S1 June 2016 Q1
1. A biologist is studying the behaviour of bees in a hive. Once a bee has located a source of food, it returns to the hive and performs a dance to indicate to the other bees how far away the source of the food is. The dance consists of a series of wiggles. The biologist records the distance, \(d\) metres, of the food source from the hive and the average number of wiggles, \(w\), in the dance.
| Distance, \(d\) m | 30 | 50 | 80 | 100 | 150 | 400 | 500 | 650 |
|---|---|---|---|---|---|---|---|---|
| Average number of wiggles, \(w\) | 0.725 | 1.210 | 1.775 | 2.250 | 3.518 | 6.382 | 8.185 | 9.555 |
[You may use \(\sum w = 33.6 \quad \sum dw = 13\,833 \quad \mathrm{S}_{dd} = 394\,600 \quad \mathrm{S}_{ww} = 80.481\) (to 3 decimal places)]
A new source of food is located 350 m from the hive.
| Scheme | Marks |
|---|---|
| \(\mathrm{S}_{dw} = 13833 - \dfrac{\text{"}1960\text{"} \times 33.6}{8}\) or \(13833 - \dfrac{65856}{8}\) (But 13833 – 8232 is M0) | M1 |
| \(= \)5601 (*) | A1 cso |
| (2) |
Notes
M1 for clear attempt to find \(\Sigma d\) and use in a correct formula. Accept \(1300 \lt \Sigma d \lt 2500\)
For the M1 we can condone a single slip e.g. using 1383 instead of 13833 etc
A1cso for correct \(\Sigma d\) and 5601 only. Must see the formula and so have scored M1
| Scheme | Marks |
|---|---|
| \(w\), since the number of wiggles depends on the distance or \(w\) depends on \(d\) | B1 |
| (1) |
Notes
B1 Must select \(w\) (or wiggles) and reason based on the idea that \(w\) is dependent on \(d\)
Allow \(w\) “changes according to”/ “is determined/affected by” Must mention \(w\) and \(d\)
B0 for “\(w\) is measured” or “\(d\) is explanatory/indep’t” or “\(w\) can’t be controlled” or “\(w\) responds to \(d\)”
| Scheme | Marks |
|---|---|
| \(r = \dfrac{5601}{\sqrt{394600 \times 80.481}},\ = 0.99389\ldots\) awrt 0.994 | M1,A1 |
| (2) |
Notes
M1 for a correct expression (Allow ft of their incorrect \(\mathrm{S}_{dw}\))
A1 for awrt 0.994 (Answer only 2/2) [Answer only of 0.99 scores M1A0]
| Scheme | Marks |
|---|---|
| \(b = \dfrac{5601}{394600},\ = 0.014194\ldots\) (awrt 0.014) | M1, A1 |
| \(a = \dfrac{33.6}{8} - \text{"}0.01419\ldots\text{"} \times \dfrac{\text{"}1960\text{"}}{8} = 4.2 - \text{"}0.01419\ldots\text{"} \times 245\ [= 0.72244..]\) | M1 |
| \(w = 0.722 + 0.0142d\) | A1 |
| (4) |
Notes
1st M1 for a correct expression for \(b\). (Allow ft of their incorrect \(\mathrm{S}_{dw}\))
1st A1 for awrt 0.014 No fractions. [Answer only 2/2] Can be given at final equation.
[Must come from correct formula not gradient of line from e.g. (650, 9.555) to (30, 0.725)]
2nd M1 for a correct method for \(a\). Follow through their value of \(b\) and their \(\Sigma d\)
2nd A1 for a correct equation for \(w\) and \(d\) with \(a\) = awrt 0.722 and \(b\) = awrt0.0142 No fractions
Equation in \(x\) and \(y\) is A0 Answer only 4/4
| Scheme | Marks |
|---|---|
| (i) \([0.722 + 0.0142 \times 350 = ]\) awrt: 5.7 or 5.6 | B1 |
| (ii) Reliable since 350 m is in the range of the data | B1 |
| (2) | |
| (11 marks) |
Notes
1st B1 for awrt 5.7 or awrt 5.6
2nd B1 for a reason citing 350 (m) or mentioning \(d\) is in the range of the data and stating reliable. Allow “Interpolation (or not extrapolation) therefore reliable”.
Saying “5.7 (or \(w\) or just “it”) is in the range” is B0 “accurate” instead of “reliable” is B0 “strong correlation” (without mention of interpolation o.e.) is B0 Apply ISW if a correct comment is seen.