Mathematics: Post your doubts here!

[amina1300]

How do we draw |z-5| =|z|
where |z|=5 is a circle with radius 5 and center at the origin.
I know that it's going to be a perpendicular bisector of the |z-5| line but is |z-5| a horizontal line along the x-axis with magnitude 5 and the perpendicular bisector at 2.5?

 

[Hunzlah Malik]

How do we draw |z-5| =|z|
where |z|=5 is a circle with radius 5 and center at the origin.
I know that it's going to be a perpendicular bisector of the |z-5| line but is |z-5| a horizontal line along the x-axis with magnitude 5 and the perpendicular bisector at 2.5?

For this you have to plot 2 points
(5,0) and (0,0)
draw perpendicular bisector of these two points
Yes, it is at x=2.5

 

[amina1300]

For this you have to plot 2 points
(5,0) and (0,0)
draw perpendicular bisector of these two points
Yes, it is at x=2.5

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
ty can you solve part 3 please

 

[Krypton36]

Thank you! But I was asking for the Mark Scheme!!

 

[DudeWithoutName]

Common perpendiculars??? finding the intersection line of these two planes(other method)

Ok nevermind that. If you want a plane that is perpendicular to both, then the line of intersection of the two planes must act as a perpedicular to the third plane correct?
basically want to find the equation of that line and then we can proceed from there. We have point A on the line with y coordinate of 2 so lets find its x and y components
x+2+3z=8....x+3z=6
2x-2(2)+z=3....2x+z=7
rearrage the first equation to make x the subject
x=6-3z
substitute x into the second equation
2(6-3z)+z=7
12-5z=7
z=1
x=3
so A: (3,2,1)
Thats one part down. Now we need to find ANY other point on that line so we can figure out its direction. Let us take y=3
x+3+3z=8....x+3z=5
2x-2(3)+z=3....2x+z=9
rearrage the first equation to make x the subject
x=5-3z
substitute x into the second equataion
2(5-3z)+z=9
10-5z=9
z=0.2
x=4.4
so the other point is (4.4,3,0.2)
Let us find the direction of the line then:
[4.4i+3j+0.2k]-[3i+2j+k]=[1.4i+j-0.8k] This is the normal to the plane in question

setting up the cartesian equation of the plane: 1.4x+y-0.8z=[1.4i+j-0.8k].[3i,2j,k]

1.4x+y-0.8z=5.4
1.75x+1.25y-z=6.75
7x+5y-4z=27

 

[DudeWithoutName]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
Q4 part ii) Can anyone give me the working? Can the formula be sqrt(2p+3) -p rather than this in ms --> p-sqrt(2p+3) ?

Yes it can. Whats important is that you substitute 1.8 and 2.0 and show that the two values obtained have opposite signs meaning the root lies inbetween theme

 

[DudeWithoutName]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
part ii) Do we only use sinx for the angle between line and plane?

part iii) The point C lies on the line and is such that the distance between C and B is twice the distance between A and B. Find the coordinates of each of the possible positions of the point C.
(can anyone solve this?)

The angle between the line and the plane can be thought of as 90-the angle between the normal and the line

First we find the angle between the normal and the line:
(i-3j+4k).(4i-j+5k)=sqrt(1^2+3^2+4^2)*sqrt(4^2+1^2+5^2)cos(theta)
solve for theta
theta=35.2
90-theta=54.8

 

[DudeWithoutName]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
part ii) Do we only use sinx for the angle between line and plane?

part iii) The point C lies on the line and is such that the distance between C and B is twice the distance between A and B. Find the coordinates of each of the possible positions of the point C.
(can anyone solve this?)

Writing the second part in chat is far too tedious so i hope this picture is clear. Whats left is putting the two values of t into OC

 

[DudeWithoutName]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
ty can you solve part 3 please

Which question?

 

[amina1300]

Which question?

Thankyou you've solved it already.

 

[DudeWithoutName]

Thankyou you've solved it already.

"oops"

 

[amina1300]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_s16_qp_61.pdf
I can get how Q6 part (a) is done?! It's so confusing HELP!

 

[amina1300]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_s16_qp_61.pdf
Q5 part ii) 180 ==> 179.5
When exactly do we use continuity corrections?? Can someone quote some other questions?

 

[DudeWithoutName]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_s16_qp_61.pdf
I can get how Q6 part (a) is done?! It's so confusing HELP!

Find the number of ways to arrange the digits 0,1,2,3,4,5,6,7,8,9 into 3 slots. That is 10P3=720
Now we need to take away all that starts with 0 because its less than 100 so we find the number of ways to arrange the digits 1,2,3,4,5,6,7,8,9 into the last 2 slots. This equals the number of instances in which 0 is the first digit and can be calculated by 9P2=72

720-72=648

 

[amina1300]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w17_qp_32.pdf
Q1 (ii) Explain, with reference to the diagram, why the trapezium rule may be expected to give a good approximation to the true value of the integral in this case.
WHAT TO WRITE?
Graph on both sides of the y-axis is approximately trapezium shaped?

 

[DudeWithoutName]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w17_qp_32.pdf
Q1 (ii) Explain, with reference to the diagram, why the trapezium rule may be expected to give a good approximation to the true value of the integral in this case.
WHAT TO WRITE?
Graph on both sides of the y-axis is approximately trapezium shaped?

That the gradient is roughly constant over that period so the trapezium drawn will have one edge that follows the curve's edge making their areas very similar

 

[amina1300]

That the gradient is roughly constant over that period so the trapezium drawn will have one edge that follows the curve's edge making their areas very similar

THANKYOU FOR YOUR HELP.

 

[DudeWithoutName]

THANKYOU FOR YOUR HELP.

youre welcome

 

[Holmes]

https://papers.gceguide.com/A Levels/Mathematics (9709)/9709_w15_qp_33.pdf
part ii) Do we only use sinx for the angle between line and plane?

part iii) The point C lies on the line and is such that the distance between C and B is twice the distance between A and B. Find the coordinates of each of the possible positions of the point C.
(can anyone solve this?)

Yup remember this:
plane-plane = cos x
line-line = cos x
line-plane = sin x

 

[Holmes]

Ok nevermind that. If you want a plane that is perpendicular to both, then the line of intersection of the two planes must act as a perpedicular to the third plane correct?
basically want to find the equation of that line and then we can proceed from there. We have point A on the line with y coordinate of 2 so lets find its x and y components
x+2+3z=8....x+3z=6
2x-2(2)+z=3....2x+z=7
rearrage the first equation to make x the subject
x=6-3z
substitute x into the second equation
2(6-3z)+z=7
12-5z=7
z=1
x=3
so A: (3,2,1)
Thats one part down. Now we need to find ANY other point on that line so we can figure out its direction. Let us take y=3
x+3+3z=8....x+3z=5
2x-2(3)+z=3....2x+z=9
rearrage the first equation to make x the subject
x=5-3z
substitute x into the second equataion
2(5-3z)+z=9
10-5z=9
z=0.2
x=4.4
so the other point is (4.4,3,0.2)
Let us find the direction of the line then:
[4.4i+3j+0.2k]-[3i+2j+k]=[1.4i+j-0.8k] This is the normal to the plane in question

setting up the cartesian equation of the plane: 1.4x+y-0.8z=[1.4i+j-0.8k].[3i,2j,k]

1.4x+y-0.8z=5.4
1.75x+1.25y-z=6.75
7x+5y-4z=27

Thanks boyz