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January 22, 2022, 08:31:30 am

Author Topic: QCE Maths Methods Questions Thread  (Read 14450 times)

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Phytoplankton

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Re: QCE Maths Methods Questions Thread
« Reply #45 on: October 20, 2021, 01:34:16 pm »
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Hi, I'm struggling with this question I'm not sure how the textbook gets to the answer. Would anyone be able to help?

Q: The Apache Orchard grows a very juicy apple called the Fuji apple. Fuji apples are picked and then sorted by diameter into three categories:
•   small — diameter less than 60 mm
•   jumbo — the largest 15% of the apples
•   standard — all other apples.
f) Some apples are selected before sorting and are packed into bags of 6 to be sold at the front gate of the orchard. Determine the probability, correct to 4 decimal places, that one of these bags contains at least 2 jumbo apples.

The answer given is


Hey Gracey1415,

I believe the distribution they give i.e. Y~Bi(6,0.15) is correct as the number of apples (n) is 6 and the probability of having a jumbo apple (p) is 15%=0.15. However, the probability the textbook states is incorrect. As they ask for the probability that one of these bags contains at least 2 jumbo apples, this means that the probability is actually P(Y≥2) and not P(Y≤2). From here, you can either use the binomial probability formula (on the QCAA formula sheet) or use the Bcd function on your calculator to figure the answer out. I entered it into my calculator (as I'm too lazy to algebraically work it out) and the answer was indeed 0.2235.

Hope this helps! If you have any other questions or want me to elaborate, feel free to reply back! Good luck!

Amity H

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Re: QCE Maths Methods Questions Thread
« Reply #46 on: October 26, 2021, 11:09:37 am »
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I’ve just gone back in the textbook a bit and am revising motion in a straight line (8J q 1 if anyone has the Cambridge textbook) and am a little confused on how they know where the line turns around with what you know at this point in the book. Like I could use second derivatives I think but this hasn’t been taught yet. It seems you would make the first derivative equal zero but that value doesn’t seem quite right.

Sorry I tried to attach stuff but it was either too big or was the wrong file type.

Question was x = t^2 - 6t + 8, t greater than or equal to zero, t is in mins, x is in cm
A find its initial velocity
B when does its velocity equal zero, and what is its position at this time?
C what is its average velocity for the first 4 seconds?
D determine its average speed for the first 4 seconds.

I was fine with a-c but not sure about d.

External is on Thursday so any help would be greatly appreciated. Thanks heaps!
“People don’t care about how much you know until they know how much you care.”

Graduating yr 12 in Qld 2021
I study General English, Maths Methods, Music, Biology and Latin (any fellow Latin people here?)

I’m selling methods notes (units 1-4), pm me for details.

Gracey1415

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Re: QCE Maths Methods Questions Thread
« Reply #47 on: October 27, 2021, 07:20:33 pm »
+1
I have a question with binomial probabilities and inputting into the calculator.
It is a binomial probability
with p = 0.18
and sample of 10
calculate Pr(P' < 0.2)

I have
P' = X/n = X/10
Pr(P' < 0.2) = Pr(X/10 < 0.2) = Pr(X<2)

The answers tell me in the calculator use binomial distribution function with n = 10, p=0.18
and the answer given is 0.4392.
But I can't get that I have no idea what to put in the x value part of the calculator, and should I be using binompdf or binom cdf?

Commercekid2050

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Re: QCE Maths Methods Questions Thread
« Reply #48 on: October 27, 2021, 08:52:54 pm »
+4
I have a question with binomial probabilities and inputting into the calculator.
It is a binomial probability
with p = 0.18
and sample of 10
calculate Pr(P' < 0.2)

I have
P' = X/n = X/10
Pr(P' < 0.2) = Pr(X/10 < 0.2) = Pr(X<2)

The answers tell me in the calculator use binomial distribution function with n = 10, p=0.18
and the answer given is 0.4392.
But I can't get that I have no idea what to put in the x value part of the calculator, and should I be using binompdf or binom cdf?

Hi,

It says Pr(x<2)

This does not include 2 and as this is discrete the x would become 1.

Also as it says x<2 you would be using Binominal CDF. It would be lower being 0 and higher being 1. N as you said would be 10 and the probability would be 0.18

Hope this helps.
2021 VCE- English, Math Method, Further Math,Accounting and Economics

2022-2026 Bachelors in Business (Taxation) and Accounting in Monash

bia234

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Re: QCE Maths Methods Questions Thread
« Reply #49 on: November 21, 2021, 03:07:00 pm »
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Hey guys, is anyone able to help me on how to integrate this?
I've attached the function below.

Cheers! :)

fun_jirachi

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Re: QCE Maths Methods Questions Thread
« Reply #50 on: November 21, 2021, 03:27:09 pm »
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In general, \(\int a^x \ dx = \frac{1}{\ln a} a^x + C\). (Try looking into why this is the case if you can; this will help you understand this question better. It's just a combination of log laws and the integral of the natural exponential). Can you adapt this to the function you're trying to integrate in this case?

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GreenNinja

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Re: QCE Maths Methods Questions Thread
« Reply #51 on: December 27, 2021, 07:06:50 pm »
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Hi

Could someone please show how to answer this question. I would show some working out if I am able to, however I am thoroughly confused on even beginning to answer this.

Thanks.
« Last Edit: December 27, 2021, 07:12:50 pm by GreenNinja »

fun_jirachi

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Re: QCE Maths Methods Questions Thread
« Reply #52 on: December 27, 2021, 07:49:17 pm »
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By the product rule,
\(\frac{d}{dx} e^{-3x}\sin (2x) = -3e^{-3x}\sin (2x) + 2e^{-3x}\cos (2x) = e^{-3x} (2\cos (2x) -3\sin (2x))\)
\(\frac{d}{dx} e^{-3x}\cos (2x) = -3e^{-3x}\cos(2x) - 2e^{-3x}\sin(2x) = e^{-3x} (-2\sin (2x) -3\cos(2x))\)

There's not much else to do for part b) if you get that differentiation is pretty much an inverse operation to integration.

For part c), try and manipulate the equations so that you can eliminate \(\int e^{-3x} \cos (2x) \ dx\), and thus get an integral of \(\int e^{-3x} \sin(2x) \ dx\) only, in terms of \(e^{-3x} \sin(2x) \ dx\) and \(e^{-3x} \cos (2x) \ dx\).
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