ConceptConceptDocsDocuments

Pearson Edexcel IAL Mathematics P4.5.1 Differentiation of simple functions

Practise finding dy/dx for implicit and parametric curves, then using exact gradients to write tangents and normals.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • differentiate implicit equations involving e^x, ln terms or products to find exact dy/dx
  • use dy/dx=(dy/dt)/(dx/dt) to find parametric tangent and normal gradients
  • form tangent or normal equations in integer form from a point and exact gradient

P4.5.1 - Differentiation of simple functions question 1

[Maximum number: 7]
Figure 3

Figure 3

Figure 3 shows a sketch of the curve C with parametric equations

x=6t−3sin⁡2ty=2cos⁡t0⩽t⩽π2x=6 t-3 \sin 2 t \quad y=2 \cos t \quad 0 \leqslant t \leqslant \frac{\pi}{2}

The curve meets the y-axis at 2 and the x-axis at k, where k is a constant.

Question (a)

(a)

Use parametric differentiation to show that

dy dx=λcosec⁡t\frac{\mathrm{d} y}{\mathrm{~d} x}=\lambda \operatorname{cosec} t

where λ\lambda is a constant to be found.

The point P with parameter t=π4t=\frac{\pi}{4} lies on C.
The tangent to C at the point P cuts the y-axis at the point N.

[ 4 ]

Question (b)

(b)

Find the exact y coordinate of N, giving your answer in simplest form.

The region bounded by the curve, the x-axis and the y-axis is rotated through 2π2 \pi radians about the x-axis to form a solid of revolution.

[ 3 ]
All question bank results loaded