Advanced Maths Predictions/Thoughts (6 Viewers)

[bigupsanky]

ub

where did u get this info?

intuition education or smth idk if its valid but quite a few people have predicted a stats heavy paper

 

[bigupsanky]

can someone do question 33(b) from Girraween 2025 advanced trial paper? I got part a, but I'm stuck with part b with some random quadratic

 

[kittyc4tkittycar]

hi guys
i have a random kinda pedantic question
when using the trapezoidal rule or estimates in general, can we use squiggly equal sign instead of the dotted equal sign?
I always use the squiggly one and I'm used to that one, it's on the reference sheet for trapezoidal but all HSC answers use the dotted one.
I remember my math teacher saying somethign about how the squiggly ones aren't reccomended in HSC. Does it matter?

 

[bigupsanky]

hi guys
i have a random kinda pedantic question
when using the trapezoidal rule or estimates in general, can we use squiggly equal sign instead of the dotted equal sign?
I always use the squiggly one and I'm used to that one, it's on the reference sheet for trapezoidal but all HSC answers use the dotted one.
I remember my math teacher saying somethign about how the squiggly ones aren't reccomended in HSC. Does it matter?
View attachment 49698

no not really i use squiggly lines and theyre fine

 

[bigupsanky]

Also, how do I calculate return on interest for different scenarios, like for e.g. continuously adding money into the savings account every month or so, or like withdrawing money from that account every month or so. I always get questions like those wrong.

 

[ALolly]

can someone do question 33(b) from Girraween 2025 advanced trial paper? I got part a, but I'm stuck with part b with some random quadratic

Here, hopefully it makes sense:

 

[bigupsanky]

t

Here, hopefully it makes sense:

View attachment 49702

yea got it i just realised i diffed it incorrectly lol!

 

[zodiacocean]

Also, how do I calculate return on interest for different scenarios, like for e.g. continuously adding money into the savings account every month or so, or like withdrawing money from that account every month or so. I always get questions like those wrong.

wait ok so this is only three months so afaik you have to do it manually. so for the first month, $200000 earns interest of 0.5% for one month to make $201000, then $2000 is withdrawn to make $199000. for the second month $199000 earns interest of 0.5% for one month to make $199995, then $2000 is subtracted to make $197995. for the third month $197995 earns interest of 0.5% for one month to make $198984.98, then $2000 is subtracted to make $196984.98. does that make sense

 

[Trial&Error]

Also, how do I calculate return on interest for different scenarios, like for e.g. continuously adding money into the savings account every month or so, or like withdrawing money from that account every month or so. I always get questions like those wrong.

a)
R = 1+ 0.06/12 = 1.005

A1 = 200,000R - 2000

A2 = 200,000R^2 - 2000R - 2000

A3 = 200,000R^3 - 2000R^2 - 2000R - 2000

= $196,984.98

This question was straight forward since the numner of periods was small but if its largher then you need to find a general equation for "An" for exampe if you wanted to find the money left after 7 months:

An = 200,000R^n - 2000R^n-1 -... 2000R - 2000
so that = 200,000R^n - 2000 (1 + ... R^n-1)

so for 7 months: 200,000R^7 - 2000 ( 1 +...R^6)

then use the sum formula: 200,000R^7 - 2000 (1(1-R^7) / (1-R))
= 192,894,12

 

[bigupsanky]

h

a)
R = 1+ 0.06/12 = 1.005

A1 = 200,000R - 2000

A2 = 200,000R^2 - 2000R - 2000

A3 = 200,000R^3 - 2000R^2 - 2000R - 2000

= $196,984.98

This question was straight forward since the numner of periods was small but if its largher then you need to find a general equation for "An" for exampe if you wanted to find the money left after 7 months:

An = 200,000R^n - 2000R^n-1 -... 2000R - 2000
so that = 200,000R^n - 2000 (1 + ... R^n-1)

so for 7 months: 200,000R^7 - 2000 ( 1 +...R^6)

then use the sum formula: 200,000R^7 - 2000 (1(1-R^7) / (1-R))
= 192,894,12

no i got part a i got part b wrong my fault should've explained it clearer

 

[Trial&Error]

Also, how do I calculate return on interest for different scenarios, like for e.g. continuously adding money into the savings account every month or so, or like withdrawing money from that account every month or so. I always get questions like those wrong.

for part b)

withdrawals = 3x2000 = $6000

If no interest was added the money left would be: 200,000-6000 = $194,000

So the difference between the interest added amount from part a and the hypothetical non-intrest amount is
196,984.98 - 194,000 = $2984.98
That's the interest added over the 3 periods.

 

[bigupsanky]

for part b)

withdrawals = 3x2000 = $6000

If no interest was added the money left would be: 200,000-6000 = $194,000

So the difference between the interest added amount from part a and the hypothetical non-intrest amount is
196,984.98 - 194,000 = $2984.98
That's the interest added over the 3 periods.

ohh thats how u work it out thanks a lot

 

[kittyc4tkittycar]

Here, hopefully it makes sense:

View attachment 49702

This is a rlly dumb question but why did you chose 0 and a as the two y values to check? Like I understand everyhting but is there a reason? So I can know and use it in a similar question where the values tested are variables...

 

[bigupsanky]

This is a rlly dumb question but why did you chose 0 and a as the two y values to check? Like I understand everyhting but is there a reason? So I can know and use it in a similar question where the values tested are variables...

basically she's checking how the gradient sign changes when the value is less than sqrt(a)/2 but u really don't know the value of a, so u can use 0 and a instead because sqrt(a)/2 is greater than 0 and a is greater than sqrt(a)/2

 

[bigupsanky]

basically she's checking how the gradient sign changes when the value is less than sqrt(a)/2 but u really don't know the value of a, so u can use 0 and a instead because sqrt(a)/2 is greater than 0 and a is greater than sqrt(a)/2

i meant a/sqrt(2)

 

[ALolly]

Yea i meant since we don't know the value of a but we know its greater than zero and a/root2 will be less than a so thats why i used 0 and a

 

[kittyc4tkittycar]

i meant a/sqrt(2)

ohhh i see. so it's relying on the fact that a>0 and k>0 completely (?) but you couldn't check with a number such as -1, right? Because of the variables in the question.
(I just worked it out with a and 0 and I understand it! )
Also would it be better to check w second derivative via concavity?

 

[bigupsanky]

ohhh i see. so it's relying on the fact that a>0 and k>0 completely (?) but you couldn't check with a number such as -1, right? Because of the variables in the question.
(I just worked it out with a and 0 and I understand it! )
Also would it be better to check w second derivative via concavity?

1. no you can't check with -1 cuz dimensions cant be negative so they will deduct marks for that.
2. You can go for a second derivative but it will become too complex since the first derivative is complex.
3. Im not sure whether it relies on a > 0 and k>0 completely.

 

[kittyc4tkittycar]

1. no you can't check with -1 cuz dimensions cant be negative so they will deduct marks for that.
2. You can go for a second derivative but it will become too complex since the first derivative is complex.
3. Im not sure whether it relies on a > 0 and k>0 completely.

thank you for the clairification

 

[bigupsanky]

i guessed the answer right but i dont know how to go about it. i found a pattern where like the difference between the numbers increases by the powers of 2 but i dont know how to do it properly