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Gradients, Tangents & Normals (AQA AS Maths): Revision Note

Exam code: 7356

Roger B

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Roger B

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AQA Maths: PureCambridge (CIE) Maths: Pure 1OCR Maths A: PureEdexcel Maths: Pure

Gradients, tangents & normals

How do I find the gradient at a point on a curve?

  • To find the gradient of a curve y= f(x) at any point on the curve, substitute the x‑coordinate of the point into the derivative f'(x)

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

How do I find the equation of a tangent to a curve?

  • At any point on a curve, the tangent is the line that goes through the point and has the same gradient as the curve at that point

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

  • For the curve y = f(x), you can find the equation of the tangent at the point (a, f(a)) using y minus straight f left parenthesis a right parenthesis space equals space straight f to the power of apostrophe left parenthesis a right parenthesis left parenthesis x minus a right parenthesis

How do I find the equation of a normal to a curve?

  • At any point on a curve, the normal is the line that goes through the point and is perpendicular to the tangent at that point

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

  • For the curve y = f(x), you can find the equation of the normal at the point (a, f(a)) using y minus straight f left parenthesis a right parenthesis space equals space minus fraction numerator 1 over denominator straight f to the power of apostrophe left parenthesis a right parenthesis end fraction left parenthesis x minus a right parenthesis

Examiner Tips and Tricks

  • The formulae above are not in the exam formulae booklet, but if you understand what tangents and normals are, then the formulae follow from the equation of a straight line combined with parallel and perpendicular gradients (see Worked Example below).

Worked Example

Grad Tang Norm Example, A Level & AS Maths: Pure revision notes
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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.