Higher November 2021 Paper 1 Q7
7 Write \(3.6 \times 10^3\) as a product of powers of its prime factors.
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
| E.g. \(2 \times 2 \times 900\) or \(2^2 \times 900\) or \(2 \times 3 \times 600\) or \(2 \times 5 \times 360\) or \(3 \times 3 \times 400\) or \(3^2 \times 400\) or \(3 \times 5 \times 240\) or \(5 \times 5 \times 144\) or \(5^2 \times 144\) E.g. ![]() | M1 |
| E.g. \(2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5\) E.g. ![]() | 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 \(3.6 \times 2^3 \times 5^3\))

