Intermediate June 2023 Unit 1 Q12
12.
(a) Express 675 as a product of its prime factors in index form. [3]
(b) 360 expressed as a product of its prime factors in index form is \(2^3 \times 3^2 \times 5\).
What is the smallest whole number that 360 can be multiplied by to give a square number? [1]
What is the smallest whole number that 360 can be multiplied by to give a square number? [1]
Smallest whole number is ……………………
| Scheme | Marks | Comments |
|---|---|---|
| For a single method that produces 2 prime factors from the set {3, 3, 3, 5, 5} before the 2nd error. | M1 | Must be a method that involves only division. Check for errors in the method before checking the 2 prime factors from the set. (Note 675 = 5 × 135 675 = 3 × 225 135 = 5 × 27 135 = 3 × 45) |
| 3, 3, 3, 5, 5 | A1 | CAO. For sight of the five correct factors (Ignore 1s) |
| \(3^3 \times 5^2\) | B1 | Do not FT non-primes. FT ‘their primes’ provided at least one index form used with at least a square. Allow \((3^3)(5^2)\) and \(3^3.5^2\) and \(3^35^2\) Do not allow \(3^3,5^2\) Inclusion of 1 as a factor gets B0. |
| Scheme | Marks | Comments |
|---|---|---|
| 10 | B1 | Do not accept 2 × 5. |