Skip to content

Course home

1.7.19 Parametric and implicit differentiation (A-level only)

1.7.19 Parametric and implicit differentiation (A-level only)

MediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576
Question 52

A robotic arm is programmed to sweep across a linear welding track. Its horizontal position xxx (in cm) relative to a central sensor is modeled by the equation

x=5tan⁡(y−π4)x∈R,−π4<y<3π4 x = 5\tan\left(y - \frac{\pi}{4}\right) \quad x \in \mathbb{R}, \quad -\frac{\pi}{4} < y < \frac{3\pi}{4} x=5tan(y−4π​)x∈R,−4π​<y<43π​

where y y\,y is the angle of rotation of the arm in radians.

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.

[4]
b.

The point P P\,P on the curve C C\,C has yyy-coordinate π2\displaystyle \frac{\pi}{2}2π​. 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

1.7.19 Parametric and implicit differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.7.19 Parametric and implicit differentiation (A-level only)

82 exam-style questions on OCR A Level Maths 1.7.19 Parametric and implicit differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank