Will you be penalised if you prove it as RHS = LHS (2 Viewers)

[obviouslyme]

Hey guys, so when a question says, "Prove/show that expression x = expression y"
Can you start from RHS like this:
RHS = expression y
=...
=expression x
= LHS

Will you be penalised? Because sometimes i can't see how to work from LHS to RHS (especially when LHS is simplified and RHS is expanded). I've asked my teacher and she said, "The marker won't like it, yes you will get penalised". So i reckon that's too risky to do it in internal assessments but how about a HSC exam? Thanks!

If you don't understand what i mean, here's an example

Show that u/(u+1) = 1 - 1/(u+1)

And well i can't do it from LHS, so i go
RHS = 1 - 1/(u+1)
= (u+1) - 1 / (u+1)
= u/ (u+1)
= LHS

Also if you can, can you show me how to get from a simplified version to an expanded one? Thanks guys

 

[QZP]

Hey guys, so when a question says, "Prove/show that expression x = expression y"
Can you start from RHS like this:
RHS = expression y
=...
=expression x
= LHS

Will you be penalised? Because sometimes i can't see how to work from LHS to RHS (especially when LHS is simplified and RHS is expanded). I've asked my teacher and she said, "The marker won't like it, yes you will get penalised". So i reckon that's too risky to do it in internal assessments but how about a HSC exam? Thanks!

If you don't understand what i mean, here's an example

Show that u/(u+1) = 1 - 1/(u+1)

And well i can't do it from LHS, so i go
RHS = 1 - 1/(u+1)
= (u+1) - 1 / (u+1)
= u/ (u+1)
= LHS

Also if you can, can you show me how to get from a simplified version to an expanded one? Thanks guys

LHS = u/(u+1)
= (u+1) - 1 / (u+1)
= 1 - 1/(u+1)
= RHS

 

[RealiseNothing]

It's fine.

 

[study1234]

Yes, you work from either LHS to RHS or RHS to LHS. A general tip is to work from the more 'complex' or longer side to the 'simpler' side.

 

[braintic]

Who knows why some teachers have rules like this. Of course you can go right from right to left, there's no difference.
Some idiotic teachers will even penalise when solving equations and inequations if you write
2=x
or
2>x
I know one who will even penalise for writing b+a instead of a+b.

 

[seanieg89]

Who knows why some teachers have rules like this. Of course you can go right from right to left, there's no difference.
Some idiotic teachers will even penalise when solving equations and inequations if you write
2=x
or
2>x
I know one who will even penalise for writing b+a instead of a+b.

Some of the things I got marked wrong for in high school were just ridiculous.

Eg1. A question showed a graph and asked you to provide a possible function which had this graph.
Apparently my |1-x| was incorrect, because the marker was looking for |x-1|.

Eg2. A marker did not understand my use of the converse of Pythagoras to establish that two things were perpendicular, so assumed it was wrong.

Not to mention countless simple arithmetic answers leading to the answers simply being wrong.

Good to see such intelligent people charged developing the quantitative skills of future generations.

 

[Kiraken]

Hey guys, so when a question says, "Prove/show that expression x = expression y"
Can you start from RHS like this:
RHS = expression y
=...
=expression x
= LHS

Will you be penalised? Because sometimes i can't see how to work from LHS to RHS (especially when LHS is simplified and RHS is expanded). I've asked my teacher and she said, "The marker won't like it, yes you will get penalised". So i reckon that's too risky to do it in internal assessments but how about a HSC exam? Thanks!

If you don't understand what i mean, here's an example

Show that u/(u+1) = 1 - 1/(u+1)

And well i can't do it from LHS, so i go
RHS = 1 - 1/(u+1)
= (u+1) - 1 / (u+1)
= u/ (u+1)
= LHS

Also if you can, can you show me how to get from a simplified version to an expanded one? Thanks guys

if you get penalised for doing RHS=LHS your teacher has no respect for maths lol

 

[asianese]

What you can also do is:

Prove LHS = RHS

You can do:

LHS = ... = ... = ... = other expression.

(and then separately)

RHS = ... = ... = ... = ... = ... = same 'other expression' as above.

Hence LHS = RHS

 

[tywebb]

Yeah. That's based on Euclid's common notion 1 which states that

Things which equal the same thing also equal one another.

Ask your teacher have they read Euclid. If not change your teacher. Or tell the teacher to go away, read it and don't come back till they have finished.

 

[QZP]

What you can also do is:

Prove LHS = RHS

You can do:

LHS = ... = ... = ... = other expression.

(and then separately)

RHS = ... = ... = ... = ... = ... = same 'other expression' as above.

Hence LHS = RHS

But isn't that a 'show' not a 'prove'? I've lost marks doing that.

 

[tywebb]

If you've shown a=c and that b=c then you've proved a=b

 

[asianese]

Everything except maybe approximately's are transitive so a=b and b=c implies a=c.

 

[tywebb]

This thread has probably more to do with what the teacher can understand and how limitations in their knowledge and understanding may lead to incorrect marking of students 100% correct mathematics.

This is very unfair if one student does it correctly and gets 100% because their teacher is qualified, whereas another who does exactly the same thing but looses marks because their teacher is unqualified and doesn't know what they are doing.

 

[obviouslyme]

But isn't that a 'show' not a 'prove'? I've lost marks doing that.

I don't really get the difference between show and prove in maths haha. Aren't they the same thing?

And thanks for the replies guys!

 

[asianese]

It's basically the same thing, especially for the HSC.

 

[QZP]

I don't really get the difference between show and prove in maths haha. Aren't they the same thing?

And thanks for the replies guys!

Shows are a subset of proofs. You cannot prove something by showing. It is to do with formality/rigor. At least this is how I learnt it.

Example of show a = c
LHS: a = b
RHS: c = b

Therefore I have shown a = c as they converge to the same value b.

Example of prove a = c
LHS: a = b = c = RHS

Therefore I have proven a = c as (you can think of it like this) c is derived from a.

 

[asianese]

You've used the word converge in a very incorrect context... there is nothing converging to anything the way you've written it.

Proofs may be thought of as a larger entity, for example, Prove that the derivative of the exponential function is itself.

And then it could be broken into parts like: Show, using the definition of the derivative that... and then another part: Show that ... and all these make up the 'proof'.

But certainly in the HSC sense there is really no difference in the word.

 

[QZP]

Converge: to come together or meet

If I have some weird LHS expression that goes to a certain expression. And some entirely different RHS expression that goes to the same aforementioned expression. Then you can think of the LHS and RHS coming together and meeting to the same expression i.e. converging.

LHS --> middleman expression < --- RHS

Is that more visual for you

 

[asianese]

Converge: to come together or meet

If I have some weird LHS expression that goes to a certain expression. And some entirely different RHS expression that goes to the same aforementioned expression. Then you can think of the LHS and RHS coming together and meeting to the same expression i.e. converging.

LHS --> middleman expression < --- RHS

Is that more visual for you

Lol. There is nothing 'moving' or 'converging' here at all. The fact that the LHS = RHS is a mathematical statement which is true. By you SHOWING that the LHS = RHS doesn't actually 'move' the LHS closer to the RHS at all. They are the same thing inherently, and you are just showing this to a marker.

The words converge and diverge are used quite explicitly in terms of infinite series (and limits in general), which you learn about in university (LOLJOKES 2U series ahem |r|<1, and lim x->0 sinx/x). Don't use the word lightly because it has some important mathematical ramifications.

An example of this would be: The series

 

[QZP]

Does that mean I can't use converge in the sense of english language to explain something? Especially when I wasn't even in the field of series/sequences (yes I know their meanings here).