A specialized drone's vertical displacement from a reference altitude, hhh (in meters), is modeled by the function
h(t)=at3+3t2+bt−10 h(t) = at^3 + 3t^2 + bt - 10 h(t)=at3+3t2+bt−10where t t\,t is the time in seconds since the drone began its descent and a a\,a and b b\,b are constants.
When h(t)h(t)h(t) is divided by (t−3)(t - 3)(t−3), the remainder is 44.
Use the remainder theorem to show that
9a+b=9 9a + b = 9 9a+b=9Given also that (t+1)(t + 1)(t+1) is a factor of h(t)h(t)h(t),
find the value of a a\,a and the value of bbb.
Find h′(t)h'(t)h′(t).
Hence find the exact coordinates of the stationary points of the curve with equation y=h(t)y = h(t)y=h(t).
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.