Tangents and normalsEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

How do you find the gradient of the tangent at x=a?
Equation of a straight line through (x1,y1) with gradient m?
What is a normal to a curve?
Tangent gradient m: normal gradient?
What is the product of the gradients of two perpendicular lines?
What does a horizontal tangent tell you about the gradient?
Tangent gradient \frac25: normal gradient?
What are the three steps to find the equation of a tangent?
How do you find where a normal meets the x-axis?
How do you find points on a curve where the tangent has gradient k?
What is special about the equation after equating a tangent with the curve?
Tangent to y=x^2 at (1,1)?
Normal to y=x^2 at (1,1)?

Exam questions on Tangents and normals

The curve $C$ has equation $y=x^2-3x+4$ . The point $P(3,4)$ lies on $C$ .
Find an equation of the tangent to $C$ at $P$ .2 marks
A curve has equation $y=x^3-6x$ .
The tangent to the curve at the point where $x=2$ is parallel to the tangent at another point $B$ . Find the coordinates of $B$ .2 marks
The curve $C$ has equation $y=2x^2-\dfrac{8}{x}$ for $x\neq0$ . The point $A(2,4)$ lies on $C$ .
Find an equation of the tangent to $C$ at $A$ , giving your answer in the form $y=mx+c$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).