f(t)=0, you get t=5 and t=11. From here you could expand and use -b/2a to find your turning point, or derive and let f'(t)=0. We can also see that it's a negative parabola because it will expand to have a negative in front of the t^2 term.

Make sense?

[Shadowxo]

http://imgur.com/a/DwVSl
For. 3b why is my working out wrong
And how do i do 5a

Also for 3b) somehow a negative appeared in the first line, it should be integral of 12x²-12x³, not -12x²-12x³.

Hence, you don't need the double negative.

For 5a) I don't think you'd be required to find the turning point, as long as you have at least 2 points marked and they don't explicitly ask for it
You should (almost always) find the x (in this case t) and y intercepts though. From the formula you can see the t intercepts are t=5 and t=11, letting t=0 shows the y intercept is -55/36. And, as evandowsett said, you can see the coefficient of the t² term is negative, hence it will be a negative parabola. This should give you enough info to sketch it

[gnaf]

hello

how do I do this question? I got d, but the answer is e

[Shadowxo]

hello

how do I do this question? I got d, but the answer is e

I think you're right, that's what I got as well. It's probably a mistake in the book, if it's non-zero between 1 and 3, the mean shouldn't be at 3 - the end point shouldn't be the average.

[TheCommando]

Thank you!
But sorry i meant 5b

[Shadowxo]

Thank you!
But sorry i meant 5b

Since it's a probability density function, the area under the graph represents the probability. So, the probability that symptoms appear within the first 7 days is the integral of the formula between t=5 and t=7 (ie the area under the graph between t=5 and t=7)

Note: The probability density function is essentially 0 when t<5 or t>11, and f(t) between t=5 and t=11 (as you can't have a negative probability)