Higher June 2025 Paper 3 Q20
20
(a) Factorise fully \(\quad 3n^2 + 5n + 2\) [2 marks]
(b) A sequence has \(n\)th term \(\quad 3n^2 + 5n + 2\)
Are any of the terms in the sequence a prime number?
Tick a box.
- Yes
- No
Give a reason for your answer. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \((3n + 2)(n + 1)\) | B2 | oe product of brackets any consistent letter condone = 0 ignore any attempt to solve B1 \((3n + 2)\) or \((n + 1)\) seen in a product of 2 linear brackets or \(3n(n + 1) + 2(n + 1)\) or \(n(3n + 2) + (3n + 2)\) |
Additional guidance
| \((3n + 2)(n + 1) + k\) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| No and valid reason | B1 | valid reasons include the sequence is always even and greater than 2 \(n + 1\) and \(3n + 2\) cannot be equal to 1 each term can be made by multiplying (whole) numbers together not equal to 1 \(n + 1\) and \(3n + 2\) are factors not equal to 1 |
Additional guidance
| Yes ticked | B0 |
| No reason given | B0 |
| No ticked, and every term in the sequence is even and the first term is 10 | B1 |
| No ticked, and odd + odd + 2 is even, even + even + 2 is even and first term is 10 | B1 |
| No ticked, and every term in the sequence is even | B0 |
| No ticked, and \(3n^2\) can never be prime | B0 |
| No ticked, and + 2 means it can never be prime | B0 |