Numeracy Intermediate November 2024 Unit 2 Q10
10. Aderyn is a company that makes bird feeders.
Squirrels often try to steal food from bird feeders.
To make this more difficult, Aderyn has designed a new bird feeder.
Aderyn tests its new feeder to check how long it takes squirrels to reach the food inside.
The results are displayed in the cumulative frequency diagram below.
Aderyn has the following information about the time it took squirrels to reach the food in its original bird feeder.
| Original bird feeder | |
|---|---|
| Modal group | 60 to 80 seconds |
| Median time | 75 seconds |
| Interquartile range | 20 seconds |
Aderyn compared the times squirrels take to reach the food in the original bird feeder and the times they take to reach food in the new bird feeder.
Complete this sentence:
‘The modal group for the new bird feeder is between …………… and …………… seconds.’
Does the modal group for the new bird feeder imply that there is an improvement in the times? [1]
Yes ☐ No ☐
Use the cumulative frequency diagram and the table to give the best estimate to complete each of the following sentences.
Use the cumulative frequency diagram to give the best estimate to complete the following sentence. [3]
‘20% of the squirrels took …………… seconds or more to reach the food in the new bird feeder.’
The population density of grey squirrels in forests depends on the variety of tree that grows there.
| Variety of tree | Typical population density of grey squirrels per km2 |
|---|---|
| Oak | 1200 |
| Chestnut | 100 |
| Pine | 45 |
Rhian says,
‘I know that Maesgwyn forest has only one variety of tree:
oak, chestnut or pine.’
Maesgwyn forest covers an area of 21 500 m2.
There are 24 grey squirrels living in Maesgwyn forest.
From this information, which variety of tree is most likely to be found in Maesgwyn forest?
You must show working to support your answer. [3]
Oak ☐ Chestnut ☐ Pine ☐
| Scheme | Marks | Comments |
|---|---|---|
| (i) States 80 (and) 100 (seconds) AND indicates ‘Yes’ | B1 | Allow written as 100 and 80 Answer space takes precedence |
| (ii) I. (80 – 75 =) 5 (seconds) | B1 | Not from incorrect working Answer space takes precedence |
| II. Answer in the inclusive range 12 to 14 (seconds) | B2 | Allow in this range only provided it not from incorrect working Answer space takes precedence B1 for sight of 92 – 60 (– 20) to 94 – 60 (– 20) or 32 (–20) to 34 (– 20) |
| Scheme | Marks | Comments |
|---|---|---|
| 96 (seconds) | B3 | Answer space takes precedence B2 for sight of or indication of 64 (squirrels), B1 any one of the following:
20% of 120 = 24, with time 64 seconds B0 for 96 seconds from incorrect working, 80% of 120 = 96, with time 96 seconds |
| Scheme | Marks | Comments |
|---|---|---|
| (24 ÷ 21 500) × 1 000 000 (squirrels per km2) | M2 | Accept using estimation: (24 ÷ 20 000) × 1 000 000 M1 for any one of the following, including if embedded:
|
| 1116(.27...) (squirrels per km2) AND Conclusion indicated or unambiguously implied ‘Oak’ | A1 | Accept 1200 from estimating, i.e. (24 ÷ 20 000) × 1 000 000 =1200 (squirrels per km2) If no marks, award SC1 for appropriate sight of a calculation of 24 ÷ ‘a number with only non-zero digits 215’, provided not embedded in further working apart from multiplication or division by powers of 10 |
Alternative
10(c) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (If oak, number of squirrels likely in Maesgwyn Forest) 21 500 × 1200 ÷ 1 000 000 | M2 | Allow M2 for (If chestnut) 21 500 × 100 ÷ 1 000 000 (= 2.15) or (if pine) 21 500 × 45 ÷ 1 000 000 (= 0.9675) M1 for any one of the following, including if embedded:
|
| 25.8 (squirrels) AND ‘Oak’ indicated as conclusion | A1 | Allow from correct working either 2.15 (squirrels for Chestnut so must be) Oak, or 0.9675 or 1 (squirrels for Pine so must be) Oak If no marks, award SC1 for appropriate sight of any 1 of the following calculations:
|