Skip to content
MathsGenie logo
Open app

Course home

  1. A Level
  3. Maths AQA
  5. Question bank

1.10 G: Differentiation

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281
Question 218

The height of a biological culture, H(t)H(t)H(t) millimetres, is observed over time t t\,t hours for t>0t > 0t>0.

Given that

  • H′(t)=10t14+kt2−4\displaystyle H'(t) = 10t^{\frac{1}{4}} + \frac{k}{t^2} - 4H′(t)=10t41​+t2k​−4, where k k\,k is a constant
  • H′′(t)=0H''(t) = 0H′′(t)=0 when t=16t = 16t=16
a.

Determine the value of kkk.

[3]
b.

Given also that

  • H(t)=20H(t) = 20H(t)=20 when t=1t = 1t=1

Find an expression for H(t)H(t)H(t), giving each term in simplest form.

[4]

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank