Maths Ext 2 Predictions (2 Viewers)

[appleali]

Actually, the word "plane" is used everywhere in HSC Maths e.g. "complex plane", "x-y plane" or "inclined plane". It's even in one of the vector topic dot points:
View attachment 45037
Seems pretty obvious that students are expected to know what the word "plane" actually means.

Even if they don't explicitly use the word "plane" there is no reason why they can't just synonymously label it as a region or a set of points in the number space that satisfies a set of conditions.

What I mean in my earlier post is that there is nothing stopping them technically asking something like this:
View attachment 45039

If we honestly think they can't use the word "plane", then what's stopping them replacing the word "plane P" with "region R" or "a set of points P"?

The point is that students can answer this question with the tools they have within the syllabus and it doesn't require knowledge outside the syllabus. All you need to do is compute the dot product of two perpendicular vectors to derive the result. This is simply an "application" of something in the syllabus to explore something unfamilar.

If you want to dismiss this as being "outside of syllabus", then you do so at your own risk. The HSC exams have time and time again proven otherwise throughout history because they can lean on this "application" side of the syllabus (which is why Ext2 has this reputation for being so challenging in the first place).

at this point is it worth it learning it

 

[K2Trappy]

guys i been getting around high 80s for some trial papers (nsb, sths, ruse)
how difficult are these papers in comparison to hsc?

high 80s... r we doing the same papers bruh

 

[Trebla]

at this point is it worth it learning it

You don't need to "learn" about the equations of planes per se, but you shouldn't be surprised if something like this pops up the in HSC. The only thing to "learn" is really to broaden your familiarity with applications of dot product.

 

[C2H6O]

I got this question in one of my school's past papers... No clue how to do any of it, so if it comes up in the exam tmr I'm cooked

 

[C2H6O]

high 80s... r we doing the same papers bruh

Same bro I did those papers and got mid 70s at BEST, some nearly 60

 

[appleali]

watch me get 50 in the hsc

 

[appleali]

View attachment 45049

I got this question in one of my school's past papers... No clue how to do any of it, so if it comes up in the exam tmr I'm cooked

i believe this is not covered by the syllabus as i requires the triple product i think

 

[ringading]

high 80s... r we doing the same papers bruh

fr i get above 68s but DEFINITELY below 80

 

[ringading]

watch me get 50 in the hsc

no fr goal is to get at least 65 to get scaling to at least 90 smt

 

[ringading]

i believe this is not covered by the syllabus as i requires the triple product i think

really? i swear we've done that b4 idk could be wrong

 

[appleali]

triple product is definitely not covered

 

[appleali]

View attachment 45049

I got this question in one of my school's past papers... No clue how to do any of it, so if it comes up in the exam tmr I'm cooked

if you think about it, for i you can show coplanarity by showing either:
- the lines are parallel
- the lines intersect at a point

 

[K2Trappy]

triple product is definitely not covered

nah it was in my school trials, u basically let some parameter equal each of the components, so for x => 2a+2 then u get ur vector line, and show direction vectors are parallel which implies same plane

 

[appleali]

nah it was in my school trials, u basically let some parameter equal each of the components, so for x => 2a+2 then u get ur vector line, and show direction vectors are parallel which implies same plane

elaborate

 

[K2Trappy]

elaborate

on which part? finding the line or co-planarity (is that even a word)

 

[K2Trappy]

elaborate

also out of the papers u have done, which one have u found challenging? i need to go to sleep crying and suffering

 

[Edward34245]

Actually, the word "plane" is used everywhere in HSC Maths e.g. "complex plane", "x-y plane" or "inclined plane". It's even in one of the vector topic dot points:
View attachment 45037
Seems pretty obvious that students are expected to know what the word "plane" actually means.

Even if they don't explicitly use the word "plane" there is no reason why they can't just synonymously label it as a region or a set of points in the number space that satisfies a set of conditions.

What I mean in my earlier post is that there is nothing stopping them technically asking something like this:
View attachment 45039

If we honestly think they can't use the word "plane", then what's stopping them replacing the word "plane P" with "region R" or "a set of points P"?

The point is that students can answer this question with the tools they have within the syllabus and it doesn't require knowledge outside the syllabus (i.e. notice it's not asking you to recall the equation of a plane). All you need to do is compute the dot product of two perpendicular vectors (with a bit of work to figure out what those vectors are) to derive the result. This is simply an "application" of something in the syllabus to explore something unfamilar.

If you want to dismiss this as being "outside of syllabus", then you do so at your own risk. The HSC exams have time and time again proven otherwise throughout history because they can sneakily lean on this "application" side of the syllabus (which is why Ext2 has this reputation for being so challenging in the first place).

Any chance you have worked solutions for this? How fo you find the two perpendicular vectors with the given information?

 

[C2H6O]

elaborate

I think it goes like this:

set the line equal to λ
(x-2)/2=(Y+1)/-1=(z-4)/3=λ

x=2λ+2, y=-λ-1, z=3λ+4

Now just put that in ijk notation and you've got your line equation

line = (2 -1 4) + λ(2 -1 3)

then prove coplanarity using what you said earlier, prove the vectors intersect or are parallel

no clue how to do ii though

 

[K2Trappy]

I think it goes like this:

set the line equal to λ
(x-2)/2=(Y+1)/-1=(z-4)/3=λ

x=2λ+2, y=-λ-1, z=3λ+4

Now just put that in ijk notation and you've got your line equation

line = (2 -1 4) + λ(2 -1 3)

then prove coplanarity using what you said earlier, prove the vectors intersect or are parallel

no clue how to do ii though

im prob very wrong but for ii could u use one of the points on either line, and have the difference of direction vectors be the resultant direction? or have any point on both lines and just have that difference as the direction vector?

 

[appleali]

also out of the papers u have done, which one have u found challenging? i need to go to sleep crying and suffering

bruh i am not that good at maths imma get 52 tmrw
probably ruse/nsb are the hardest ones i've done? abbotsleigh was kinda hard as well