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Edexcel A-Level Mathematics AS P1.4 Differentiation Questions

Practise differentiating functions, interpreting gradients and forming tangents, normals and rates of change from algebraic models.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • differentiate powers of x, roots and reciprocal terms before simplifying dy/dx
  • use dy/dx at a point to form tangent or normal equations in y=mx+c form

Covered syllabus points

P1.4.1 - Derivative as gradient and rate of changeP1.4.2 - Differentiating powers of xP1.4.3 - Tangents, normals and gradients

Question 1

[Maximum number: 2]

A curve C has equation y=f(x) where

f(x)=(2−kx)5f(x)=(2-k x)^{5}

and k is a constant.
Given that when f(x) is divided by (4 x-5) the remainder is 24332\frac{243}{32}

find the gradient of C at the point where x=0

Question 2

[Maximum number: 3]
f(x)=10−2x−12x−1x3x>0\mathrm{f}(x)=10-2 x-\frac{1}{2 \sqrt{x}}-\frac{1}{x^{3}} \quad x>0

Determine f′(x)\mathrm{f}^{\prime}(x).

Question 3

[Maximum number: 4]

The curve C has equation y=f(x) where x>0

Given that
- f′(x)=(x+3)2xx\mathrm{f}^{\prime}(x)=\frac{(x+3)^{2}}{x \sqrt{x}}
- the point P(4,20) lies on C

Question (a)

(a)

find the value of the gradient at P

[ 1 ]

Question (b)

(b)

Hence find the equation of the tangent to C at P, giving your answer in the form
ax+by+c=0 where a, b and c are integers to be found.

[ 3 ]
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