Mathematics Question Thread

[RuiAce]

Heyy! How do we know the procedure to solve this?

[nibblez16]

The answer is different, its 91/216

[emilyf]

Sorry if this has been answered previously but could someone help me out with this question please?
The answers can be found here - http://www.pasthsc.com.au//HSC_Mathematics_files/Maths2U07WorkedSolutions.pdf - on page eight however I don't understand part (i).

For the first part, I got tan(x) =√3, yet I then used this to say that x = π/3, and that the intercepts occur at π/3 and 2π/3. I don't understand why the 2π/3 isn't right and why it's 4π/3 instead??

[RuiAce]

The answer is different, its 91/216

[:3]

Sorry if this has been answered previously but could someone help me out with this question please?
The answers can be found here - http://www.pasthsc.com.au//HSC_Mathematics_files/Maths2U07WorkedSolutions.pdf - on page eight however I don't understand part (i).

For the first part, I got tan(x) =√3, yet I then used this to say that x = π/3, and that the intercepts occur at π/3 and 2π/3. I don't understand why the 2π/3 isn't right and why it's 4π/3 instead??

tan(x) is positive in the first and 3rd quadrant.
Therefore, the respective values for x are 60 (π/3) and 180 +60 (240, 4π/3; not 2π/3).

[RuiAce]

Sorry if this has been answered previously but could someone help me out with this question please?
The answers can be found here - http://www.pasthsc.com.au//HSC_Mathematics_files/Maths2U07WorkedSolutions.pdf - on page eight however I don't understand part (i).

For the first part, I got tan(x) =√3, yet I then used this to say that x = π/3, and that the intercepts occur at π/3 and 2π/3. I don't understand why the 2π/3 isn't right and why it's 4π/3 instead??

You're looking at the wrong quadrants.

Tan is positive in the first and THIRD quadrants, not first and second. (Rule of ASTC.)

So the valuse are π/3, and π + π/3, which is 4π/3
Not π/3 with π - π/3 , which is 2π/3

Edit: Done above

[nibblez16]

Okay! But y do we cube it?

[RuiAce]

Okay! But y do we cube it?

They give you the probabilities for 1 week.

You want the probability for a 3 week period. Not just 1.

So you want the same event to happen 3 times. It's like saying I lost, and then I lost again, and then yet I lost one more time.
So if the probability I lose is, say, 1/2
The probability I lose 3 times is 1/2 times 1/2 times 1/2, which is 1/8


Successive events, if you will

[nibblez16]

Does anyone have prelim formula sheet?

[RuiAce]

Does anyone have prelim formula sheet?

What's a prelim formula sheet? You're going to be given that same reference sheet as you have been tomorrow

[:3]

For iii), I'm unsure as to why AP = AC (according to the answer, its because of part II).


Also, any tips on drawing a displacement graph from a velocity graph or acceleration and vice versa? (without knowing the function itself)

[RuiAce]

For iii), I'm unsure as to why AP = AC (according to the answer, its because of part II).
(Image removed from quote.)

Also, any tips on drawing a displacement graph from a velocity graph or acceleration and vice versa? (without knowing the function itself)

AP is not equal to AC. AP/AC = 1/2 according to (ii)

[:3]

AP is not equal to AC. AP/AC = 1/2 according to (ii)

Here are the answers from BOSTE 2009 HSC exam.

[RuiAce]

Here are the answers from BOSTE 2009 HSC exam.
(Image removed from quote.)

That's CP. Not AC.

[Rikahs]

For iii), I'm unsure as to why AP = AC (according to the answer, its because of part II).
(Image removed from quote.)

Also, any tips on drawing a displacement graph from a velocity graph or acceleration and vice versa? (without knowing the function itself)

First of all AC= 2AP

Then for iii) I would use congruent triangles, my proof:

In triangle AMP and traingle MPC

MP is common

AC = 2AP ( from ii))

Since AC = AP + PC
therefore AP = PC

Angle MPA = Angle MPC = 90 (MP bisects AC)
Therefore Triangle AMP is congruent to Triangle MPC (SAS)

Therefore Angle MAP = Angle MCP ( corresponding angles in congruent triangles)

Therefore Triangle AMC is Isos ( base angles are equal)