Higher June 2024 Paper 2R Q1
1 Write 1400 as a product of powers of its prime factors.
Show your working clearly.
(3)
| Scheme | Marks | ||||||
|---|---|---|---|---|---|---|---|
| eg 2 × 2 × 350 or 2 × 7 × 100 or 2 × 5 × 140 or 5 × 7 × 40 or 5 × 5 × 56 or (14 × 100 =) 2 × 7 × 100 or (28 × 50 = 4 × 7 × 50 =) 2 × 2 × 7 × 50 = or
| M1 | ||||||
| eg 2, 2, 2, 5, 5, 7  | M1 | ||||||
| Working required Answer: \(2^3 \times 5^2 \times 7\) | 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, 350 (see LHS for examples of the amount of work needed for the award of this mark).
Example of 3 stages with 1 incorrect stage:
1400 = 10 × 14 = 2 × 5 × 2 × 7
M1: dep on M1 for 2 × 2 × 2 × 5 × 5 × 7 or 23, 52, 7 or 23 + 52 + 7
(Ignore 1’s)
(may be seen in a fully correct factor tree or ladder)
A1: dep on M2 (do not allow 1 in the final answer)
Can be in any order (allow 23 . 52 . 7 ) but must be in index form as asked for.