Intermediate June 2022 Unit 1 Q5
5.
(a) Find a whole number value of \(n\), so that \(7n - 9\) is a multiple of 4.
You must show all your working. [2]
You must show all your working. [2]
When \(n =\) ………………, \(7n - 9\) is a multiple of 4.
(b) Find a whole number value of \(n\), so that \(3n - 5\) is a prime number.
You must show all your working. [2]
You must show all your working. [2]
When \(n =\) ………………, \(3n - 5\) is a prime number.
| Scheme | Marks | Comments |
|---|---|---|
| Any \(n\), as a whole number, which results in \(7n - 9\) being a multiple of 4 | B2 | Answer space takes precedence and must not be from incorrect working. Do not ignore crossed-out work for this question. Award B1 for any one of:
e.g. if 7 × 4 – 9 = 19, then \(n\) = 19 on the answer line. |
Table
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | …… |
| \(7n\) - 9 | -2 | 5 | 12 | 19 | 26 | 33 | 40 | 47 | 54 | 61 | 68 | …… |
(This table is printed in the comments column, after the list above. The highlighted columns were shaded in the original.)
| Scheme | Marks | Comments |
|---|---|---|
| Any \(n\), as a whole number, which results in \(3n - 5\) being a prime number | B2 | Answer space takes precedence and must not be from incorrect working. Do not ignore crossed-out work for this question. Award B1 for any one of:
e.g. if 3 × 4 – 5 = 13, then \(n\) = 13 on the answer line. |
Table
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | …… |
| \(3n\) - 5 | -2 | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 22 | 25 | 28 | …… |
(This table is printed in the comments column, after the list above. The highlighted columns were shaded in the original.)