Tangents and normalsEdexcel International A Level Maths: Subtopic test

1. 1
   The curve $C$ has equation $y=x^2-3x+4$. The point $P(3,4)$ lies on $C$.

   (a)

   Find the gradient of the tangent to $C$ at $P$.

   [1 mark]

   • A$3$
   • B$6$
   • C$4$
   • D$-\frac13$

   (b)

   Find the gradient of the normal to $C$ at $P$.

   [1 mark]

   • A$3$
   • B$-3$
   • C$-\frac13$
   • D$\frac13$

   (c)

   Find an equation of the tangent to $C$ at $P$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A curve has equation $y=x^3-6x$.

   (a)

   Find the gradient of the curve at the point where $x=2$.

   [1 mark]

   • A$-4$
   • B$6$
   • C$12$
   • D$-\frac16$

   (b)

   Which of the following is an equation of the normal to the curve at the point where $x=2$?

   [1 mark]

   • A$6x+y-8=0$
   • B$x+6y-26=0$
   • C$6x-y-16=0$
   • D$x+6y+22=0$

   (c)

   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]

   Total for question 2: 4 marks

3. 3
   The curve $C$ has equation $y=2x^2-\dfrac{8}{x}$ for $x\neq0$. The point $A(2,4)$ lies on $C$.

   (a)

   Find an equation of the tangent to $C$ at $A$, giving your answer in the form $y=mx+c$.

   [3 marks]

   (b)

   Find an equation of the normal to $C$ at $A$, and the coordinates of the point where this normal meets the $x$-axis.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The curve $C$ has equation $y=x^3-3x^2-x+7$. The point $P$ on $C$ has $x$-coordinate $2$.

   (a)

   Find an equation of the tangent to $C$ at $P$.

   [6 marks]

   (b)

   The tangent to $C$ at $P$ meets $C$ again at the point $Q$. Find the coordinates of $Q$.

   [6 marks]

   Total for question 4: 12 marks

End of questions