Higher June 2019 Unit 1 Q1
1.
(a) Express 315 as a product of its prime factors in index form. [3]
(b) What is the Highest Common Factor (HCF) of 315 and 42? [2]
| Scheme | Marks | Comments |
|---|---|---|
| For a method that produces 2 prime factors from the set {3, 3, 5, 7} before the 2nd error. | M1 | |
| 3, 3, 5, 7 | A1 | C.A.O. For sight of the four correct factors (Ignore 1s) |
| \(3^2 \times 5 \times 7\) | B1 | FT ‘their primes’ provided at least one index form used with at least a square. Allow (32)(5)(7) and 32.5.7 Inclusion of 1 as a factor gets B0. |
| Scheme | Marks | Comments |
|---|---|---|
| 42 = 2 × 3 × 7 or equivalent correct strategy. | M1 | M1 for sight of 2, 3, 7 ‘together’. (Not for 2x21, 3x14 and 6x7.) (Not for just listing all factors 1,2,3,6,7,14,21.) |
| (HCF =) 21 | A1 | M1A0 for 3 × 7. FT ‘their answer to 1(a)’ only if of equivalent difficulty (at least two common prime factors). |