Revision NotesExam QuestionsPast PapersMock Exams
A LevelMathsCambridge (CIE)Pure 1Revision NotesDifferentiationDifferentiationDefinition of Gradient

Definition of Gradient (Cambridge (CIE) A Level Maths): Revision Note

Exam code: 9709

Roger B

Author

Roger B

Last updated

Cambridge (CIE) Maths: Pure 1OCR Maths A: PureAQA Maths: PureEdexcel Maths: Pure

Definition of gradient

What is the gradient of a curve?

  • At a given point the gradient of a curve is defined as the gradient of the tangent to the curve at that point

  • A tangent to a curve is a line that just touches the curve at one point but doesn't cut the curve at that point

Def Grad Illustr 1, A Level & AS Maths: Pure revision notes

  • A tangent may cut the curve somewhere else on the curve

Def Grad Illustr 2, A Level & AS Maths: Pure revision notes

  • It is only possible to draw one tangent to a curve at any given point

  • Note that unlike the gradient of a straight line, the gradient of a curve is constantly changing

Examiner Tips and Tricks

  • A tangent only exists at points where a curve is smooth.

  • For example, there is no tangent (or gradient) at one of the 'corners' in a modulus function. 

    Def Grad Illustr 3, A Level & AS Maths: Pure revision notes

Worked Example

Def Grad Example, A Level & AS Maths: Pure revision notes
For teachers

Ready to test your students on this topic?

  • Create exam-aligned tests in minutes
  • Differentiate easily with tiered difficulty
  • Trusted for all assessment types
Explore Test Builder
Test Builder in a diagram showing questions being picked from different difficulties and topics, and being downloaded as a shareable format.
Test yourself
Previous:Modelling with SequencesNext:Definition of Derivatives
Roger B

Author: Roger B

Expertise: Maths Content Creator

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.