Cambridge Prelim MX1 Textbook Marathon/Q&A (1 Viewer)

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I get it now.

Except for how you went from 2 + | N - 2 | = 2 + 2 - N
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Use a right angle triangle to show that :

sin(cos^-1 x) = ( 1 - x^2)^1/2
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-09 at 10.30.18 am.png

How do you do question a)

The answer is 56/65
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-09 at 11.47.29 am.png

How do you do this question.

I used compound angle formula to get

cos a cos b = sin a sinb

Then plugged in a = inverse sin x

and b = inverse tan x

Not sure where to go from here. Were those the correct initial steps??
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

View attachment 32774

How do you do this question.

I used compound angle formula to get

cos a cos b = sin a sinb

Then plugged in a = inverse sin x

and b = inverse tan x

Not sure where to go from here. Were those the correct initial steps??
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I have done that, and got

sin a = x

where - pi/2 < x < pi/2

I presume in 1st quad

And drew a diagram of it

now if i do cos a : how do I know what the sides lengths are, I am only given 'x'.
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I have done that, and got

sin a = x

where - pi/2 < x < pi/2

I presume in 1st quad

And drew a diagram of it

now if i do cos a : how do I know what the sides lengths are, I am only given 'x'.
For side lengths, you can let one of them be unit length (length 1) and another x, choosing them so that the sine of the correct angle is x in your diagram. The remaining side can be found via Pythagoras.
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Thanks it worked finally.

But now I am having trouble with part b)

So using the equation cos( a + b ) = ..... from a)

I used the fact given that a + b = pi/2 from question

so subing it in and RHS becomes 0

Then I got rid of the fraction on the LHS by multiplying the equation by it

Now I am unsure where to go from here....

Is what I have done correct??
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Thanks it worked finally.

But now I am having trouble with part b)

So using the equation cos( a + b ) = ..... from a)

I used the fact given that a + b = pi/2 from question

so subing it in and RHS becomes 0

Then I got rid of the fraction on the LHS by multiplying the equation by it

Now I am unsure where to go from here....

Is what I have done correct??




 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-09 at 3.59.36 pm.png

Could someone explain this function.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread





Useless if you don't know what mod means.
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I don't know what mod is
 

integral95

Well-Known Member
Joined
Dec 16, 2012
Messages
779
Gender
Male
HSC
2013
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

View attachment 32775

Could someone explain this function.
it's essentially a straight line y = x defined between -pi/2 and pi/2 (not inclusive since that's undefined, so there would be open circles there) followed by the exact same line between pi/2 and 3pi/2, and another between 3pi/2 and 5pi/2 etc.

This is why the period is pi and the range is strictly between -pi/2 and pi/2.
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Screen Shot 2016-01-10 at 9.25.50 am.png

I can't seem to simplify to get the answer for the second derivative

Maybe my first derivative is wrong?

For the first derivative I got : ( x( tan^-1 x - 1) ) / (1 + x^2)

Is that correct?
 

appleibeats

Member
Joined
Oct 30, 2012
Messages
375
Gender
Male
HSC
2016
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Find the derivative of in the simplest form :

sin^-1 1/4 . ( 2x - 3)

Answer says 2/ (7 + 12x - 4x^2)^1/2

Not sure what to do with the 1/4
Do you multiply it with the numbers in the brackets??
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top