The vertical displacement sss (in metres) of a high-performance drone during a test maneuver is modelled by the polynomial function
s(t)=2t4+pt3−8t2+qt+22 s(t) = 2t^4 + pt^3 - 8t^2 + qt + 22 s(t)=2t4+pt3−8t2+qt+22where ttt represents the time in seconds after the maneuver begins, and ppp and qqq are constant coefficients.
When s(t)s(t)s(t) is divided by (t+1)(t + 1)(t+1), the remainder is 777. Show that p+q=9p + q = 9p+q=9.
When s(t)s(t)s(t) is divided by (t−2)(t - 2)(t−2), the remainder is 101010. Find the value of ppp and the value of qqq.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.