Higher June 2023 Paper 1R Q1
1 Write 2250 as a product of powers of its prime factors.
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
| e.g. 2 × 5 × 225 or 5 × 5 × 90 or \(5^2 \times 90\) 3 × 5 × 150 or 3 × 3 × 250 or \(3^2 \times 250\)  | M1 |
e.g. 2 × 3 × 3 × 5 × 5 × 5 | M1 |
| Working required Answer: \(2 \times 3^2 \times 5^3\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for 2 correct stages in prime factorisation with 0 incorrect stages
or at least 3 stages in prime factorisation with no more than 1 incorrect stage.
Each stage gives 2 factors – may be in a factor tree or a table or listed eg 2, 2, 225
(see LHS for examples of the amount of work needed for the award of this mark).
Example of 3 stages with 1 incorrect stage:
2250 = 225 × 100 = 3 × 5 × 15 × 100
or 225 = 3 × 5 × 15
M1: for 2, 3, 3, 5, 5, 5 or
2 × 3 × 3 × 5 × 5 × 5 or
2, \(3^2\), \(5^3\) oe or
\(2 + 3^2 + 5^3\)
(ignore 1s)
(may be a fully correct factor tree or ladder)
A1: dep on M2
can be any order (allow \(2 . 3^2 . 5^3\))