Graded assessment problems
Level 1
In an experiment, values of x and y were obtained as follows:

x    2    3    4    5
y    57    234    640    1398

It is expected that the relation between x and y is of the form,
y=ax^n
Use a graphical method to obtain the values of a and n.

Current I and resistance R are thought to be related by the law.
R=aI^n
An experiment was carried out and the following results were obtained.

I    3.7    5.9    7.4    9.1    11.6    13.8
R    6.2    3.9    3.1    2.5    2.0    1.7

Determine if the above relationship is valid and if so find the value of a and n.

Level 2
The periodic time, T, of oscillation of a pendulum is believed to be of the form T= kln, where l is the length, k and n are constants.

T (s)    1.0    1.2    1.4    1.6    1.8    2.0    2.4
l (m)    2.4    3.5    4.8    6.3    7.9    9.8    14.1

Prove the above law is true and determine the values of k and n. State the law.

Level 3
The following experimental results were obtained, determine the relationship between the parameters
The e.m.f of a thermocouple E (mv) was measure against the temperature at the hot junction (oc)

t (oc)    200    300    400    500    600    700    800    900    1000
E (mv)    6    9.1    12.0    14.8    18.2    21.0    24.1    26.8    30.2

The admittance Y of an electrical socket with the apply voltage is as shown:
V (volts)    0.37    0.51    0.74    0.98    1.13    1.34
Y (siemens)    2.24    1.62    1.12    0.85    0.73    0.62

The approximate number of a type of bacteria B is checked regularly and recorded in the table below
Bacteria, B (x 103)    5    28.5    41.0    113.0    253.6    450.0
Time, t (hours)    1.0    2.5    3.0    5.0    7.5    10.0

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