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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 65

An experimental physicist is using the trapezium rule to estimate the total impulse (the area under a force-time graph) for four different test engines over the interval 0≤t≤50 \le t \le 50≤t≤5. The force F(t)F(t)F(t) (in Newtons) for each engine is modeled by the following functions:

Engine A: F(t)=1.5t+20F(t) = 1.5t + 20F(t)=1.5t+20 Engine B: F(t)=0.4t2+10F(t) = 0.4t^2 + 10F(t)=0.4t2+10 Engine C: F(t)=6t+4F(t) = 6\sqrt{t+4}F(t)=6t+4​ Engine D: F(t)=60t+3\displaystyle F(t) = \frac{60}{t+3}F(t)=t+360​

Identify the engine model for which the trapezium rule will produce an underestimate of the actual impulse over this interval. Justify your answer by considering the concavity of the models.

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1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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