2u Mathematics Marathon v1.0 (1 Viewer)

[YBK]

I'll leave this one for someone else to do

Here's a hint if you need it:

Spoiler

Draw a diagram and label what is given in the question.

I'd do it... but i'm playing mini soccer on a soccer table... it's sooo fun!!

 

[Riviet]

Aw I love those mini soccer tables, they're so addictive! Wish I could come over and play against you.

 

[sando]

can't find my calculator... damn... i was motivated there for a minute

 

[YBK]

Aw I love those mini soccer tables, they're so addictive! Wish I could come over and play against you.

True that!!

6 hrs straight!!!!!!!!!!!

 

[Riviet]

So that's where you were... XD

We better not spam this thread anymore.

 

[Jono_2007]

I'M NOT SURE IF I UNDERSTAND BY THE QUESTION, BUT is supose id draw a diagram to represent the data in the question. make the flag pole x. then solve for x. This isnt HSC stuff is it.

 

[bananasmoothy]

I'M NOT SURE IF I UNDERSTAND BY THE QUESTION, BUT is supose id draw a diagram to represent the data in the question. make the flag pole x. then solve for x. This isnt HSC stuff is it.

Maths is unique in the sense that all topics covered (or meant to be covered according to the syllabus ) in Prelim's AND HSC are testable (is that a word?) in the Maths HSC exam, whether 2 unit or 3 unit.

 

[Riviet]

I'M NOT SURE IF I UNDERSTAND BY THE QUESTION, BUT is supose id draw a diagram to represent the data in the question. make the flag pole x. then solve for x. This isnt HSC stuff is it.

Anything done in preliminary maths and hsc maths of course is examinable, but the majority of preliminary maths is extended onto the hsc course, so in a way, it is examined indirectly because it requires knowledge of the basics.

Yes, the wording for the last question posted is a little confusing, and I will try to reword the first sentence a little:

The angle of elevation to the top of a flagpole from a point, horizontal to the base of a flagpole, is 20 degrees. After walking 80m toward the flagpole, the angle of elevation is 75 degrees. Find the height of the flagpole to the nearest metre.

That should make it clearer now.

 

[Jono_2007]

The angle of elevation to the top of a flagpole from a point, horizontal to the base of a flagpole, is 20 degrees. After walking 80m toward the flagpole, the angle of elevation is 75 degrees. Find the height of the flagpole to the nearest metre.

HERE GOES!

find the length of BD;
a/sinA=d/SinD
a/sin20=80/sin55
a=80sin20/sin 55
=33 (nearest metre)

find the hight;
in triangleDCB, sin75=DC/DB
therefore DC =Dbsin75
therefore the hight of the flag pole is 32 metres (nearest metre)

 

[Jono_2007]

THE next question:
Find the Equation of the tangent to the curve:
y=x^3 at (-1,-1)

There you are faily simple!

 

[Riviet]

THE next question:
Find the Equation of the tangent to the curve:
y=x^3 at (-1,-1)

Spoiler

dy/dx = 3x²
at (-1,-1)
m=3
y-y₁=m(x-x₁)
y+1=3(x+1)
y+1=3x+3
3x-y+2=0

Next question:

Show that x²-8x+23 is positive for all real x.

 

[SoulSearcher]

Next question:

Show that x²-8x+23 is positive for all real x.

Spoiler

to show this, we need to prove that the graph of y = x²-8x+23 does not cut the x-axis, i.e. the discriminant of the graph is negative

discriminant = b² - 4ac, where a=1, b = -8 and c = 23

= 64 - 4 * 23 * 1
= 64 - 92
< 0

since the discriminant < 0, x²-8x+23 has no real roots and so x²-8x+23 is positive for all real x

 

[SoulSearcher]

next question

A bag contains 12 jellybeans. 3 are coloured red, 4 are black and 5 are green. Peter eats 3 jellybeans chosen ramdomly from the bag. Find the probability that:

(i) the first jellybean is black
(ii) all 3 jellybeans eaten are black
(iii) exactly one of the jellybeans eaten is black

 

[Riviet]

Spoiler

to show this, we need to prove that the graph of y = x²-8x+23 does not cut the x-axis, i.e. the discriminant of the graph is negative

discriminant = b² - 4ac, where a=1, b = -8 and c = 23

= 64 - 4 * 23 * 1
= 64 - 92
< 0

since the discriminant < 0, x²-8x+23 has no real roots and so x²-8x+23 is positive for all real x

Spoiler

Don't forget that also need to state that a>0, and after showing that it has no real roots, it therefore is always positive and concave up when sketched on a number plane. ;D

 

[Riviet]

Hint #1:

Spoiler

Draw a tree diagram!!

Hint #2:

Spoiler

If you have 12 jelly beans and you eat 1, how many do you have now to eat? If you have 11 jelly beans and eat 1, etc.

 

[Jono_2007]

But was it right or wrong and which ones. ect

 

[Riviet]

The third one's definitely wrong, because it can happen, don't have time to check your other two answers, have to go watch a movie now.

 

[Jono_2007]

The third one's definitely wrong, because it can happen, don't have time to check your other two answers, have to go watch a movie now.

I'm such an idiot, how could i not have seen that.
I cant really understand something until i learn it properly....probablity is one of these so called things i havent mastered.
P.S deleted my post of shame...

 

[Jono_2007]

I'll let someone else handle this question!

 

[Jono_2007]

Is knowone else going to answer it.