Higher November 2021 Paper 4 Q5
5
(a) Fountain A squirts water every 24 minutes.
Fountain B squirts water every 42 minutes.
They squirt water together at 15:19.
Fountain B squirts water every 42 minutes.
They squirt water together at 15:19.
Find the next time they squirt water together. [4]
(b) A school sends 60 students from Year 8 and 105 students from Year 9 to a museum.
The school divides these students into groups using the following rules.
- The groups must all be the same size.
- All students in any group must be from the same year.
- There should be as few groups as possible.
Find the size of each group and the total number of groups. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 18 07 [pm] or 6 07 pm | 4 | B3 for 18 07 am or 6 07 [am] OR B2 for listing the next three correct times of both fountains, i.e. 15 43, 16 07, 16 31 and 16 01, 16 43, 17 25 OR B1 for listing the next three correct times of one fountain, i.e. 15 43, 16 07, 16 31 or 16 01, 16 43, 17 25. | Condone use of 12 hour clock e.g. [0]3 43 and 3 43 am for B1 and B2 |
| Alternative method B3 for 2[h] 48[m] OR B2 for [LCM=] 168 OR B1 for listing the next three multiples of 24 and 42, i.e. 48, 72, 96 and 84, 126, 168 OR M1 for [24 =] 2 × 2 × 2 × 3 or [42 =] 2 × 3 × 7 allow in a factor tree or table or [LCM=] 168\(k\) (\(k \ne 1\)) and M1 for correctly converting their time(mins) to hours and mins | their time must be over 60 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [size] 15 [number] 11 | 4 | B3 for 15 and 11 OR B2 for [HCF or group size =] 15 or M2 for [60] = 2 × 2 × 3 × 5 and [105] = 3 × 5 × 7 or for listing complete factors of both numbers allow in a factor tree or table | accept any correct method [60] 1,2,3,4,5,6,10,12,15,20,30,60 [105] 1,3,5,7,15,21,35,105 |
| OR M1 for one of 2 × 2 × 3 × 5 or 3 × 5 × 7 allow in a factor tree or table or for common factors 3 or 5 AND B1 for [size] 3 [number] 55 or [size] 5 [number] 33 | |||