3U Maths Question Thread

[jakesilove]

I was able to get the answer for this one (B) just by subbing in values, but just wondering if there's a better way to work out this kind of question, just in case subbing in values isnt going to work?

Still, for multiple choice, always use the 'subbing-in' method if possible! It's just way quicker than anything else, and you'll always be right

[FallonXay]

Hello, How would you do part ii of this question? Thanks.

[jakesilove]

Hello, How would you do part ii of this question? Thanks.

Hey! To do questions like this, we need to find the equations for velocity. We can do this by differentiating the x and y equation with respect to t. Then, sub in your t value to find the velocity in the y direction, and the velocity in the x direction. Draw yourself a right angled triangle, with the x and y velocities as two of the sides, and find the relevant angle! Let me know if you need a fully worked through solution

[Hua Fei]

Hi there!
I know how to do part ii) but I don't understand how to do i) - please help
The answer to i) is 2/5
Thank you for your help in advance!

[FallonXay]

Hey! To do questions like this, we need to find the equations for velocity. We can do this by differentiating the x and y equation with respect to t. Then, sub in your t value to find the velocity in the y direction, and the velocity in the x direction. Draw yourself a right angled triangle, with the x and y velocities as two of the sides, and find the relevant angle! Let me know if you need a fully worked through solution

Ahh right - got it. Thanks for the explanation! 

[jakesilove]

Hi there!
I know how to do part ii) but I don't understand how to do i) - please help
The answer to i) is 2/5
Thank you for your help in advance!

Hey! We just need to think of all the cases. If Kim spins a 1, there's a 0/5 chance she wins. If she spins a 2, there's a 1/5 chance she wins. If she spins a 3, there's a 2/5 chance she wins, and if she spins a 4 there's a 3/5 chance she wins. Finally, if she spins a 5, there's a 4/5 chance she wins. We add this up as follows



As required!

[:3]

How would we do part iv)?

[jakesilove]

How would we do part iv)?

(Image removed from quote.)

Hey! Would you not just let your equation for velocity (found in Part iii) equal 2 or negative 2? Then, you can use your general solution formulas on your formula sheet to solve for t! Where are you having problems?

[:3]

Hey! Would you not just let your equation for velocity (found in Part iii) equal 2 or negative 2? Then, you can use your general solution formulas on your formula sheet to solve for t! Where are you having problems?

I've got the general solution for both -2 and 2, but I'm unsure as to where to go from there (i.e. to get the values).

Probably simple, but I only recall being taught as to how to get the general solution.

[jakesilove]

I've got the general solution for both -2 and 2, but I'm unsure as to where to go from there (i.e. to get the values).

Probably simple, but I only recall being taught as to how to get the general solution.

No problem! Once you get the general solution (ie. with 'n's in it) you just need to sub in any values of n that give you a solution within the desired range. In this case, sub in n=0, n=1, n=-1 etc. until your value for t is outside of 0 to Pi! Your n values can only be integers, ie. n=0, 1, -1, 2, -2, 3, -3 etc. etc. etc. etc. Does that help?

[imtrying]

Im struggling a bit with part iii) of this question. I've included the working because i understand up to the line y^2= - ln(x) but from there i'm getting a bit lost. Does -ln(x) become ln (x^-1)??

[RuiAce]

Im struggling a bit with part iii) of this question. I've included the working because i understand up to the line y^2= - ln(x) but from there i'm getting a bit lost. Does -ln(x) become ln (x^-1)??

[jakesilove]

Im struggling a bit with part iii) of this question. I've included the working because i understand up to the line y^2= - ln(x) but from there i'm getting a bit lost. Does -ln(x) become ln (x^-1)??

Yep, you're absolutely right! By our log laws, we know that



Therefore



As shown in the answers! We square root both sides, and then convert the logarithm as above. Does that make sense? Let me know if I can clarify anything!

[imtrying]

Thanks:) Looks like another instance of me seriously needing to memorize the log laws oops

[:3]

No problem! Once you get the general solution (ie. with 'n's in it) you just need to sub in any values of n that give you a solution within the desired range. In this case, sub in n=0, n=1, n=-1 etc. until your value for t is outside of 0 to Pi! Your n values can only be integers, ie. n=0, 1, -1, 2, -2, 3, -3 etc. etc. etc. etc. Does that help?

Got it, thanks Jake! <3