Mathematics: Post your doubts here!

[ahmed abdulla]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s06_qp_1.pdf
Question 9, part i, i did uptil finding the equation, but what about after that?! how did they find the points?

since both sides of tangent equal and you studied in ur IGCSE"S that angle between tangent and radi is 90 degree!
so < OAT and <OBT are 90 degree,,,, so you got a triangle OAT or OBT and use trignometry to find the half of < AOT and then multiply with 2 !

same thing for area ... find area of one of the tiangle and multiply with two A=0.5 *bas*height

 

[ahmed abdulla]

I will give you idea, if you still have doubt i will try to solve.

7 (i) see make a triangle OAT use watever sin cos or tan then find angle then multiply by 2 to got AOB angle.
(iii)the same triangle as up can be used and find area 1/2bh formula then multiply by 2

u gotta now the reason! its a congruent triangle .. all sides are equal ...so use trignometry

 

[Asad]

hey PhyZac, Is there any rule about when to use the dot product and when to use cross product in vectors?

Because I get confused in these two sometimes.

 

[surinr]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s10_qp_31.pdf
Really need some help with Q9
Thank you

 

[PhyZac]

hey PhyZac, Is there any rule about when to use the dot product and when to use cross product in vectors?

Because I get confused in these two sometimes.

Ofcourse, they are so different.

Dot product, gives you the cos of the angle between lines.

Cross product, gives you a vector, this vector is perpendicular to both line.

I will see if i can gather when is each used, but see when a vector perpendicular to two line is to be found cross product is used.
Dot is used for angles.

 

[PhyZac]

Asad

You see I will give a tip for vectors.

When ever you solve make a sketch of all the stuff they told you, and then try to figure out how will you get an answer.

You see in the question of complex you gave I couldn't figure the answer until I made a sketch and tried to use all values I have. So in such questions do try making sketchs, mainly needed to know which two line needed to use cross product to find the perpendicular line to both.

 

[Asad]

PhyZac:

True. But I find it a bt hard to sketch a 3d vector with x, y and z components.
how do u suggest i should go about it?

 

[PhyZac]

Asad

Well, see when you draw sketch don't try to assume where or how the numbers will make the plane or a line look like. Just make and x and y axis and draw a rectangle dont see what is the number or anything, just make a rectangle, and if they say a line is parallel make it as if it is parallel or perpendicular etc.

Check this as an example. https://www.xtremepapers.com/commun...st-your-doubts-here.9599/page-352#post-504194

 

[PANDA-]

Asad
Draw an upside down Y, something like this

and use it like a template to guide you as to where the axis are

 

[PANDA-]

Is it only me or is solving P1 papers very very boring?
I can't finish a whole paper without taking like 3 breaks in between, it's just that boring lol.

 

[Sarah22]

Hi...
1. A function f is defined by f : x → (2x − 3)3 − 8, for 2 ≤ x ≤ 4.
(i) Find an expression, in terms of x, for f(x) and show that f is an increasing function. [4]
(ii) Find an expression, in terms of x, for f−1(x) and find the domain of f−1. [4]
I want the domain part..

2. The equation of a curve is xy = 12 and the equation of a line l is 2x + y = k, where k is a constant.
(i) In the case where k = 11, find the coordinates of the points of intersection of l and the curve. [3]
Ans: ((1.5,8) & (4,3))
(ii) Find the set of values of k for which l does not intersect the curve. [4]
Ans: -√96 < k < √96
(iii) In the case where k = 10, one of the points of intersection is P (2, 6). Find the angle, in degrees
correct to 1 decimal place, between l and the tangent to the curve at P. [4]
Ans: 8.1° or 8.2°
The (ii) and the (iii) part pls..
It would be great help..
Thank you..

 

[Tkp]

Hi...

Thank you..

domain of f-1 is range of fx
so the ramge of fx is >-8 and its the domain also


Xy=12
2x+y=k
2x+12/x=k
2x2+12-kx=0
2x2-kx+12=0
B2-4ac<0
A=2,b=-k,c=12
K2-96<0
K<+-√96
So -√96<k<+√96

 

[Tkp]

Hi...
Thank you..

r u sure about c3?cn u tell me it is in which year

 

[Alice123]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w03_qp_6.pdf
help needed in qs 4i n ii

 

[Muhammad Muneeb]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_11.pdf
q4...

 

[A star]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w03_qp_6.pdf
help needed in qs 4i n ii

4i ) probability of success is (0.05) and failure is (0.95) .
he must fail in all the tries to not complete collection hence (0.95)^5
4ii use binomial approximation =5C1 x (0.15)^1 (0.95)^4

 

[A star]

shouldnt u guys concentrate on p1 now :/

 

[A star]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_11.pdf
q4...

Q4 to find k use the value of M=3.2kg and r= 10 in the formulae
(3.2)=k(10)^3
3.2/1000=k or k=2/625
now use the formulae
dM/dt = dM/dr x dr/dt
here dr/dt =0.1 (given)
find dM/dr =3kr^2 put the value of k and r you will get 0.96
therefore
dM/dt= 0.96 x 0.1 =0.096

 

[immie.rose]

(i) Sketch, on a single diagram, the graphs of y = cos 2q and y = 1
2 for 0 ≤ q ≤ 2p. [3] ( where q= theta)
(ii) Write down the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 0 ≤ q ≤ 2p. [1]
Ans=4
(iii) Deduce the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 10p ≤ q ≤ 20p. [1]
Ans=20

Someone please explain part (iii)!

 

[A star]

(i) Sketch, on a single diagram, the graphs of y = cos 2q and y = 1
2 for 0 ≤ q ≤ 2p. [3] ( where q= theta)
(ii) Write down the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 0 ≤ q ≤ 2p. [1]
Ans=4
(iii) Deduce the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 10p ≤ q ≤ 20p. [1]
Ans=20

Someone please explain part (iii)!

well part ii you found out there are four roots in a cycle that is 0-2p well there are 5 such cycles in 10p to 20p (20-10)/2=5
so if 4 : 1
theta: 5 sycles cross multiply you will get 20