Foundation June 2019 Paper 1 Q20
20.
(a)
\(120 = 2^3 \times 3^k \times 5\)
Find the value of \(k\). [1]
(b) Write 168 as a product of its prime factors. [2]
(c)
LoWatts Ltd makes light bulbs that are identical in size.
They have regular orders from Company A for 120 light bulbs and from Company B for 168 light bulbs.
LoWatts Ltd uses one size of box to supply both Company A and Company B.
Each box used contains the same number of light bulbs and is full.
The number of boxes used is as few as possible.
How many light bulbs does each box hold? [3]
| Scheme | Marks | Comments |
|---|---|---|
| 1 | B1 | May be embedded |
| Scheme | Marks | Comments |
|---|---|---|
| Method to find prime factors with two correct prime factors seen before the second error | M1 | Ignore 1’s; the two prime factors may be correct or correct FT after one error |
| 2 × 2 × 2 × 3 × 7 oe | A1 | ISW |
| Scheme | Marks | Comments |
|---|---|---|
| Attempts to find a common factor of 168 and 120 | S1 | e.g. May list some of the factors of both 168 and 120 or draw a Venn diagram with the factors of 168 and 120 correctly positioned |
| Finds at least one common factor of 168 and 120 greater than 3 | M1 | FT ‘their (a) and their (b)’ 4, 6, 8, 12, 24 |
| 24 | A1 | CAO Mark final answer |
| (6) |