Graphs 8
4 marks · NormalThe graph below shows the temperature (in °C) of a liquid as it cools over time.
Estimate the rate of temperature change at min.
Describe how the rate of temperature change varies as time increases.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Approximately -7 °C/min
(b) The rate of temperature change decreases in magnitude (gets less negative) as time increases; the liquid cools more slowly.
Common mistakes: Using average rate and not tangent; Mixing up sign of rate
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Draws or describes an appropriate tangent at min.
A1 (a) · 1 mark · Estimates a rate close to -7 °C/min (accept answers between -5.5 and -8.5).
M2 (b) · 1 mark · Describes that the rate of cooling decreases as time increases, i.e., the temperature drops more slowly.
A2 (b) · 1 mark · Correctly interprets the meaning in context (accept: 'liquid cools more slowly as time passes', 'rate of temperature change gets smaller').
Worked solution
a) Draw a tangent to the curve at , and estimate the gradient. For example, use (1,71) and (3,55):
b) As time increases, the line’s gradient becomes less steep, indicating the cooling slows down—the temperature drops more slowly.