3U Maths Question Thread

[de]

Hi,
Can someone please help me with this Probability question?
1. Two girls, Jan and Alison, throw two dice each. If Jan scores a total of 10, what is the probability that Alison will score higher?
Thank you!!

Check the ways that Alison can get 11 or 12
to get 11 you can get 5 and 6 or 6 and 5 with probability (1/6)^2+(1/6)^2=1/18
to get 12 you need 6 and 6 with probability (1/6)^2=1/36
So the total chance is 3/36=1/12

[RuiAce]

Hi,
Can someone please help me with this Probability question?
1. Two girls, Jan and Alison, throw two dice each. If Jan scores a total of 10, what is the probability that Alison will score higher?
Thank you!!

Basically as de suggested, if you want the sum of numbers on DICE then just considering all possible outcomes (listing) is the best approach

Edit: bad grammar.

[VydekiE]

Thank you so much!! 

[anotherworld2b]

thank for your help
Could i get help with this question

Use \(m=\tan{\theta}\) to find the gradient, and then sub the point into y=mx+b to find the eqn

[jamonwindeyer]

thank for your help
Could i get help with this question

You are on the right track! We form two equations. First, we know the first derivative must be equal to the gradient of the line when \(x=1\), so:



Then we also know that substituting \(x=1\) into the tangent equation and the curve should yield the same \(y\) value:



Solve those simultaneously!

[anotherworld2b]

thank you very much for your help
I have some questions
1. Is there a particular order that brackets of a cubic equation should be placed?
2. When you are asked to find a possible equation of a cubic curve, with exactly two roots x= -1, 1 and y intercept at (0,-6)
How do you know which bracket (root) bounces off the x axis?
3. A rectangular hyperbola has asymptotes with equation x=-2 and y=4
Write two possible equations for this function?
4. Does anyone have anyone tips on how to tackle arithmetic and geometric word equations?

You are on the right track! We form two equations. First, we know the first derivative must be equal to the gradient of the line when \(x=1\), so:



Then we also know that substituting \(x=1\) into the tangent equation and the curve should yield the same \(y\) value:



Solve those simultaneously!

[Shadowxo]

thank you very much for your help
I have some questions
1. Is there a particular order that brackets of a cubic equation should be placed?
2. When you are asked to find a possible equation of a cubic curve, with exactly two roots x= -1, 1 and y intercept at (0,-6)
How do you know which bracket (root) bounces off the x axis?
3. A rectangular hyperbola has asymptotes with equation x=-2 and y=4
Write two possible equations for this function?
4. Does anyone have anyone tips on how to tackle arithmetic and geometric word equations?

1. Unsure of what you mean here
2. If you plot the points (-1,0) , (1,0) and (0,-6) you can see that it must bounce off one of those points. You know which one it is depending on if it is a positive cubic (going up, positive number in front of the x³)  in which case it would bounce off (-1,0), and if it was negative (going down) it must bounce off (1,0) in order for it to pass through all those points.
3. The equation for a rectangular hyperbola is a/(x-h) +k. The asymptotes are either where the denominator of a/(x-h) is equal to zero (as it results in undefined / infinity), or where a/(x-h) equals zero ( as no matter how large x is, it will never equal zero).
First asymptote: x-h = 0. sub in x=-2 as that's the asymptote, so -2-h = 0, h=-2. Other asymptote, a/(x-h) =0, so y = k. Sub in y=4 as that's the other asymptote, so k=4.
Sub in h and k, so final equation is
y=a/(x+2) +4
a can be any number as it will keep the same asymptotes. If it says to write 2 possible equations, just put in any two numbers
4. I don't have many, but see what information you have and if it's worded I like to write it numerically as the worded questions can be quite long and confusing. I then like to see what I need so I can figure out how to get that information from what I have.

Any other questions just ask

[QC]

Hey, for some reason I can't get this even though I know it is easy, all I can get is a+b=190. I've tried splitting the quadrilateral into two triangles and I'm getting no new information.

[kiwiberry]

Hey, for some reason I can't get this even though I know it is easy, all I can get is a+b=190. I've tried splitting the quadrilateral into two triangles and I'm getting no new information.

You're able to use the fact that the angle at the circumference is half the angle at the centre standing on the same arc to find a (look at the reflex angle!)

[RuiAce]

Hey, for some reason I can't get this even though I know it is easy, all I can get is a+b=190. I've tried splitting the quadrilateral into two triangles and I'm getting no new information.

Basically, kiwiberry is stating that since obtuse angle COB is 130deg, we know that reflex angle COB is 230deg.

So by the theorem stated, angle CAB equals 115deg.

[anotherworld2b]

Thank you very much for your help
1. I meant for equations like this

1. Unsure of what you mean here
2. If you plot the points (-1,0) , (1,0) and (0,-6) you can see that it must bounce off one of those points. You know which one it is depending on if it is a positive cubic (going up, positive number in front of the x³)  in which case it would bounce off (-1,0), and if it was negative (going down) it must bounce off (1,0) in order for it to pass through all those points.
3. The equation for a rectangular hyperbola is a/(x-h) +k. The asymptotes are either where the denominator of a/(x-h) is equal to zero (as it results in undefined / infinity), or where a/(x-h) equals zero ( as no matter how large x is, it will never equal zero).
First asymptote: x-h = 0. sub in x=-2 as that's the asymptote, so -2-h = 0, h=-2. Other asymptote, a/(x-h) =0, so y = k. Sub in y=4 as that's the other asymptote, so k=4.
Sub in h and k, so final equation is
y=a/(x+2) +4
a can be any number as it will keep the same asymptotes. If it says to write 2 possible equations, just put in any two numbers
4. I don't have many, but see what information you have and if it's worded I like to write it numerically as the worded questions can be quite long and confusing. I then like to see what I need so I can figure out how to get that information from what I have.

Any other questions just ask

[Shadowxo]

Thank you very much for your help
1. I meant for equations like this

Since they're all multiplied, the order doesn't really matter, I tend to do highest powers to lowest though (eg (x+2)²(x-1))

[anotherworld2b]

I see now
Could i have help with this question?

Since they're all multiplied, the order doesn't really matter, I tend to do highest powers to lowest though (eg (x+2)²(x-1))

[RuiAce]

I see now
Could i have help with this question?

These questions can easily be done by a 2U student. But it is a bit tedious, to be fair.

[bsdfjnlkasn]

These questions can easily be done by a 2U student. But it is a bit tedious, to be fair.

Hey Rui,

Could you please explain your last few lines of working (after you equated the two expressions)

Shouldn't it be:
6x(x-3) = 10