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ZIMSEC A-Level Pure Mathematics

6.5.3First-order differential equations

First-order differential equations in ZIMSEC A-Level Pure Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
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Overview

Form 6.

Learning objectives

What the syllabus expects you to be able to do.

  1. 6.5.3.1Form 6: formulate a statement involving a rate of change as a differential equation.
  2. 6.5.3.2Form 6: solve differential equations by integration when the variables are separable.
  3. 6.5.3.3Form 6: sketch typical members of the family of curves given by a general solution.
  4. 6.5.3.4Form 6: find a particular solution from initial conditions and solve problems with first-order differential equations.

Lessons

  • First-order differential equations with separable variables

    50 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

First-order differential equations: sample question

1 mark

The mass mm grams of a radioactive sample decreases at a rate proportional to mm. Which differential equation models this (k>0k > 0, tt in days)?

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