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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 175

The curve C C\,C has equation

x=2tan⁡(y+π4)x∈R,−3π4<y<π4 x = 2\tan\left(y + \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{3\pi}{4} < y < \frac{\pi}{4} x=2tan(y+4π​)x∈R,−43π​<y<4π​
a.

Show that

dydx=ax2+b \frac{dy}{dx} = \frac{a}{x^2 + b} dxdy​=x2+ba​

where a a\,a and b b\,b are integers to be found.

[5]
b.

The point P P\,P with yyy-coordinate 0 lies on CCC. The tangent to C C\,C at P P\,P crosses the xxx-axis at the point QQQ. Find the exact xxx-coordinate of QQQ.

[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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