Skip to content

Course home

Parametric Equations

Parametric Equations

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178
Question 178

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

T=3t+2,S=4t+32t+1,t>0 T = \frac{3}{t} + 2, \quad S = \frac{4t + 3}{2t + 1}, \quad t > 0 T=t3​+2,S=2t+14t+3​,t>0
a.

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

g(T)=aT+bcT+d,T>k g(T) = \frac{aT + b}{cT + d}, \quad T > k g(T)=cT+daT+b​,T>k

and a,b,c,da, b, c, da,b,c,d, and kkk are integers to be found.

[5]
b.

Hence, or otherwise, state the range of ggg.

[2]
Markscheme

Parametric Equations Questions

  1. A Level
  2. /Maths
  3. /Parametric Equations

215 exam-style questions on Edexcel A Level Maths Parametric Equations, covering 8.1 Parametric Equations, 8.2 Using Trigonometric Identities, 8.3 Curve Sketching, 8.4 Points of Intersection, and 8.5 Modelling with Parametric Equations. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank