June 2017 Paper 2 Q3
3
(a) \(p\), \(q\) and \(r\) are all integers greater than 1
\(pqr = 1365\)
Work out one possible set of values for \(p\), \(q\) and \(r\). [2 marks]
(b) \(a\) and \(b\) are both square numbers greater than 1
\(ab - 11b\) is also a square number.
By factorising \(ab - 11b\), work out one possible pair of values for \(a\) and \(b\).
You must show your working. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| 3 (×) 455 or 5 (×) 273 or 7 (×) 195 or 13 (×) 105 or 15 (×) 91 or 21 (×) 65 or 35 (×) 39 or 3 (×) 5 (×) 7 (×) 13 | M1 | oe eg \(1365 \div 5 = 273\) Any order Must be integers May be seen in a factor tree or repeated division |
| 3 5 91 or 3 7 65 or 3 13 35 or 5 7 39 or 5 13 21 or 7 13 15 | A1 | Any order Must be integers |
Additional guidance
| If using division the correct answer must be seen for M1 | |
| Correct answer can be implied by working lines eg 3 (×) 5 (×) 91 with blank answer line | M1A1 |
| Answer line correct | M1A1 |
| Allow inclusion of 1 for M1 eg 1 (×) 3 (×) 455 | M1 |
| Answer | Mark | Comments |
|---|---|---|
| \(b(a - 11)\) or \(-b(11 - a)\) | M1 | Implied by square numbers \(\gt 1\) used eg1 \(4(36 - 11)\) eg2 \(9(16 - 11)\) |
| \(a = 36\) and \(b\) = square number \(\gt 1\) with working for M1 seen | A1 | Must be in correct order Allow unprocessed squares eg \(a = 6^2\) and \(b = 5^2\) SC1 \(a = 36\) and \(b\) = square number \(\gt 1\) without working for M1 seen |
Additional guidance
| \(b(a - 11) = 0\) or \(b(a - 11)\) with further work | M1 |
| Answer line takes precedence over working lines | |
| Embedded answer eg \(81(36 - 11)\) | M1A0 |