Higher June 2022 Paper 1 Q10
10.
(a) Write 378 as a product of its prime factors.
Give your answer in index form. [3]
Give your answer in index form. [3]
(b) Use prime factors to prove that 1 is the only common factor of 378 and 275. [2]
| Scheme | Marks | Comments |
|---|---|---|
| Method to find prime factors with two correct prime factors seen | M1 | Implied by 2, 3, 3, 3, 7; ignore 1s |
| 2, 3, 3, 3, 7 | A1 | CAO. For sight of the 5 correct factors (Ignore 1’s); may be in e.g. a factor tree |
| \(2\times3^3\times7\) | B1 | FT ‘their derived primes’ provided at least one index form used with at least a square dep on M1 previously awarded Allow (2)(33)(7) and 2.33.7 Inclusion of 1 as a factor gets B0. |
| Scheme | Marks | Comments |
|---|---|---|
| 378 = \(2\times3^3\times7\) or 2, 3, 3, 3, 7 AND 275 = \(5\times5\times11\) or finds prime factors of 275 as 5, 5, 11 OR shows that 2, 3 and 7 are not factors of 275 OR shows that 5 and 11 are not factors of 378 AND a valid comment e.g. ‘They have no prime factors in common’ oe | B2 | 378 = \(2\times3^3\times7\) or 2, 3, 3, 3, 7 may be seen in (a) Valid comments: allow e.g. ‘They have no factors in common (except 1).’ or ‘They only have 1 in common’; do not allow e.g. ‘1 is the only common prime factor’ B1 for partially correct proof e.g.
|
| (5) |