Tangents and normals Quiz

1. The gradient of the tangent to a curve at a point is $4$. What is the gradient of the normal there?

• A. $-4$
• B. $\frac14$
• C. $-\frac14$
• D. $4$

2. Find the equation of the tangent to $y=x^2$ at $(1,1)$.

• A. $y=2x+1$
• B. $y=2x-1$
• C. $y=x-1$
• D. $y=-\frac12x+\frac32$

3. Find the equation of the normal to $y=x^2$ at $(1,1)$.

• A. $x+2y-3=0$
• B. $2x-y-1=0$
• C. $x-2y+1=0$
• D. $2x+y-3=0$

4. Find the point on $y=x^2-4x+5$ where the tangent is horizontal.

• A. $(0,5)$
• B. $(2,1)$
• C. $(2,-1)$
• D. $(-2,17)$

5. Two lines are perpendicular. Which statement about their gradients $m_1$ and $m_2$ is correct?

• A. $m_1m_2=1$
• B. $m_1+m_2=0$
• C. $m_1=m_2$
• D. $m_1m_2=-1$