4MA0 Foundation June 2014 Paper 2R Q22
22
(a) Write 252 as a product of its prime factors. (2)
Given that \(240 = 2^4 \times 3 \times 5\)
and that \(y = 240 \times 252\)
(b) write \(y\) as a product of powers of its prime factors. (2)
| Scheme | Marks |
|---|---|
| 252 = 2 × 126 = 2 × 2 × 63 = 2 × 2 × 3 × 21 | M1 |
| 2×2×3×3×7 | A1 |
| (2) |
Notes
M1: for a process that isolates at least 2 correct prime factors e.g. 252 = 2 × 126, 126 = 3 × 42 or a factor tree with 2 primes from 2, 3 or 7 identified or repeated division
A1: for 2×2×3×3×7 oe with correct prime factors
| Scheme | Marks |
|---|---|
| \(2^2 \times 3^2 \times 7 \times 2^4 \times 3 \times 5\) | M1 |
| \(2^6 \times 3^3 \times 5 \times 7\) | A1 |
| (2) | |
| (Total 4 marks) |
Notes
M1: \(\text{“}2^2 \times 3^2 \times 7\text{”} \times 2^4 \times 3 \times 5\) or a fully correct factor tree or fully correct repeated division
A1: cao accept in any order eg \(3^3 \times 2^6 \times 7 \times 5\)