Exam (elaborations)

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

Rating

Sold

Pages

Grade

A+

Uploaded on

05-03-2024

Written in

2023/2024

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*

Institution

Course

Content preview

Please check the examination details below before entering your candidate information

Candidate surname Other names

Centre Number Candidate Number

Pearson Edexcel Level 3 GCE
reference 9FM0/3A
Paper
Time 1 hour 30 minutes
Further Mathematics  

Advanced
PAPER 3A: Further Pure Mathematics 1

You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator

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)

Q:1/1/1/1/ *P65497A0132*

P65497A
©2022 Pearson Education Ltd.

, 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
*P65497A0232*


,Question 1 continued
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

(Total for Question 1 is 7 marks)
3

 *P65497A0332* Turn over

, 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*



Report Copyright Violation

Written for

Study Level: A/AS Level
Examinator: PEARSON (PEARSON)
Subject: MATHEMATICS
Unit: FURTHER MATHEMATICS

Document information

Uploaded on: March 5, 2024
Number of pages: 53
Written in: 2023/2024
Type: Exam (elaborations)
Contains: Questions & answers

Subjects

further pure mathematics
a level pearson edexcel level 3 gce
a level further mathematics 9fm0

$11.01

Get access to the full document:

Written by students who passed

Immediately available after payment

Read online or as PDF

Get to know the seller

StudyTimeOT

5.0

(1)

Also available in package deal

Get to know the seller

StudyTimeOT

View profile

Sold

Member since

2 year

Number of followers

Documents

246

Last sold

1 year ago

Your Assignment P.A

Need academic assistance? Look no further! From assignments to exams, essays to study guides, I've got you covered. Specializing in top-notch writing services, including essay writing, report drafting, and research & citation assistance. Whether you need help with assignments, online classes, exams, or academic writing tasks, I'm here to support you every step of the way. I also offer test banks, study guides, and exams for any subject at a favorable price. Access study materials from Stuvia, Docsity, Docmerit, and Course Hero. Feel free to DM me for more information. If you're satisfied with my service, I'd greatly appreciate a positive review! Your feedback helps me improve and assist more students like you. For compliments and complaints, please DM me. Additionally, I'm open to discussing any document or topic you need help with. Let's achieve academic success together! Contact Information: E m a i l: revisionmaterials01 at g mail dot com D i s c o r d S e r v e r: Your Assignment Handler T w i t t e r: @Assignment_P_A Feel free to reach out anytime for any academic assistance you need! Let’s Ace The Course Together…..!!!!!!!

Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.

Didn't get what you expected? Choose another document

No worries! You can instantly pick a different document that better fits what you're looking for.

Pay as you like, start learning right away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

“Bought, downloaded, and aced it. It really can be that simple.”

Alisha Student

Frequently asked questions

Can't I just make this for free with AI?

AI tools give you vast, general information. They don't know your course, your professor, or what actually gets asked in your exam. This document was written by a fellow student who understood the nuances of exactly this course and passed it. You get focused, curated study material, not a generic starting point you still have to rework.

Is this document still relevant for my course?

Every document shows the academic year, the linked textbook, and the institution, so you can check upfront whether it matches your course. Take a look at the free preview too to see if it fits.

What if the document isn't what I hoped?

No worries! If you change your mind within 14 days of purchase and have not downloaded the document yet, you will get a refund. Your purchase is completely risk-free.

Who am I buying these notes from?

Stuvia is a marketplace: you buy directly from the student who created the document. Stuvia handles payment securely and backs every purchase with the free exchange guarantee, so you never take on any risk.

Will I be stuck with a subscription?

No. You pay $11.01 once for this document and nothing more. No subscription, no auto-renewal, no fine print.

What do I get when I buy this document?

You get a PDF that is available immediately after payment. You can read the document online or download it, and it stays accessible through your profile indefinitely.

Can Stuvia be trusted?

4.6 stars on Google and Trustpilot from over 2,000 reviews. In the past 30 days 32257 documents were sold through Stuvia internationally. And we have been doing this for 16 years now. Every document also shows its rating and how many times it has been sold.

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*

Content preview

Written for

Document information

Subjects

Also available in package deal

Get to know the seller

Why students choose Stuvia

Created by fellow students, verified by reviews

Didn't get what you expected? Choose another document

Pay as you like, start learning right away

Working on your references?

Frequently asked questions

Can't I just make this for free with AI?

Is this document still relevant for my course?

What if the document isn't what I hoped?

Who am I buying these notes from?

Will I be stuck with a subscription?

What do I get when I buy this document?

Can Stuvia be trusted?

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