Skip to content

Course home

3.8 Numerical Methods (A-level only)

3.8 Numerical Methods (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109
Question 52

The power output, P P\,P kW, of a solar array is monitored over a 12-hour period. The graph of P P\,P against time ttt (hours after 00:00) shows the system's performance between t=8t = 8t=8 and t=20t = 20t=20. Readings taken from the graph at regular 4-hour intervals are recorded in the table below.

t8121620P1.26.85.40.6 \begin{array}{|c|c|c|c|c|} \hline t & 8 & 12 & 16 & 20 \\ \hline P & 1.2 & 6.8 & 5.4 & 0.6 \\ \hline \end{array} tP​81.2​126.8​165.4​200.6​​

Graph of solar-array power output P in kilowatts against time t from 8 to 20 hours, passing through the four recorded readings.

a.

Use the trapezium rule with three strips of equal width to estimate the total energy produced, in kilowatt-hours (kWh), over the interval 8≤t≤208 \le t \le 208≤t≤20.

[4]
b.

It is suggested that the power output P P\,P can be modelled by a quadratic function of t t\,t for 8≤t≤208 \le t \le 208≤t≤20. Explain how this model could be used to find an alternative estimate for the total energy produced during this time interval.

[1]
Markscheme

3.8 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.8 Numerical Methods (A-level only)

129 exam-style questions on WJEC A Level Maths 3.8 Numerical Methods (A-level only), covering 3.8.1 Numerical Methods (A-level only), 3.8.2 Numerical Methods (A-level only), 3.8.3 Numerical Methods (A-level only), 3.8.4 Numerical Methods (A-level only), and 3.8.5 Numerical Methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank