Mathematics Question Thread

[jamonwindeyer]

Hi, how do you completely factorise the following:
5x² +10xy-25xy²
Thanks

Hey! You can start by taking out a common factor:



Unless there is a typo in the question, I think that's as far as you can go! It is almost a quadratic factorisation but the terms don't quite match up! Not what I expected to happen

[RuiAce]

Hi, how do you completely factorise the following:
5x² +10xy-25xy²
Thanks

Are you sure that's -25xy² and not just -25y²?

Because if so...
edit, damn it Jamon.

Hey guys! Has anyone got any study resources in terms of practise questions? Like topic specific worksheets with solutions on half yearly content?

You could find some ones you wish to target here.

However there's nothing wrong with simply extracting relevant questions from past trial papers. Half yearly exams follow a similar format.

[laurenf58]

Hey!

How do I find points of inflexion? (stationary points have already been found)

Really hoping someone can help! Thanks!

[RuiAce]

Hey!

How do I find points of inflexion? (stationary points have already been found)

Really hoping someone can help! Thanks!

Checklist:
1. Set second derivative to 0 to single out the candidate points
2. Verify a change in sign occurs

[Hplovers]

Hey!

I'm getting confused with the wording of these two probability questions;

The ratio of girls to boys at a school is four to five. Two students are surveyed at random from the school. Find the probability that the students are
a) both boys
b) a girl and a boy
c) at least one girl

I have attached the probability tree i have used and i'm pretty sure its correct.
I have a ratio of 4/9 for girls and 5/9 for boys

However, what im confused about; am I supposed to use the same ratio for both the first AND second step?
For a), I have been doing ( 5/9 x 4/8 ) to find the probability of 'both boys', because after you take one boy out doesn't it then lower the numerator and denominator and numerator for the next boy to be picked?

My answers were;
a) 5/18
b) 5/9
c) 13/18

The textbooks answers were;
a) 25/81
b) 40/81
c) 56/81
( It appears they do not change the ratio for each additional student picked)

Am I reading it wrong? I thought this question was like the lottery ticket questions where it is without replacement, because in those questions they don't specify 'without replacement' they just assume it, and I assumed in this question the student was not replaced for the next random survey.


The second question I have the exact same issue with;

The number of cats to dogs at a pet hotel is in the ratio of 4 to 7. If 3 pets are chosen at random, find the probability that
a) they are all dogs
b) just one is a dog
c) at least one is a cat

Same issue, with the answers keeping the same ratio throughout, but I thought you were supposed to remove an animal from the numerator and denominator at each animal chosen.

Thankyou!!

[RuiAce]

Hey!

I'm getting confused with the wording of these two probability questions;

The ratio of girls to boys at a school is four to five. Two students are surveyed at random from the school. Find the probability that the students are
a) both boys
b) a girl and a boy
c) at least one girl

I have attached the probability tree i have used and i'm pretty sure its correct.
I have a ratio of 4/9 for girls and 5/9 for boys

However, what im confused about; am I supposed to use the same ratio for both the first AND second step?
For a), I have been doing ( 5/9 x 4/8 ) to find the probability of 'both boys', because after you take one boy out doesn't it then lower the numerator and denominator and numerator for the next boy to be picked?

My answers were;
a) 5/18
b) 5/9
c) 13/18

The textbooks answers were;
a) 25/81
b) 40/81
c) 56/81
( It appears they do not change the ratio for each additional student picked)

Am I reading it wrong? I thought this question was like the lottery ticket questions where it is without replacement, because in those questions they don't specify 'without replacement' they just assume it, and I assumed in this question the student was not replaced for the next random survey.


The second question I have the exact same issue with;

The number of cats to dogs at a pet hotel is in the ratio of 4 to 7. If 3 pets are chosen at random, find the probability that
a) they are all dogs
b) just one is a dog
c) at least one is a cat

Same issue, with the answers keeping the same ratio throughout, but I thought you were supposed to remove an animal from the numerator and denominator at each animal chosen.

Thankyou!!

The question's wording is very hard to decrypt.

All we are saying is that the ratio of girls to boys at a school is 4:5.
But this doesn't mean there's only 9 students. Yes, if you treat it as exactly 9 students there, that's what you get.

But what if there's 900 students instead?
If the ratio of girls to boys at a school is 4:5, then there would be 400 girls and 500 boys.

So for a), technically the answer would be 500/900 * 499/899 now, right? Which is not equal to 5/9 * 4/8



The question is most certainly tricky, and the appearance of this sort of ambiguity is unlikely in the HSC. However, the ultimate purpose of this question is to not treat ratios as representative of the bigger picture - the total. Hence, the safest bet is to assume that in general, if we take one out, the ratio isn't varied much.

Note that something like 400:499 is approximately equal to 400:500 anyhow, which is 4:5. So since in general schools have quite a large population (and not just a mere 9 students), we assume that by choosing one, the ratio is not greatly disturbed (the disturbance is negligible).

[Hplovers]

Ah okay, thankyou for your help!

[kiwiberry]

Financial maths questions:
1) in the first year of joining a superannuation fund a women invests $400. The interest rate is 12% pa. Each year she invests an additional 10% of the amount invested in the previous year to allow for inflation. How much does she receive after 20 years?

2) A man put $500 savings into a bank for 2 years, where it earned interest at 6% pa, paid twice a year. He then changed to a credit union and his money earned 8% pa, paid quarterly. if he withdrew all his savings and had $633.75, how long was the money kept in the credit union?

Thank you

[jakesilove]

Financial maths questions:
1) in the first year of joining a superannuation fund a women invests $400. The interest rate is 12% pa. Each year she invests an additional 10% of the amount invested in the previous year to allow for inflation. How much does she receive after 20 years?

2) A man put $500 savings into a bank for 2 years, where it earned interest at 6% pa, paid twice a year. He then changed to a credit union and his money earned 8% pa, paid quarterly. if he withdrew all his savings and had $633.75, how long was the money kept in the credit union?

Thank you

Hey!

It's easiest to tackle these questions 'by year'.

So, in the first year, we will have a deposit, and interest.



The second year will have another (greater) deposit, and more interest



And... the third year



Can you see a pattern? We can tell that



Pulling out the 400, we get a series



We're DIVIDING by 1.12, and MULTIPLYING by 1.1. This is a geometric series,



After 20 years, n=20, so



Therefore, the total will be 400*111.18=$44,473

Don't quite have time for Q2 (maybe someone else will step in), but try taking the same approach!

[RuiAce]

2) A man put $500 savings into a bank for 2 years, where it earned interest at 6% pa, paid twice a year. He then changed to a credit union and his money earned 8% pa, paid quarterly. if he withdrew all his savings and had $633.75, how long was the money kept in the credit union?

Thank you

P.S. Jake assumed that the interest was compounded annually for Q1. This makes the most intuitive sense to me, however the question did not explicitly state this. The question therefore lacks information.

[kiwiberry]

Thanks Jake and Rui

[Nialllovespie]

Hiiii!!

Could someone please help me with this Integration question?

Find the volume of the paraboloid when y=x^2 is rotated about the y axis from y=0 to y=3

Thanks so much!!

[jakesilove]

Hiiii!!

Could someone please help me with this Integration question?

Find the volume of the paraboloid when y=x^2 is rotated about the y axis from y=0 to y=3

Thanks so much!!

Hey!

Our formula for volumes is



So, we start off by finding our limits. By subbing them into the equation, we know that they are 0 and the square root of three.




Between 0 and the square root of 3, which will be



I rotated around the X-AXIS, not the y-axis. Need to do what Rui did below instead!

[RuiAce]

Hiiii!!

Could someone please help me with this Integration question?

Find the volume of the paraboloid when y=x^2 is rotated about the y axis from y=0 to y=3

Thanks so much!!

Hey!

Our formula for volumes is



So, we start off by finding our limits. By subbing them into the equation, we know that they are 0 and 9.




Between 0 and 9, which will be

Jake. What are you doing. Wrong axis.

[joyg]

I was just wondering how to do this log question:

3000 = 100e^n