WMA12/01 Jan 2021, Question 7: The Trapezium Rule
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks
The question, in short
Given a power model P = 0.95 + 2^(t − 12) + 2^(12 − t) − (t − 12)² for 8.5 ≤ t ≤ 15.2, complete a table of P values and estimate energy from the shaded area under the curve.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Substitute t = 10, 10.5, 11, 11.5, 12 into the given equation to fill the missing P values, giving answers to 4 significant figures where appropriate.
- 1t = 10: P = 0.95 + 2⁻² + 2² − (−2)² = 0.95 + 0.25 + 4 − 4 = 1.2
- 2t = 11.5: P = 0.95 + 2^(−0.5) + 2^(0.5) − (−0.5)² = 0.95 + 0.7071 + 1.4142 − 0.25
- 3P = 2.821 (4 s.f.)
AnswerAt t = 10, P = 1.2; at t = 11.5, P = 2.821
Part (b) · 4 marks
Use the trapezium rule with all completed table values to estimate the energy in kWh between 10:00 and 12:00, giving the answer to 2 decimal places.
- 1h = 0.5
- 2E ≈ ½ × 0.5 × [1.2 + 2.95 + 2(1.882 + 2.45 + 2.821)]
- 3= 0.25 × [4.15 + 14.306]
- 4= 0.25 × 18.456 = 4.614
- 5E ≈ 4.61 kWh
Answer4.61 kWh
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