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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 127

A chemical reaction's equilibrium state is represented by a curve CCC with the equation

2x−xy+y2=28,y≥0 2^x - xy + y^2 = 28, \quad y \ge 0 2x−xy+y2=28,y≥0

where xxx and yyy represent the concentrations of two specific reagents in mol dm−3^{-3}−3. A specific experimental state PPP lies on CCC where the concentration x=4x = 4x=4.

a.

Find the concentration yyy at state PPP.

[2]
b.

Find dydx\frac{\text{d}y}{\text{d}x}dxdy​ in terms of xxx and yyy.

[3]
c.

The tangent to CCC at PPP intersects the xxx-axis at the point QQQ.

Find the xxx-coordinate of QQQ, giving your answer in the form aln⁡2+bcln⁡2+d\frac{a \ln 2 + b}{c \ln 2 + d}cln2+daln2+b​ where a,b,ca, b, ca,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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