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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 169

The thermal profile of a synthetic crystal is modeled by the equation

5t−3tT+T2=23,T≥0 5^t - 3tT + T^2 = 23, \quad T \ge 0 5t−3tT+T2=23,T≥0

where TTT is the temperature in degrees Celsius and ttt is the time in hours. A specific observation point PPP on the profile has t=1t = 1t=1.

a.

Find the temperature TTT at point PPP.

[2]
b.

Find an expression for dTdt\frac{dT}{dt}dtdT​ in terms of TTT and ttt.

[3]
c.

The tangent to the profile at point PPP intersects the horizontal ttt-axis at point QQQ.

Determine the ttt-coordinate of QQQ, giving your answer in the form aln⁡5+bcln⁡5+d\frac{a \ln 5 + b}{c \ln 5 + d}cln5+daln5+b​ where a,b,c,a, b, c,a,b,c, and ddd are integers to be found.

[4]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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