Tangents and normalsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

What does \frac{dy}{dx} at x=a represent?
Equation of a line with gradient m through (x1,y1)?
What is a normal to a curve?
Gradient of the normal if the tangent has gradient m?
Condition for two lines to be perpendicular?
If the tangent is horizontal, what is the normal?
How do you find where a tangent is parallel to a given line?
Where do you get the y-coordinate of the point of contact?
How do you find where a tangent meets the x-axis?
How do you find where a normal meets the curve again?
Gradient of y=2x^3-5x+1 at x=2?
How are unknown constants in a curve found from a tangent condition?

Exam questions on Tangents and normals

The curve $C$ has equation $y=2x^3-5x+1$ and passes through the point $P$ where $x=2$ .
Find the equation of the normal to $C$ at $P$ , giving your answer in the form $ax+by+c=0$ where $a$ , $b$ and $c$ are integers.2 marks
The curve $C$ has equation $y=x+\frac{12}{x}$ for $x\neq0$ and passes through the point $P(3,7)$ .
Find the coordinates of the other point on $C$ at which the tangent is parallel to the tangent at $P$ .2 marks
The curve $C$ has equation $y=x^2+px+q$ , where $p$ and $q$ are constants. The tangent to $C$ at the point $(1,2)$ has gradient $5$ .
Find the values of $p$ and $q$ .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).