HSC Maths Ext2 Questions + Answers (1 Viewer)

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Post your questions here and I'll try my best to answer them, doesn't matter how hard they are, I just want some practise and it's good to have a thread for this.

You can also look here for some practise questions yourself if you're bored or studying.
 

5uMath

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here is a hard one, please have full working out
This is 3 unit binomial probabiliy. Set up a binomial distribution in the form X~Bi(n,p) then use the formula P(X=x) = nCx × (1-p)^(n-x) × p^x. Whats so hard is that its very worded and you need to apply different conditions for each situation, as given byhe question. Although this may not be the case for everything, look back at 3 unit Y11 probability.
 
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here is a hard one, please have full working out
Yep, this one is actually an application of binomial probability - an extension 1 topic that's no longer covered in ext2. This question is hard mainly because of all the reading-and-understanding - it's very wordy.
 

Arrowshaft

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This is fairly easy but I think it‘s pretty nice. I was inspired by Margaret Grove’s erroneous statement in the old Maths in Focus textbook that 1/x is discontinuous at x=0 two years ago in year 11.

 
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Drongoski

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Binomial distribution is written B(n,p), not Bi(n,p).
 

fan96

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This is fairly easy but I think it‘s pretty nice. I was inspired by Margaret Grove’s erroneous statement in the old Maths in Focus textbook that 1/x is discontinuous at x=0 two years ago in year 11.

When we discuss real-valued functions it's often convenient or more practical for us to take "continuous" to mean "continuous on ".
Most people accept this because whatever meaning we take is usually clear to the reader from context.

In this case it is (probably) not, so you should be more specific about what is meant for a function to be continuous or differentiable.
 

stupid_girl

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This is fairly easy but I think it‘s pretty nice. I was inspired by Margaret Grove’s erroneous statement in the old Maths in Focus textbook that 1/x is discontinuous at x=0 two years ago in year 11.

f is continuous and differentiable everywhere in its domain.
 

CM_Tutor

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When we discuss real-valued functions it's often convenient or more practical for us to take "continuous" to mean "continuous on ".
Most people accept this because whatever meaning we take is usually clear to the reader from context.

In this case it is (probably) not, so you should be more specific about what is meant for a function to be continuous or differentiable.
I agree with fan96, it is worth bearing in mind that

being continuous and differentiable throughout its domain and that it has a discontinuity at are not incompatible when considering continuity on . Yes, there is an issue to be considered here when a question or statement is ambiguous, but don't let being right in a technical sense get in the way of answering what is intended by a question, even if it is poorly expressed... and if necessary, include both answers.

Question: Is a continuous function?

Dangerous Answer: Yes

Dangerous Answer: No

Wiser Answer: Yes, it is continuous throughout its domain, which is , but it does have a discontinuity at when considered over .
 

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