Edexcel A-Level Biology AS A 4 Geometry and Trigonometry Questions

Practise Edexcel A-Level Biology geometry skills through surface area, volume, cross-sectional area, radius-diameter conversion and SA:V ratios.

Exam points

calculate surface area or volume from radius, diameter and biological measurements
convert between radius, diameter and units before using circle or sphere formulae
work out surface-area-to-volume ratios for cells, organisms or model shapes

Covered syllabus points

A.4.1—Circumference, area and volume

[Maximum number: 2]

A student used a microscope to study the tissues in a plant stem and the cell of an animal.

The photograph shows a vascular bundle in a transverse section of the plant stem, as seen using a light microscope.

Figure for Question 1 — Edexcel A-Level Biology AS

This photograph shows a high-power view of some of the cells in tissue C in the vascular bundle.

Each of the smallest units on the eyepiece graticule shown in the photograph is $3 \times 10^{-6} \mathrm{~m}$ .

Assume that the cell labelled F in the photograph is circular.
Calculate the cross-sectional area of cell F .

Answer

An answer that includes the following steps:

- measurement of cell \{diameter / radius\} in epg units and conversion to m (1)

- calculation of area using $\pi \mathrm{r}^{2}(1)$

ACCEPT 14 to 14.5 as alternatives to 13.

e.g.

$\{13 / 6.5\} \times 3 \times 10^{-6}=39 \times 10^{-6}=3.9 \times 10^{-5}$

OR $19.5 \times 10^{-6}=1.95 \times 10^{-5}$ $\pi \times\left(\left(1.95 \times 10^{-5}\right)^{2}\right)=1.195 \times 10^{-9}$

OR $3.14 \times 3.8025 \times 10^{-10}=1.194 \times 10^{-9}$

ACCEPT 1.195, 1.19, 1.2

If include units must match answer, but units not needed

(2)

[Maximum number: 1]

All living organisms are made of cells. Some cells are specialised for their function.

A human egg cell is another example of a specialised cell.

A human egg cell has a radius of $50 \mu \mathrm{~m}$ . Calculate the volume of this human egg cell. Use the formula:

\mathrm{V}=\frac{4}{3} \pi r^{3}

Answer $\mathrm{mm}^{3}$

$=5.24 \times 10^{5} / 524000\left(\mu \mathrm{~m}^{3}\right)$

ACCEPT 500000 to 524000 $5.0 \times 10^{5}$ to $5.24 \times 10^{5}$

max number of 2 dp in standard form

[Maximum number: 2]

The common wombat is endemic to Australia and Tasmania.
The photograph shows a common wombat.

Figure for Question 3 — Edexcel A-Level Biology AS

magnification $\times 0.1$

Common wombats mark areas of their habitat to signal to other wombats of the same species that they are living there. These marked areas are called territories.

Common wombats produce cube-shaped faeces. It is thought that these cubes can be stacked to mark territory without rolling away.

Calculate the surface area: volume ratio of one cube with a length of 2.5 cm .

calculation of surface area and volume (1)

- correct ratio (1)

Example of calculation:

surface area $=6 \times 2.5^{2}=37.5$ volume $=2.5^{3}=15.625$

2.4:1

ECF applies

Correct answer with no working shown scores full marks

(2)

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question 3