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Algebraic Methods

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Question 227

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.

[3]
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.

[4]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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