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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