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1.1 Algebra and functions

1.1 Algebra and functions

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Question 160

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≥0

where ttt is the time in seconds from the start of the observation.

a.

Express v(t)v(t)v(t) in the form

At+B+Ct+4 At + B + \frac{C}{t + 4} At+B+t+4C​

where AAA, BBB, and CCC are integers to be determined.

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b.

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+qln⁡3p + q \ln 3p+qln3, where ppp and qqq are integers.

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Markscheme

1.1 Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.1 Algebra and functions

306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

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