king's property (1 Viewer)

tito981

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Is King's property assumed knowledge or are they more likely to tell you to derive it before using?
 

icycledough

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Is King's property assumed knowledge or are they more likely to tell you to derive it before using?
Not going to lie, having done Extension 2 last year, I've never come across the King's property nor have I seen it in writing anywhere (whether in a textbook, exam or in the syllabus)
 

CM_Tutor

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The King property has appeared in MX2 and 4u Maths exams (HSCs and Trials) over many years. I don't recall a case where it was needed in an HSC without a suitable introduction, so I certainly would not take it as assumed knowledge... though it is a technique of which all MX2 students should be aware. I also can't recall having seen it mentioned in an HSC context as the "King property". In any case, it is the property that


that is usually introduced with a substitution. It is perhaps best known for questions like


where it allows us to show that


and thus gives the simplification, on adding equations (1) and (2)


It can be applied to solving integrals like




and



 

mathsbrain

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The King property has appeared in MX2 and 4u Maths exams (HSCs and Trials) over many years. I don't recall a case where it was needed in an HSC without a suitable introduction, so I certainly would not take it as assumed knowledge... though it is a technique of which all MX2 students should be aware. I also can't recall having seen it mentioned in an HSC context as the "King property". In any case, it is the property that


that is usually introduced with a substitution. It is perhaps best known for questions like


where it allows us to show that


and thus gives the simplification, on adding equations (1) and (2)


It can be applied to solving integrals like




and



how do we do the last two?
 

5uckerberg

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how do we do the last two?
For this one
We will first let
Next step change the variables and there it becomes
The next step is the fun step because we will be doing here is this. We want . In turn, to retrieve from is to multiply by and there we have noting that u is the dummy variable. Notice anything here, J=1-I
therefore, we have
 
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5uckerberg

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I think the first one could be in the HSC because it comes from the syllabus. However the second one I really think a little bit of hand-holding is needed to complete the question. Otherwise you will get nowhere.
 

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CM_Tutor

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I think the first one could be in the HSC because it comes from the syllabus. However the second one I really think a little bit of hand-holding is needed to complete the question. Otherwise you will get nowhere.
Fair point. If this was an HSC question, it would likely tell you to use before the King property.
 

stupid_girl

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Does this one require a little bit of hand-holding?:p






By the way, there are variants that I often find more useful.

Two common cases are b=-a and b=0.



One more example for fun:









 

5uckerberg

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Does this one require a little bit of hand-holding?:p






By the way, there are variants that I often find more useful.

Two common cases are b=-a and b=0.



One more example for fun:



Now, suppose







Actually do you mean . If that is the case then surely it exists and is the general form of the King Property. I reckon a little introduction might help and the rest is just what they were taught.
 
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