4400 Higher June 2007 Paper 4 Q21
21
(a) Factorise \(16x^2 - 1\) (1)
(b) Hence express as the product of its prime factors
(i) 1599
(ii) \(1.599 \times 10^6\) (5)
| Scheme | Marks |
|---|---|
| \((4x - 1)(4x + 1)\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| (i) \(16 \times 10^2 - 1\) seen or implied | M1 |
| \((4 \times 10 - 1)(4 \times 10 + 1)\) or 39 × 41 | M1 |
| 3 × 13 × 41 | A1 |
| (ii) \(1599 \times 10^3\) or 1599 × 1000 | M1 |
| ‘3×13×41’ \(\times 2^3 \times 5^3\) oe | A1ft |
| (5) | |
| (6 marks) |
Notes
M1: 13 or 39 or 41 or 123 as factor
M1: factors 3, 13, 41 or 39, 41 or 13, 123
A1: Ans 3 × 533 M0A0
M1: or tree including 1000 or 10 and 100
A1ft: ft her (i) \(\times 2^3 \times 5^3\)