Iteration: locating roots and using iterative formulas
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 6 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
- When algebra gives up
- Locating a root
Read the transcript of the teaching part
Last time
Before we start: last time, in Integration by parts, substitution and differential equations, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
When algebra gives up
Some equations have no neat solution. Try to solve x cubed equals x plus three exactly and you will not get far. But you can sneak up on the answer: guess, improve the guess, improve it again, until the digits stop changing. That is iteration, and it is a gift of marks in Pure 3.
Locating a root
A root of f of x equals zero is where the graph of f crosses the x-axis. If f is continuous, and f of a and f of b have opposite signs, then there is a root between a and b. Always say two things: the values you found, and the words change of sign.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Iteration from a derivative condition · Sketching graphs to locate a root.
The whole chapter: Numerical Solution of Equations.
Chapter 3.6: Numerical solution of equations
- Iteration: locating roots and using iterative formulas 7 min
- A definite integral that defines a constant, and solving it by iteration 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.