4MA0 Higher January 2015 Paper 4R Q8
8
(a) Write 224 as a product of powers of its prime factors.
Show your working clearly. (3)
Show your working clearly. (3)
(b) Write down 3 different factors of 224 with a sum between 99 and 110 (2)
| Scheme | Marks |
|---|---|
| 224 = 2 × 112 = 2×2×56 = 2×2×2×28 = 2×2×2×2×14 2×2×2×2×2×7 | M1 |
| A1 | |
| \(2^5 \times 7\) | A1 |
| (3) |
Notes
M1: for at least 2 correct steps in repeated factorisation (may be seen in a tree diagram)
A1: 2, 2, 2, 2, 2, 7 ( condone inclusion of 1)
A1: \(2^5 \times 7\)
NB: Candidates showing no working score 0 marks
| Scheme | Marks |
|---|---|
| 56 + 32 + 16 56 + 32 + 14 56 + 28 + 16 | M1 |
| eg. 56, 32, 16 or 56, 32, 14 or 56, 28, 16 | A1 |
| (2) | |
| (5 marks) |
Notes
M1: for any 3 correct distinct factors (excluding 1 and 224)
A1: correct and have a sum between 99 and 110