VCE Methods Question Thread!

[cosine]

Silly question, but what exactly does  mean before the function?

means we are talking about the function f(x). If our function was g(x), we would have

Is the domain of the function, in this case all real numbers and the arrow indicates 'as you approach the range', or more specifically the codomain of the function.

[2jzgte]

So you can just disregard the ?

[cosine]

So you can just disregard the ?

Well in order to fully define the function, to obtain full marks, you would have to include it.

[keltingmeith]

means we are talking about the function f(x). If our function was g(x), we would have

Is the domain of the function, in this case all real numbers and the arrow indicates 'as you approach the range', or more specifically the codomain of the function.

It's actually incorrect notation for it, but they mean to right "maps to" - so, it's read "as R maps to R".

But yes, you have to include it if you plan on writing it like f: dom ----> codom, f(x)=blah. If you just write f(x)=blah, you don't need to include it, for obvious reasons.

[cosine]

It's actually incorrect notation for it, but they mean to right "maps to" - so, it's read "as R maps to R".

But yes, you have to include it if you plan on writing it like f: dom ----> codom, f(x)=blah. If you just write f(x)=blah, you don't need to include it, for obvious reasons.

According to tsfx it's read 'as you approach the range'. Im guessing there are multiple ways of interpreting it

[keltingmeith]

According to tsfx it's read 'as you approach the range'. Im guessing there are multiple ways of interpreting it

Oh, that's what the symbol means, definitely.
But that's not what VCAA are trying to say. VCAA are famous for using bad notation (for example, R is a random variable. refers to the set of real numbers).

[2jzgte]

Solve for , expressing your answer in terms of a of base :

[keltingmeith]

Solve for , expressing your answer in terms of a of base :

Log both sides:



Apply log laws:



Solve the now-linear equation:

[2jzgte]

Thanks for the help, the explanation was very detailed.

[knightrider]

How would you do this question?

The frame of a container in the shape of a cuboid is shown at right.If it is to be made with a total length of 18 metres of steel edging, find: the value of L in terms of x

[nerdgasm]

With these sorts of questions, it's important to identify or 'pick out' what the question is asking you to do, and how the information provided is related to that goal.

So in this question, an important piece of information is, "[the frame of the container] is to be made with a total length of 18 metres of steel edging". At this point, you should ask yourself, "what does this mean/imply?" This piece of information is not simply 'fluff' in the question. What could this piece of information possibly have to do with L and/or x?
If this is where you're getting stuck, then I encourage you to think about this for a while. Try to work out how the fact that there are 18 metres of steel edging, is related to the construction of the cuboid. Look at the diagram in the question- where would the 18 metres of steel edging be used?

An answer to this part

The 18 metres of steel edging will be used to form the 12 edges of the cuboid in the diagram (note that this includes the three dotted edges). One way to show that there are 12 edges is to note that four edges make up the front face, four make up the back face, and four connect each front corner to its corresponding back corner. Furthermore, you have to use all 18 metres of steel to make the cuboid. No exceptions.

So, now you've made some progress. What do you think the next step in solving the question might be? We now have to understand how the 18 metres of steel and the 12 edges of the cuboid are related to the variables L and x. Let's start by trying to relate the 12 edges of the cuboid to L and x. Specifically, how are the lengths of the 12 edges related to L and x? Could you work out an expression for the sum of all these lengths? Again, see if you can come up with an answer to these two questions.

An answer to this part

The key idea is in noticing that the 12 edges of the cuboid are made up of 4 edges of length 'x' (these are the horizontal edges), 4 edges of length '2x' (these are the vertical edges) , and 4 edges of length 'L' (these are the ones running at an angle, and which connect the front and back face of the cuboid). What this means, is that the total length of the edges of the cuboid is 4(x) + 4(2x) + 4(L) = 4x + 8x + 4L = 12x + 4L.

Hopefully, at this point, you're having a "Eureka!" moment. If not, think about what you know now. From what you just did, you have a formula that relates the total length of the edges of the cuboid to the variables x and L (total length = 12x+4L). But hang on! What about what we found out at the very beginning? You have to use all 18 metres of steel to make the cuboid. No exceptions. Surely there is some connection between these two facts. What could it be?

An answer to this part

The formula tells us that the total length of the edges of the cuboid is 12x + 4L. However, the key point is to realise that because the 18 metres of steel edging will be used to make the cuboid (specifically the edges of the cuboid), then the total length of the edges of the cuboid MUST be 18 metres as well. Because we now have two expressions for the exact same thing, we can equate them. That is, 12x + 4L = 18 = the total length of the cuboid edges.

And now, we have finally pulled out the algebraic expression that lets us express L in terms of x (it was 12x + 4L = 18). Notice that this algebraic expression is not particularly difficult to solve - it was 'nutting out' the algebraic expression that was the tough part. I'll pose you one final challenge: this problem was posed in a 'real-world' context. You weren't simply asked to solve 12x + 4L = 18. These values are lengths of a (presumably) real-world object. Can you work out what values would make sense 'in the real world' for L and x?

I hope that this post has made the thinking process behind solving 'worded questions' such as these ones a bit easier. With practice, you'll naturally get better at extracting and interpreting the key information from questions such as these. At some point you may even find that upon looking at the question, the key bits of information and how to use them together to solve the question will 'jump out' at you. This is a part of 'mathematical intuition' - and by learning to approach questions in this way, you're developing it.

Of course, not all problems will be this simple. Some problems will really require a lot of work and insight in order to put together, identify, and even deduce important pieces of information that might not be apparent in the question stem. But this kind of approach and thinking (along with many other methods and processes in mathematics) will hopefully help you to approach such questions without much fear, both in VCE, and (if you so choose) beyond.

[knightrider]

With these sorts of questions, it's important to identify or 'pick out' what the question is asking you to do, and how the information provided is related to that goal.

So in this question, an important piece of information is, "[the frame of the container] is to be made with a total length of 18 metres of steel edging". At this point, you should ask yourself, "what does this mean/imply?" This piece of information is not simply 'fluff' in the question. What could this piece of information possibly have to do with L and/or x?
If this is where you're getting stuck, then I encourage you to think about this for a while. Try to work out how the fact that there are 18 metres of steel edging, is related to the construction of the cuboid. Look at the diagram in the question- where would the 18 metres of steel edging be used?

An answer to this part

The 18 metres of steel edging will be used to form the 12 edges of the cuboid in the diagram (note that this includes the three dotted edges). One way to show that there are 12 edges is to note that four edges make up the front face, four make up the back face, and four connect each front corner to its corresponding back corner. Furthermore, you have to use all 18 metres of steel to make the cuboid. No exceptions.

So, now you've made some progress. What do you think the next step in solving the question might be? We now have to understand how the 18 metres of steel and the 12 edges of the cuboid are related to the variables L and x. Let's start by trying to relate the 12 edges of the cuboid to L and x. Specifically, how are the lengths of the 12 edges related to L and x? Could you work out an expression for the sum of all these lengths? Again, see if you can come up with an answer to these two questions.

An answer to this part

The key idea is in noticing that the 12 edges of the cuboid are made up of 4 edges of length 'x' (these are the horizontal edges), 4 edges of length '2x' (these are the vertical edges) , and 4 edges of length 'L' (these are the ones running at an angle, and which connect the front and back face of the cuboid). What this means, is that the total length of the edges of the cuboid is 4(x) + 4(2x) + 4(L) = 4x + 8x + 4L = 12x + 4L.

Hopefully, at this point, you're having a "Eureka!" moment. If not, think about what you know now. From what you just did, you have a formula that relates the total length of the edges of the cuboid to the variables x and L (total length = 12x+4L). But hang on! What about what we found out at the very beginning? You have to use all 18 metres of steel to make the cuboid. No exceptions. Surely there is some connection between these two facts. What could it be?

An answer to this part

The formula tells us that the total length of the edges of the cuboid is 12x + 4L. However, the key point is to realise that because the 18 metres of steel edging will be used to make the cuboid (specifically the edges of the cuboid), then the total length of the edges of the cuboid MUST be 18 metres as well. Because we now have two expressions for the exact same thing, we can equate them. That is, 12x + 4L = 18 = the total length of the cuboid edges.

And now, we have finally pulled out the algebraic expression that lets us express L in terms of x (it was 12x + 4L = 18). Notice that this algebraic expression is not particularly difficult to solve - it was 'nutting out' the algebraic expression that was the tough part. I'll pose you one final challenge: this problem was posed in a 'real-world' context. You weren't simply asked to solve 12x + 4L = 18. These values are lengths of a (presumably) real-world object. Can you work out what values would make sense 'in the real world' for L and x?

I hope that this post has made the thinking process behind solving 'worded questions' such as these ones a bit easier. With practice, you'll naturally get better at extracting and interpreting the key information from questions such as these. At some point you may even find that upon looking at the question, the key bits of information and how to use them together to solve the question will 'jump out' at you. This is a part of 'mathematical intuition' - and by learning to approach questions in this way, you're developing it.

Of course, not all problems will be this simple. Some problems will really require a lot of work and insight in order to put together, identify, and even deduce important pieces of information that might not be apparent in the question stem. But this kind of approach and thinking (along with many other methods and processes in mathematics) will hopefully help you to approach such questions without much fear, both in VCE, and (if you so choose) beyond.

Thank you so so much  nerdgasm   

really awesome explanation and it helped me understand everything 

[Arithmetic]

How would you do this question?

Is the only way to graph polynomials by factorising them? Or is there a quicker way to do so? Thank you

[Apink!]

Hello!
Could someone please help me with this question?
if x+ y =m and x-y =n, then (x²-y²)-2x is equal to (find in terms of m and n)

Thank you!

[lzxnl]

Hello!
Could someone please help me with this question?
if x+ y =m and x-y =n, then (x²-y²)-2x is equal to (find in terms of m and n)

Thank you!

Try multiplying and adding the two equations you're given together. See what happens.