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1.3 Functions

1.3 Functions

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Question 95

The rate of production of a biofuel in a research facility, R(t)R(t)R(t) kilolitres per hour, is modelled by the formula

R(t)=4t3+5t2+8t+15t2+3,1≤t≤3 R(t) = \frac{4t^3 + 5t^2 + 8t + 15}{t^2 + 3}, \quad 1 \le t \le 3 R(t)=t2+34t3+5t2+8t+15​,1≤t≤3

where ttt is the time in hours from the start of a production cycle. Given that

R(t)≡At+B+Ct+Dt2+3 R(t) \equiv At + B + \frac{Ct + D}{t^2 + 3} R(t)≡At+B+t2+3Ct+D​
a.

(i) find the values of the constants AAA, BBB and CCC.

(ii) show that D=0D = 0D=0.

[4]
b.

Hence, using algebraic integration, calculate the total volume of biofuel produced between t=1t = 1t=1 and t=3t = 3t=3, giving your answer in the form p+qln⁡kp + q \ln kp+qlnk, where ppp, qqq and kkk are integers and kkk is prime.

[5]
Markscheme

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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