100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
Previously searched by you
A-LEVEL Pearson Edexcel LEVEL 3 GCE In A Level Further Mathematics (9FM0) Paper 3A Further Pure Mathematics 1 Exam Question paper (AUTHENTIC MARKING SCHEME ATTACHED) *P65497A0132* $9.74
Add to cart
A-LEVEL Pearson Edexcel LEVEL 3 GCE In A Level Further Mathematics (9FM0) Paper 3A Further Pure Mathematics 1 Exam Question paper (AUTHENTIC MARKING SCHEME ATTACHED) *P65497A0132*
3 views 0 purchase
Course
FURTHER MATHEMATICS
Institution
PEARSON (PEARSON)
Q:1/1/1/1/
A-LEVEL Pearson Edexcel LEVEL 3 GCE
In A Level Further Mathematics (9FM0)
Paper 3A Further Pure Mathematics 1 Exam Question paper
(AUTHENTIC MARKING SCHEME ATTACHED)
*P65497A0132*
, x2 y2
1. An ellipse has equation 1 and eccentricity e 1
16 4
A hyperbola has equation x2 y2 1 and eccentricity e 2
a2 b2
Given that e 1 × e 2 = 1
(a) show that a 2 = 3b 2
(4)
Given also that the coordinates of the foci of the ellipse are the same as the coordinates
of the foci of the hyperbola,
(b) determine the equation of the hyperbola.
(3)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
, 2. During 2029, the number of hours of daylight per day in London, H, is modelled by
the equation
x – 4 cos x + 11.5
H = 0.3 sin 0 x < 365
60 60
where x is the number of days after 1st January 2029 and the angle is in radians.
(a) Show that, according to the model, the number of hours of daylight in London on
the 31st January 2029 will be 8.13 to 3 significant figures.
(1)
x
(b) Use the substitution t tan to show that H can be written as
120
H at 2 bt c
2
1 t
where a, b and c are constants to be determined.
(2)
(c) Hence determine, according to the model, the date of the first day of 2029 when
there will be at least 12 hours of daylight in London.
(4)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4
*P65497A0432*
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller StudyTimeOT. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.74. You're not tied to anything after your purchase.
