Higher June 2023 Paper 1 Q8
8
Show your working clearly. (2)
\(A = 2 \times 2 \times 2 \times 3 \times 3 \times 5\)
\(B = 2 \times 2 \times 3 \times 3 \times 3 \times 5\)
Show your working clearly. (2)
| Scheme | Marks | ||||||
|---|---|---|---|---|---|---|---|
| eg 2 × 2 × 75 or 3 × 5 × 20 or 2 × 3 × 50 or 5² × 12 or
| M1 | ||||||
| Working required Answer: 2 × 2 × 3 × 5 × 5 | A1 | ||||||
| (2) |
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, 75 (see LHS for examples of the amount of work needed for the award of this mark). Example of 3 stages with 1 incorrect stage:
300 = 100 × 30 = 2 × 50 × 5 × 6
A1: dep on M1, oe eg \(2^2 \times 3 \times 5^2\)
| Scheme | Marks |
|---|---|
| (5\(A\) =) 2 × 2 × 2 × 3 × 3 × 5 × 5 oe (= 1800) or (5\(A\) =) \(2^3 \times 3^2 \times 5^2\) (= 1800) or (7\(B\) =) 2 × 2 × 3 × 3 × 3 × 5 × 7 oe (= 3780) or (7\(B\) =) \(2^2 \times 3^3 \times 5 \times 7\) (= 3780) | M1 |
| Working required Answer: 37 800 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for method to find 5\(A\) or 7\(B\) as prime factors (may be seen in factor tree, table or Venn diagram) or as an integer
or for listing at least 3 multiples of each number eg 1800, 3600, 5400... and 3780, 7560, 11 340...
or for an answer of 1080 oe eg \(2^3 \times 3^3 \times 5\)
A1: dep on M1, oe eg \(2^3 \times 3^3 \times 5^2 \times 7\)