Intermediate June 2017 Unit 1 Q12
12.
(a) Express 700 as a product of its prime factors in index form. [3]
(b) The number 33 554 432 is equal to \(2^{25}\).
Explain how this tells you that 33 554 432 is not a square number. [1]
| Scheme | Marks | Comments |
|---|---|---|
| For a method that produces 2 prime factors from the set {2, 2, 5, 5, 7} before the 2nd error. | M1 | |
| 2, 2, 5, 5, 7 | A1 | C.A.O. For sight of the five correct factors (Ignore 1s) |
| \(2^2 \times 5^2 \times 7\) | B1 | F.T. ‘their primes’ provided at least one index form used with at least a square. Do not F.T. non-primes. Allow (22)(52)(7) and 22.52.7 Do not allow 22,52,7. Inclusion of 1 as a factor gets B0. |
| Scheme | Marks | Comments |
|---|---|---|
| Any reference to the index being an odd number. e.g. ‘power must be even’, ’25 is odd’ etc. | E1 | Do not accept e.g. ‘should be 224 ‘, ‘it isn’t even’. |