Learning objective
I1 Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well behaved; understand how change of sign methods can fail.
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Topic
Pure Mathematics
Subtopic
Root location
Aqa A Level MathematicsPaper 1
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I1 Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well behaved; understand how change of sign methods can fail
- This point belongs to Pure Mathematics, especially Root location.
- You need to be able to i1 Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well behaved; understand how change of sign methods can fail.
- The key ideas to know are change of sign and roots.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Key concepts
change of signroots
Why it matters
This objective helps connect Root location to exam-style questions, flashcards, and revision notes for Pure Mathematics.
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Open revision notesRelated learning objectives
- A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs.
Proof
- B1 Understand and use the laws of indices for all rational exponents.
Laws of indices
- B2 Use and manipulate surds, including rationalising the denominator.
Surds
- B3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown.
Quadratic functions
- B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation.
Simultaneous equations