Mathematics Question Thread

[amelia20181]

what should you do if you have no motivation to study or do anything

[S200]

what should you do if you have no motivation to study or do anything

I'd say join Me and Techno in procrastinating on the NSW vs VIC thread, but the competition might be to much for us..

On the flip side, maybe dedicate half an hour to just chill, and then try to come back to work?

[Lollzza]

hi I had my trials recently (not CSSA so not security issues dw) and we had a question that asked us to integrate lnx and i was so confused because I thought 2U wasn't taught integration by parts? Isnt that a low blow??? Is there any other way to integrate it? I didnt actually get this in exam, it was an awful epiphany five minutes after the fact.

Thanks!

[RuiAce]

hi I had my trials recently (not CSSA so not security issues dw) and we had a question that asked us to integrate lnx and i was so confused because I thought 2U wasn't taught integration by parts? Isnt that a low blow??? Is there any other way to integrate it? I didnt actually get this in exam, it was an awful epiphany five minutes after the fact.

Thanks!

There is if it's a definite integral.

[amelia20181]

for this question for b can you do 1- probability of all of the plants
1- (0.85x0.85x0.85)

a certain type of plant has a probability of 0.85 of producing a variegated leaf. if i grow 3 of these plants, find the probability of getting a variegated leaf in
a) 2 of the plants
b) none of the plants
c) at least 1 plant


when you're integrating 4/x can you integrate 4x^-1 or do you have to In

[fun_jirachi]

for this question for b can you do 1- probability of all of the plants
1- (0.85x0.85x0.85)

a certain type of plant has a probability of 0.85 of producing a variegated leaf. if i grow 3 of these plants, find the probability of getting a variegated leaf in
a) 2 of the plants
b) none of the plants
c) at least 1 plant


when you're integrating 4/x can you integrate 4x^-1 or do you have to In

for part b no you can't because the part inside the brackets is only considering if all of them have variegated leaves. you're forgetting that two of them can have different leaves or one of them can have different leaves
the way to approach it would be (1-0.85)^3, using the chance of it being non-variegated on all three

also when integrating 4/x no you can't do the 4x^-1 thing because when you integrate it in the latter form, you have to add one to the power then divide by the new power, which causes you to divide by zero. the integral will always be 4 ln|x| + C.

[ilikeapples]

Hey I am having trouble with this question: There are 10 green marbles and 'W' white marbles in a bag. The probability of selecting a white marble is 4/9. How many more white marbles need to be added to the bag so that the probability of selecting a white marble from the bag is 3/5?

[RuiAce]

Hey I am having trouble with this question: There are 10 green marbles and 'W' white marbles in a bag. The probability of selecting a white marble is 4/9. How many more white marbles need to be added to the bag so that the probability of selecting a white marble from the bag is 3/5?

[ilikeapples]

Thanks so much

[Lollzza]

There is if it's a definite integral.

Oh really?! I haven't been able to find any other methods for it online. If it's alright could you please tell me the name of the method? We were never taught how to integrate lnx so the exam stooped most of us ahah. Would love to know for next time.

[RuiAce]

Oh really?! I haven't been able to find any other methods for it online. If it's alright could you please tell me the name of the method? We were never taught how to integrate lnx so the exam stooped most of us ahah. Would love to know for next time.

It's not really a method per se but more of a technique. Basically you draw out the graph, noting that \(y=\ln x\) converts to \(x = e^y\) and then do a difference of areas between a rectangle and something of the form \( \int_c^d e^y\,dy \), that of which you know how to integrate.

For example, \( \int_1^e \ln x\,dx = 1\times e - \int_0^1 e^y\,dy \)

Typically in the actual HSC it gets hinted, but for trials it's hard to say.

[Lollzza]

It's not really a method per se but more of a technique. Basically you draw out the graph, noting that \(y=\ln x\) converts to \(x = e^y\) and then do a difference of areas between a rectangle and something of the form \( \int_c^d e^y\,dy \), that of which you know how to integrate.

For example, \( \int_1^e \ln x\,dx = 1\times e - \int_0^1 e^y\,dy \)

Typically in the actual HSC it gets hinted, but for trials it's hard to say.

Oh wow okay! I'd never seen a question like this before so I'll be sure to remember for next time. Thanks for answering so well so late ahah. I think I overthought the question and didnt think on the graph too much. Thanks again, math really isn't my strong suit 

[amelia20181]

can someone pls explain simpsons and trapezoidal rule. I'm so confused rn

[jamonwindeyer]

can someone pls explain simpsons and trapezoidal rule. I'm so confused rn

Hey! They are both essentially ways of estimating the value of definite integrals/approximating the area under a curve between two points. The trapezoidal rule does so by forming multiple trapeziums and summing their areas, and the Simpson's Rule uses (you can think of it this way at least) a parabola to make the approximation.

To use either rule, you just need the value of the curve/function in question at equally spaced points along the interval you care about! Once you have that, it is just substituting into the formula. Although you can understand how the results are derived (particularly for Trapezoidal), you don't need to, you can just substitute and go!

Were there specific questions that were giving you trouble? Would be happy to lend a hand

[amelia20181]

what would happen if you didn't write your number on the exam paper