VCE Methods Question Thread!

[joejoh]

Following on from VanillaRice, the solutions need to be valid. In this case log10(x) can only accept positive x values (look at the graph of it!) and log10(x-3) can only accept  values for x>3. Hence, x=-2 is an infeasible solution. Hope that works for you

[snowisawesome]

Your solutions need to satisfy both log terms. Substituting x = -2 into the second one will give a negative number in the brackets.

Hope this helps

Following on from VanillaRice, the solutions need to be valid. In this case log10(x) can only accept positive x values (look at the graph of it!) and log10(x-3) can only accept  values for x>3. Hence, x=-2 is an infeasible solution. Hope that works for you

log10(5)+log10(5-3) = 1
log10(5)+log10(2) = 1
log10(10) = 1
10^1 = 10
10 = 10

log10(-2)+log10(-2-3) = 1
log10(-2)+log10(-5) = 1
log10(10) = 1
10^1 = 10
10 = 10

Both x = -2 and x = 5 satisfy the equation though?

[zhen]

log10(5)+log10(5-3) = 1
log10(5)+log10(2) = 1
log10(10) = 1
10^1 = 10
10 = 10

log10(-2)+log10(-2-3) = 1
log10(-2)+log10(-5) = 1
log10(10) = 1
10^1 = 10
10 = 10

Both x = -2 and x = 5 satisfy the equation though?

log10(-2) and log10(-5) are undefined. This is because 10^(any number) cannot be negative. So, you can’t have log10(negative number). So x=-2 doesn’t work.

[snowisawesome]

Thanks guys

[snowisawesome]

f(x) = √(5-2x)
if they ask you to find the graph of the inverse and it's a multiple choice and the x intercepts of the inverse are +√(5) and -√(5)
and one graph shows only +√(5) and the other graph shows only -√(5) then which one is the correct answer?

Another question
f(x) = 2e^(3x)+3
and two of your options are
(3, infinity), and [3, infinity)
then how do you determine which one is correct?

[VanillaRice]

f(x) = √(5-2x)
if they ask you to find the graph of the inverse and it's a multiple choice and the x intercepts of the inverse are +√(5) and -√(5)
and one graph shows only +√(5) and the other graph shows only -√(5) then which one is the correct answer?

Another question
f(x) = 2e^(3x)+3
and two of your options are
(3, infinity), and [3, infinity)
then how do you determine which one is correct?

For the first question, the inverse should be a reflection along the line y=x. Have a think about which answer gives this. It might help to sketch your initial function, sketch what the inverse *should* look like, and have a look at whether the x-intercept is positive or negative.

What's the second question? I'm assuming it's asking for the range. If so, think about the properties of an exponential function. What is the difference between the two options? Can the function ever achieve a value of y = 3? Why or why not?

Hope this helps

[snowisawesome]

For the first question, the inverse should be a reflection along the line y=x. Have a think about which answer gives this. It might help to sketch your initial function, sketch what the inverse *should* look like, and have a look at whether the x-intercept is positive or negative.

What's the second question? I'm assuming it's asking for the range. If so, think about the properties of an exponential function. What is the difference between the two options? Can the function ever achieve a value of y = 3? Why or why not?

Hope this helps

Don't really understand your explanations - could you perhaps elaborate on them please?
Thanks

[VanillaRice]

Don't really understand your explanations - could you perhaps elaborate on them please?
Thanks

For the first question - think about what the graph of the inverse actually looks like. It's not a full parabola - only half of one. Why? Functions can only have a inverse if they are one-to-one. The two different options you have are the two halves of the parabola. Which one should we select? Remember that inverses will be reflected along the line y = x - think of the line y=x as a mirror for a function and its inverse. You need to select the option which looks like your original function, except it is reflected along the line y=x.
Another way to think about this question is that recall for inverse functions, the x and y values are swapped. If in your original function, the y-intercept is √5, then in your inverse function, the x-intercept must be √5. This also follows on from the 'mirror image' explanation from above.

For the second question - think about the asymptote we find in exponential functions. In this case, the asymptote is at y = 3, and can be thought of as a line which the function approaches but never touches. The difference between your two options is a closed or open bracket. The closed bracket '[' means that 3 is inclusive, but I just said that an exponential function will never touch the asymptote i.e. the function never achieves a y-value of 3. So, we pick the option with the open bracket '(', which says that the range is all values above 3, but not including it.

Hope this clarifies things

[snowisawesome]

Thanks VanillaRice!
Also, does anyone know if methods 3/4 checkpoints 2016 is relevant to the current study design, and if so, which chapters (algebra+functions, differentiation, integration, discrete probability, and continuous probability+statistics) would be adequate revision for the first 3 chapters of the mathsquest 12 methods textbook?
Thanks

[Sine]

Thanks VanillaRice!
Also, does anyone know if methods 3/4 checkpoints 2016 is relevant to the current study design, and if so, which chapters (algebra+functions, differentiation, integration, discrete probability, and continuous probability+statistics) would be adequate revision for the first 3 chapters of the mathsquest 12 methods textbook?
Thanks

yeah 2016 is relevant the study design is 2016-2018 althoguh may be extended (if not already). I'm not too familar with mathsquest so can't answer that question but you should be able to work out what you have covered at what you are yet to learn by having a look at the questions/topic names.

[snowisawesome]

How beneficial would it be to do every question in an exercise as opposed to doing every second question or just the questions that the school sets us?
And would the same logic apply to the chapter review questions?

[Lear]

 Personally I have been doing the ones the School set us + ones I see and they look interesting/challenging. I don’t think it’s beneficial to do every single question. Textbook questions often are repetitive. I will be doing every single chapter review question though.
My plan is to finish the textbook doing roughly 80% of the questions and then begin exam style questions from past sacs/checkpoints/vcaa.

[Quantum44]

How beneficial would it be to do every question in an exercise as opposed to doing every second question or just the questions that the school sets us?
And would the same logic apply to the chapter review questions?

I did basically every question in the textbook and I found it was a waste of time as I already had a very good understanding of the course, and would have benefitted more from starting exam style questions earlier. I think chapter review questions are definitely worth doing as they are step up from your garden variety textbook questions and are better preparation before starting practice SACs/exams.

[snowisawesome]

Does it matter what score you're aiming for, to do every question or not though, like to get 35+ raw?

[Quantum44]

Does it matter what score you're aiming for, to do every question or not though, like to get 35+ raw?

Well it really depends on how comfortable you feel with the course. If you are a good maths student, you probably won't have to work that hard to get 35+, however some people who aren't as into maths might struggle. The textbook is there to give you a good foundation so you understand the underlying concepts, which is essential if you want to extend and apply these principals in harder exam-style questions. Once you fully grasp these concepts and have reinforced them in your mind, there is no use in continuing to do basic questions.