Skip to content

Course home

Sign up

3.6 Differentiation (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220
Question 132

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

A robotic arm's reach RRR (measured in cm) from a central hub is modeled by the equation

R(t)=3+2cos⁡t2+sin⁡t,0≤t≤2π R(t) = \frac{3 + 2 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi R(t)=2+sint3+2cost​,0≤t≤2π

where t t\,t is the time in seconds. A technician identifies a point in time M M\,M when the reach is at its absolute minimum.

a.

Show that the value of t t\,t at M M\,M is a solution of the equation

4sin⁡t+3cos⁡t=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2
[4]
b.

Hence find, to 3 significant figures, the value of t t\,t at the point MMM.

[4]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

332 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.

Question bank