Tool 3: Mathematics (SL IB Biology)

The drawing below shows part of a plant cell as seen with an electron microscope. The scale bar (measuring 45 mm in length) on this drawing represents a length of 10 μm.

Calculate the magnification of the drawing.

Calculate the actual width of the cell in part (a) between A and B.

Give your answer in micrometres (µm).

Identify two ways in which striated muscle fibres (fused muscle cells) differ from the cell shown in part (a). 

Farmers can plant their crops at different times throughout the year. Traditionally crops were planted in April and harvested in September. However, in modern times farmers have switched to planting their crops in September and harvesting in June/July.

Scientists decided to investigate the effect that the change in planting time had on the number of species of farmland birds over 10 years. The scientists counted the number of farmland birds found within a 1km radius of farm X that plants its crops in April, and within a 1km radius of farm Y that plants its crops in September.

The graph below shows the data they collected.

Describe the results seen in the graph. 

Using the graph in part (a), calculate the difference between the percentage change in bird species number across the two farms from 1992 to 2000. 

Explain the type of biodiversity that is being measured in this experiment.

[2]

The agricultural area is found to have a very low ecosystem diversity.

List three changes that could be made to improve ecosystem diversity in the area. 

[3]

In recent years, farmers have merged grazing fields together by removing hedgerows. This has resulted in a decline in the biodiversity of farmland birds. Explain why.

Ecologists studied a rocky shore habitat which contained, among other organisms, several barnacle species, purple topshell snails (Gibbula umbilicalis), seaweeds, and lichens. 

State, with a reason, which of the organisms listed above make up a single population. 

The ecologists wanted to find out whether there was an association between the distributions of purple topshell snails and the common rock barnacle, Semibalanus balanoides. 

Outline the method ecologists would use to collect data to determine whether or not such an association existed.

A chi-squared test was carried out to determine whether or not there was a significant association between purple topshells and common rock barnacles on a rocky shore. When the calculated chi-squared value was compared to values in a critical values table it was found to be smaller than the critical value at a 0.05 probability level. 

Deduce what can be concluded from this analysis?