Foundation November 2021 Paper 1 Q19
19 Write \(3.6 \times 10^3\) as a product of powers of its prime factors.
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
| E.g. 2 × 2 × 900 or \(2^2\) × 900 or 2 × 3 × 600 or 2 × 5 × 360 or 3 × 3 × 400 or \(3^2\) × 400 or 3 × 5 × 240 or 5 × 5 × 144 or \(5^2\) × 144 or e.g. a factor ladder or tree: 3600 = 2 × 1800, 1800 = 2 × 900 | M1 |
| E.g. 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 or e.g. a fully correct factor ladder or tree: 3600, 1800, 900, 450, 225, 75, 25, 5 divided in turn by 2, 2, 2, 2, 3, 3, 5, 5 | M1 |
| Working required Answer: \(2^4 \times 3^2 \times 5^2\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for at least 2 correct stages in prime factorisation which give 2 prime factors – may be in a factor tree or a table or listed eg 2, 2, 900
(see LHS for examples of the amount of work needed for the award of this mark, allow no more than one mistake ft in factor tree or table
(eg one mistake with 2 prime factors ft: 3600 = 1800 × 20 = 2 × 900 × 4 × 5 or 360 = 2 × 2 × 90)
M1: for 2, 2, 2, 2, 3, 3, 5, 5 or \(2^4\), \(3^2\), \(5^2\) or \(2^4 + 3^2 + 5^2\) (ignore 1s) (may be a fully correct factor tree or ladder)
A1: dep on M2
can be any order (allow \(2^4 . 3^2 . 5^2\))
(SCB1 for \(3.6 \times 2^3 \times 5^3\))