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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 133

A micro-robotic probe's position (x,y)(x, y)(x,y) in micrometres is tracked over time t t\,t seconds within a biological medium. The path is defined by the parametric equations

x=4×2−t−1 x = 4 \times 2^{-t} - 1 x=4×2−t−1 y=3×2t+5 y = 3 \times 2^{t} + 5 y=3×2t+5
a.

Show that dydx=−34×22t\dfrac{dy}{dx} = -\dfrac{3}{4} \times 2^{2t}dxdy​=−43​×22t.

[4]
b.

Find the Cartesian equation of the curve in the form xy+ax+by=cxy + ax + by = cxy+ax+by=c, where aaa, bbb and ccc are integers.

[4]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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