Exam (elaborations)
AS & A Level FURTHER MATHEMATICS 9231/13 Paper 1 Further Pure Mathematics 1 May/June 2023 AUTHENTIC MARKING SCHEME ATTACHED
Course
FURTHER MATHEMATICS
Institution
FURTHER MATHEMATICS
AS & A Level FURTHER MATHEMATICS 9231/13 Paper 1 Further Pure Mathematics 1 May/June 2023 AUTHENTIC MARKING SCHEME ATTACHED
[Show more]
Preview 4 out of 32 pages
Uploaded on
April 17, 2024
Number of pages
32
Written in
2023/2024
Type
Exam (elaborations)
Contains
Questions & answers
Institution
FURTHER MATHEMATICS
Course
FURTHER MATHEMATICS
$7.99
Also available in package deal from $27.99
100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached
Also available in package deal (1)
$ 125.36
$ 27.99
14 items
1. Exam (elaborations) - as & a level further mathematics 9231/13 paper 1 further pure mathematics 1 may/june...
2. Exam (elaborations) - as & a level further mathematics 9231/12 paper 1 further pure mathematics 1 may/june...
3. Exam (elaborations) - as & a level further mathematics 9231/11 paper 1 further pure mathematics 1 may/june...
4. Exam (elaborations) - as & a level further mathematics 9231/43 paper 4 further probability & statistics ma...
5. Exam (elaborations) - as & a level urther mathematics 9231/42 paper 4 further probability & statistics may...
6. Exam (elaborations) - as & a level further mathematics 9231/41 paper 4 further probability & statistics ma...
7. Exam (elaborations) - as & a level further mathematics 9231/41 paper 4 further probability & statistics ma...
8. Exam (elaborations) - as & a level further mathematics 9231/33 paper 3 further mechanics may/june 2023 aut...
9. Exam (elaborations) - As & a level further mathematics 9231/32 paper 3 further mechanics may/june 2023 auth...
10. Exam (elaborations) - As & a level further mathematics 9231/31 paper 3 further mechanics may/june 2023 aut...
11. Exam (elaborations) - As & a level further mathematics 9231/23 paper 2 further pure mathematics 2 may/june ...
12. Exam (elaborations) - As & a level further mathematics 9231/22 paper 2 further pure mathematics 2 may/june...
13. Exam (elaborations) - As & a level further mathematics 9231/22 paper 2 further pure mathematics 2 may/june...
14. Exam (elaborations) - As & a level further mathematics 9231/22 paper 2 further pure mathematics 2 may/june...
Show more
Cambridge International AS & A Level
* 0 8 3 4 5 5 7 7 1 1 *
FURTHER MATHEMATICS 9231/13
Paper 1 Further Pure Mathematics 1 May/June 2023
2 hours
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 75.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Any blank pages are indicated.
DC (CE) 311426/2
© UCLES 2023 [Turn over
, 2
BLANK PAGE
© UCLES 2023 9231/13/M/J/23
, 3
1 Prove by mathematical induction that, for all positive integers n, 5 3n + 32 n - 33 is divisible by 31. [6]
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
....................................................................................................................................................................
© UCLES 2023 9231/13/M/J/23 [Turn over
, 4
2 (a) Use standard results from the list of formulae (MF19) to show that
n
/ (6r + 6r - 5) = an + bn + cn ,
2 3 2
r=1
where a, b and c are integers to be determined. [2]
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
n
/ 6r r++6rr- 5 in terms of n.
2
(b) Use the method of differences to find 2 [4]
r=1
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
© UCLES 2023 9231/13/M/J/23