CAIE A-Level Biology Mathematical & Statistical Skills

Practise the calculations, graph interpretation and statistical decisions required across CAIE A-Level Biology investigations.

[Maximum number: 1]

Smooth muscle is a tissue composed of smooth muscle cells. The cells contain cytoplasm packed with proteins that are involved in contraction and relaxation.

When viewed in longitudinal section (LS), smooth muscle cells are elongated and taper at both ends. This is known as a fusiform shape. Each cell has a central nucleus, which also appears elongated.

Fig. 1.1 is a diagram of a smooth muscle cell to show the fusiform shape.

Fig. 1.1

A student used a microscope fitted with a calibrated eyepiece graticule to estimate that the length of one smooth muscle cell was 250 micrometres $(\mu \mathrm{m})$ .

The smallest object the student can see without the use of a microscope is 0.2 mm in length.

Explain whether the student would be able to see a cell of length $250 \mu \mathrm{~m}$ without the use of a microscope.

yes, qualified ; e.g.

$0.2 \mathrm{~mm}=\underline{200 \mu \mathrm{~m}}$

0.2 mm / smallest student can see, is less than 0.25 mm

$250 \mu \mathrm{~m}=\underline{0.25 \mathrm{~mm}}$ $250 \mu \mathrm{~m}$ / cell length, is longer than $200 \mu \mathrm{~m}$

the cell is $50 \mu \mathrm{~m}$ longer (than 0.2 mm )

the cell is 0.05 mm longer (than 0.2 mm )

Marking guidance:

allow if converted to standard form ( $2 \times 10^{-4} \vee 2.5 \times 10^{-4} \mathrm{~m}$ )

must have units

must include numerical values

[Maximum number: 1]

In mammals, the small intestine is the main site of absorption of the products of digestion.
Fig. 2.1 is a transmission electron micrograph of a longitudinal section (L.S.) of part of an epithelial cell from the small intestine of a mammal.

Fig. 2.2 is a transmission electron micrograph of a horizontal section made at the position indicated by the two arrows in Fig. 2.1.

Fig. 2.1

Fig. 2.2

A scientist measured the length and the diameter of some of the microvilli shown in Fig. 2.1 to estimate the total surface area of microvilli on the surface of the epithelial cell.

The scientist assumed that each microvillus was cylindrical in shape.
Suggest one other measurement needed to estimate the total surface area of the microvilli of the epithelial cell.

[Maximum number: 1]

The table shows the blood pressures in different parts of the circulatory system of a person sitting at rest.

Table for Question Mathematical and statistical skills question 3 — CAIE A-Level Biology AS

What is the percentage decrease in blood pressure between the arteriole and the arterial end of a capillary?

A

42%

B

58\%

C

142\%

D

240\%

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Covered syllabus points

Mathematical and statistical skills question 1

Mathematical and statistical skills question 2

Mathematical and statistical skills question 3