100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
AQA A-LEVEL MATHS QUESTIONS AND ANSWERS FOR ALL TOPICS! £7.16
Add to cart
Quickly navigate to
Preview
  2.  
  3. AQA
  4.  
  5. Mathematics
  6.  
  7. ALL MODULES

Exam (elaborations)

AQA A-LEVEL MATHS QUESTIONS AND ANSWERS FOR ALL TOPICS!
 0 purchase
  • Institution
  • AQA

Proof Algebra and functions Coordinate geometry - Sequences and series Trigonometry Exponentials and logarithms Differentiation - Integration Numerical methods (A-level only) Vectors Statistical sampling Data representation and intepretation Probability Statistical distributions Stati...

[Show more]

Preview 3 out of 16  pages

Document information

  • May 28, 2024
  • 16
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers

Subjects

Written for

All documents for this subject (1)

Seller

avatar-seller
nxv

Content preview

_______________________
Name:
_
A: Proof
_______________________
Class:
_


_______________________
Date:
_




Time: 77 minutes



Marks: 65 marks



Comments:




Page 1 of 16

,Q1.
Prove that

n is a prime number greater than 5 ⇒ n4 has final digit 1
(Total 5 marks)


Q2.
p(x) = 30x3 − 7x2 − 7x + 2

(a) Prove that (2x + 1) is a factor of p(x)
(2)

(b) Factorise p(x) completely.
(3)

(c) Prove that there are no real solutions to the equation




(5)
(Total 10 marks)


Q3.
Which of these statements is correct?

Tick one box.


x = 2 ⇒ x2 = 4


x2 = 4 ⇒ x = 2


x2 = 4 ⇔ x = 2


x2 = 4 ⇒ x = −2

(Total 1 mark)


Q4.
Prove that 23 is a prime number.
(Total 2 marks)


Q5.
Prove by contradiction that is an irrational number.


Page 2 of 16

, (Total 7 marks)


Q6.
Jessica, a maths student, is asked by her teacher to solve the equation tan x = sin x ,
giving all solutions in the range 0° ≤ x ≤ 360°

The steps of Jessica’s working are shown below.




The teacher tells Jessica that she has not found all the solutions because of a mistake.

Explain why Jessica’s method is not correct.
(Total 2 marks)


Q7.
Prove that the function f(x) = x3 − 3x2 + 15x − 1 is an increasing function.
(Total 6 marks)


Q8.
(a) Given that n is an even number, prove that 9n2 + 6n has a factor of 12
(3)

(b) Determine if 9n2 + 6n has a factor of 12 for any integer n .
(1)
(Total 4 marks)


Q9.
p(x) = 2x3 + 7x2 + 2x − 3

(a) Use the factor theorem to prove that x + 3 is a factor of p(x)
(2)



(b) Simplify the expression
(4)
(Total 6 marks)




Page 3 of 16

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

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

Quick and easy check-out

You can quickly pay through credit card for the summaries. There is no membership needed.

Focus on what matters

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 nxv. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for £7.16. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

64257 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy revision notes and other study material for 15 years now

Start selling

Recently viewed by you

Lecture notes ·

(0)

Study Notes for Exams

Other ·

(0)

Histologie 1BMLT: samenvatting

Other ·

(1)

Bewijslasten praktijkleren 4 stage HBO-verpleegkunde

Exam (elaborations) ·

(0)

HESI RN Fluid and electrolyte imbalances Notes

Exam (elaborations) ·

(0)

Army Training questions and answers already graded A+ 2024/2025

Exam (elaborations) ·

(0)

Test bank-focus-on-adult-health-medical-surgical-nursing-2nd-edition-honan complete-guide

Case ·

(0)

Afstudeerscriptie, Casestudy, Jaar 4

Summary ·

(0)

Samenvatting Van gedachten wisselen, ISBN: 9789046906781 Inleiding Praktische Filosofie Voor Pedagogen Deel A

Summary ·

(0)

Migration, identity and sovereignty guide for a level edexcel geography

£7.16
  • (0)
Add to cart
Added