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3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only)

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Question 41

A marine biologist is monitoring the environmental conditions of a coastal pool. The temperature $T$ (in degrees Celsius) and the salinity $S$ (in g/L) of the pool at time $t$ hours after high tide are modeled by the parametric equations

\frac{3}{t} + 2, \quad S = \frac{4t + 3}{2t + 1}, \quad t > 0

Show that the relationship between salinity and temperature can be written in the form $S = g (T)$ , where $g$ is the function

\frac{aT + b}{cT + d}, \quad T > k

and $a, b, c, d$ , and $k$ are integers to be found.

[5]

Hence, or otherwise, state the range of $g$ .

[2]

Markscheme

3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only) Questions

A Level
Maths
3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only)

49 exam-style questions on CCEA A Level Maths 3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only)

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3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Question 41

\frac{3}{t} + 2, \quad S = \frac{4t + 3}{2t + 1}, \quad t > 0

Show that the relationship between salinity and temperature can be written in the form $S = g (T)$ , where $g$ is the function

\frac{aT + b}{cT + d}, \quad T > k

and $a, b, c, d$ , and $k$ are integers to be found.

[5]

Hence, or otherwise, state the range of $g$ .

[2]

Markscheme

3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only) Questions

A Level
Maths
3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only)

49 exam-style questions on CCEA A Level Maths 3.2.1 Co-ordinate geometry in the (x, y) plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.