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Exam-Style Question on Conversion GraphsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 833. This question is typical of the type of question in a GCSE Higher examination. The use of a calculator is allowed.
In 1742, Swedish astronomer Anders Celsius introduced a temperature scale that was the reverse of the Celsius scale used today. On his original scale, water froze at 100 degrees and boiled at 0 degrees.
The modern Celsius scale and Celsius's original scale can both be converted to degrees Fahrenheit.
On the graph, the horizontal axis represents a reading from 0 to 100 on either Celsius scale. The vertical axis represents the equivalent temperature in degrees Fahrenheit.
(a) On the same set of axes, draw two straight-line conversion graphs:
(i) for converting modern Celsius readings to degrees Fahrenheit;
(ii) for converting readings on Celsius's original scale to degrees Fahrenheit.
You may use the following facts:
$$ 0^\circ\text{C} = 32^\circ\text{F} $$ $$ 100^\circ\text{C} = 212^\circ\text{F} $$(b) Use your graph to find the Fahrenheit temperature at which the modern Celsius scale and Celsius's original scale have the same numerical reading.
(c) A temperature is \(158^\circ\text{F}\).
Use your graph to find the reading on
(i) the modern Celsius scale;
(ii) Celsius's original scale.
(d) At a particular Fahrenheit temperature, the numerical readings on the two Celsius scales differ by 60 degrees.
Use your graph to find the two possible temperatures in degrees Fahrenheit.
Historical information: Uppsala University, Sweden.
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