Easy -1.2 This is a straightforward counter-example question requiring only testing small values of n until finding one where 6n-1 is composite. For n=2, 6(2)-1=11 is prime, but n=4 gives 6(4)-1=23 (prime), and n=5 gives 29 (prime), but n=6 gives 35=5×7 (composite). This requires minimal calculation and no sophisticated reasoning—just systematic checking, making it easier than average.
3 A student makes the following conjecture.
For all positive integers \(n , 6 n - 1\) is always prime.
Use a counter example to disprove this conjecture.
e.g. \(6\times1-1=5\); sight of any value in the table would imply the M1
e.g. \(6\times6-1=35=5\times7\) which is not prime
A1
Must show factorisation to show it's not prime and give a concluding comment e.g. 'not prime'. If they say '35 is divisible by 5' so not prime etc then A1 BUT '35 isn't prime' is A0
# Question 3:
$6n-1$ evaluated for any positive integer | M1 | e.g. $6\times1-1=5$; sight of any value in the table would imply the M1
e.g. $6\times6-1=35=5\times7$ which is not prime | A1 | Must show factorisation to show it's not prime and give a concluding comment e.g. 'not prime'. If they say '35 is divisible by 5' so not prime etc then A1 BUT '35 isn't prime' is A0
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3 A student makes the following conjecture.\\
For all positive integers $n , 6 n - 1$ is always prime.
Use a counter example to disprove this conjecture.
\hfill \mbox{\textit{OCR MEI AS Paper 2 2023 Q3 [2]}}