Mathematics Question Thread

[Shadowxo]

Hi! Could I get some help with part iii) please?

[hansolo9]

Hey guys

Is it possible to get a question in the HSC about approximating a solid of revolution using the trapezoidal or Simpson rule? Our teacher taught us this in our very last lesson but not wasn’t sure if it was actually in the syllabus

[RuiAce]

Hey guys

Is it possible to get a question in the HSC about approximating a solid of revolution using the trapezoidal or Simpson rule? Our teacher taught us this in our very last lesson but not wasn’t sure if it was actually in the syllabus

Sure, why not?

Combining concepts was never outside the scope of the course

[av-angie-er]

Hi! Could I get some help with part (i)? The solutions explain that you're meant to use the formula x/a + y/b = 1 where a = OP and b = OR to just use trigonometric ratios, but I'm not sure where this formula came from. Thanks! 

[RuiAce]

Hi! Could I get some help with part (i)? The solutions explain that you're meant to use the formula x/a + y/b = 1 where a = OP and b = OR to just use trigonometric ratios, but I'm not sure where this formula came from. Thanks! 

This was already addressed in the compilation.

Note, however, that the form x/a + y/b = 1 is referred to as the "two-intercept" form. This is a rarely used formula and usually unnecessary.

[sidzeman]

Hey could someone please explain how to do part ii to me please

[Zaye]

Hi, I really need help with similarity- basically its whole concept and rules and approach to questions i.e the fundamental steps.
thanks

[EEEEEEP]

Hey could someone please explain how to do part ii to me please

Hint: ln (e^x) = x

1. Sub the Intensity in the equation,
2. divide both sides by 10^-12
3. Times both sides by ln

The answer  should be 90.

[RuiAce]

Hi, I really need help with similarity- basically its whole concept and rules and approach to questions i.e the fundamental steps.
thanks

Start by recognising what similarity is. Two triangles are similar if one's basically another, stretched.

Then, know your tests.
1. Equiangular (two angles equal)
2. All three sides in proportion
3. Two sides in proportion, included angle equal

Of course, 1 appears the most, and you should always watch out for two angles being equal. But 3 also appears occasionally. (2 is, however, rarer.)
Know the tests, because they are self explanatory - they describe what they require FOR you (unlike congruency, which involves abbreviations). Then, think about which is appropriate.

Those are some general tips, but if you need serious help you should provide examples of questions you're struggling on, for a clearer thought process to be illustrated.

[_____]

When they tell us to "deduce" does this imply any restrictions on getting to the result, or can we just show it in any way possible?

This is an example:



Can I just express SQRT(A1) and SQRT(A2) and add them to show they equal SQRT(A)? This isn't exactly what the answer does (see below) so I'd like to make sure I'd get the marks.



Thanks

Edit:

Hey guys

Is it possible to get a question in the HSC about approximating a solid of revolution using the trapezoidal or Simpson rule? Our teacher taught us this in our very last lesson but not wasn’t sure if it was actually in the syllabus

Just to make sure I know how to do this, are these the correct steps?

1. approximate the area
2. square this result
3. multiply it by pi

[av-angie-er]

This was already addressed in the compilation.

Note, however, that the form x/a + y/b = 1 is referred to as the "two-intercept" form. This is a rarely used formula and usually unnecessary.

That makes it much clearer, thanks so much!

[RuiAce]

When they tell us to "deduce" does this imply any restrictions on getting to the result, or can we just show it in any way possible?

This is an example:

(Image removed from quote.)

Can I just express SQRT(A1) and SQRT(A2) and add them to show they equal SQRT(A)? This isn't exactly what the answer does (see below) so I'd like to make sure I'd get the marks.

(Image removed from quote.)

Thanks

Edit:

Just to make sure I know how to do this, are these the correct steps?

1. approximate the area
2. square this result
3. multiply it by pi

"Deduce" is pretty much another (but actually a stronger) way of saying hence.

Also, the word similar was given in the question, so if you find that some result follows the exact same lines of working (in which here, it does, just in a different triangle), you are allowed to use the word similarly.

That "deduce" is there for a reason. Trying to add \(\sqrt{A_1}\) and \(\sqrt{A_2}\) by brute force (i.e. without your expression for \( \sqrt{\frac{A_1}{A_2}}\) ) will be extremely messy somewhat messier, unless you make an algebra mistake.
________________________________

[sidzeman]

For the geometric series question, I got part 1 correct (cos squared theta if im remembering correctly), but cant do part ii.

For the similar triangles question Im not sure how to do part ii - Im never quite sure on how to approach plane geo questions

c) How are we meant to show part iii?

The working out for 10 is weird could someone also tell me what their answer was with working out?
Sorry for the spam thanks so much in advance guys

[RuiAce]

For the geometric series question, I got part 1 correct (cos squared theta if im remembering correctly), but cant do part ii.

For the similar triangles question Im not sure how to do part ii - Im never quite sure on how to approach plane geo questions

c) How are we meant to show part iii?

The working out for 10 is weird could someone also tell me what their answer was with working out?
Sorry for the spam thanks so much in advance guys

The first one was already addressed (and will potentially be added to the compilation)

You should either copy out the diagram and annotate this, or print off the diagram and then annotate it. You should also annotate further knowing that you now have a pair of congruent triangles, therefore all sides on the triangle are equal.


To what extent was it obvious - I do not know. But the diagram really looked suspicious - the three congruent triangles were just staring at me after I looked hard enough.

_______________________

Label some more information on your diagram.

[RuiAce]

For the geometric series question, I got part 1 correct (cos squared theta if im remembering correctly), but cant do part ii.

For the similar triangles question Im not sure how to do part ii - Im never quite sure on how to approach plane geo questions

c) How are we meant to show part iii?

The working out for 10 is weird could someone also tell me what their answer was with working out?
Sorry for the spam thanks so much in advance guys