Further Mathematics · OCR H245 · Topic OT3

Mathematical modelling

Turning a real situation into maths, using the model, then judging and improving it. Applies to every paper.

  • 5 sub-topics
  • Taught in Year 13
  • 22 practice questions
  • 5 animated lessons
Practice questions (22) Lessons Worksheets coming soon All OCR Further Mathematics topics

What the specification says

Every sub-topic OCR can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. OT3.1Build a modelY13
  2. OT3.2Use a modelY13
  3. OT3.3Interpret a model's outputsY13
  4. OT3.4Refine and evaluate a modelY13
  5. OT3.5Modelling assumptionsY13

Try 2 questions

Easy and medium questions from this topic, each with a worked solutions and the mark for every step. All 22 questions in this topic, free, no account needed.

Mathematical modelling

Easy

Building a model · Year 12 · 1 mark

  1. What is the first step in building a mathematical model of a real situation?
    (1)

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  1. Then set up equations, solve them, interpret the results and check them against reality.BB: Decide which quantities matter and which simplifying assumptions to make

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Mathematical modelling

Medium

Using a growth model · Year 12 · 1 mark

  1. A population PP is modelled by dPdt\dfrac{\mathrm{d}P}{\mathrm{d}t}=0.1P{}= 0.1P, with P=80P = 80 when t=0t = 0. What does the model predict?
    (1)

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  1. Separating the variables gives P=AektP = A\mathrm{e}^{kt}, and AA is the starting value.DD: P=80e0.1tP = 80\mathrm{e}^{0.1t}

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