The velocity, v(t)v(t)v(t) in m s−1\text{m s}^{-1}m s−1, of a high-altitude research drone during a specific phase of its descent is modeled by the function
v(t)=3t2+14t+10t+4,t≥0 v(t) = \frac{3t^2 + 14t + 10}{t + 4}, \quad t \ge 0 v(t)=t+43t2+14t+10,t≥0where ttt is the time in seconds from the start of the observation.
Express v(t)v(t)v(t) in the form
At+B+Ct+4 At + B + \frac{C}{t + 4} At+B+t+4Cwhere AAA, BBB, and CCC are integers to be determined.
By using algebraic integration, determine the total distance traveled by the drone between t=0t = 0t=0 and t=8t = 8t=8. Give your answer in the form p+qln3p + q \ln 3p+qln3, where ppp and qqq are integers.
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.