Forming and solving differential equations
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Rates that depend on size
- Forming the equation
Read the transcript of the teaching part
Last time
Before we start: last time, in Intersections, perpendiculars and distances with vectors, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Rates that depend on size
The bigger a bank balance, the faster interest piles up. The hotter a cup of tea, the faster it cools. In each case, how fast something changes depends on how much of it there is. Writing that sentence as an equation, then solving it, is the whole of this chapter, and it is worth about ten marks a year.
Forming the equation
The rate of change of y with respect to x is dy by dx. Rate of increase means dy by dx is positive. Proportional to y means equal to k times y, with k a constant. Decreasing means a minus sign. The rate of decrease of m is k m gives d m by d t equals minus k m.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Forming a differential equation.
The whole chapter: Differential Equations.
Chapter 3.8: Differential equations
- Forming and solving differential equations 6 min
Also for A Level Maths 9709 Paper 3
Which topics come up most in A Level Maths 9709 Paper 3 past papers, counted from every paper since 2004.