Higher November 2024 Paper 3 Q18
18 Maria wants to find an estimate for the number of frogs in a lake.
On Saturday she catches 40 of the frogs.
She puts a tag on each frog and releases them.
On Monday she catches 55 of the frogs.
11 of the frogs have tags.
(a) Work out an estimate for the total number of frogs in the lake.
You must show all your working. (3)
You must show all your working. (3)
(b) State one assumption you have made. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 200 | P1 | for \(\frac{55}{11}\ (= 5)\) or \(\frac{11}{55}\ (= 0.2)\) or \(\frac{40}{11}\ (= 3.63..)\) or \(\frac{11}{40}\ (= 0.275)\) or for starting to use ratio eg tagged : untagged = 11 : 44 oe |
| P1 | for \(\frac{11}{55} = \frac{40}{n}\) or \(\frac{11}{40} = \frac{55}{n}\) or \(\frac{55 \times 40}{11}\) oe or for process to find the number of untagged frogs eg \(\dfrac{55 - 11}{11} \times 40\ (= 160)\) | |
| A1 | cao |
Additional guidance
Allow decimal values truncated or rounded to at least 2dp
May be seen in ratio eg 40 : 160
A correct answer with no supportive working gets 0 marks.
| Answer | Mark | Mark scheme |
|---|---|---|
| Assumption | C1 | for a suitable assumption, Acceptable examples no frogs have left/arrived at the lake no tags have fallen off / no lost tags sample of frogs taken was a random sample / this is a representative sample tagged frogs are distributed around the lake no baby frogs / no frogs have died There are (still) 4 untagged for every tagged frog. The tagged frogs had time to blend into the population. It is a closed environment There aren’t any more frogs in the lake No other frogs in the lake Not acceptable examples She has caught all the frogs There are lots of frogs. This is the same lake |