The altitude of a research drone, h(s)h(s)h(s) in metres, relative to a fixed marker is modelled by the polynomial function
h(s)=2s4+ps3−5s2+qs+12 h(s) = 2s^4 + ps^3 - 5s^2 + qs + 12 h(s)=2s4+ps3−5s2+qs+12where s s\,s is the horizontal displacement in decametres from the marker and p p\,p and q q\,q are constants.
At a displacement of s=2s = 2s=2, the drone's altitude is 24 m. Show that 4p+q=04p + q = 04p+q=0.
At a displacement of s=−1s = -1s=−1, the drone's altitude is 15 m. Determine the value of p p\,p and the value of qqq.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.