Year 11 Introduction to Calculus

What is the derivative of  $3x^5-4x^2+2$  ?

•  $15x^4-8x$  

•  $15x^4-8x+2$  

•  $15x^5-8x^2+2$  

•  $15x^5-8x^2$  

What is the derivative of  $5-3x+9x^4$  ?

•  $36x^3-3$  

•  $36x^3+2$  

•  $36x^4+2$  

•  $36x^4-2$  

What is the value of  $\frac{dy}{dx}$  if  $y=2\sqrt{x}$  

•  $\frac{dy}{dx}=\frac{1}{\sqrt{x}}$  

•  $\frac{dy}{dx}=\frac{2}{\sqrt{x}}$  

•  $\frac{dy}{dx}=\frac{\sqrt{x}}{2}$  

•  $\frac{dy}{dx}=2$  

What is the value of  $f'\left(3\right)$  if  $f\left(x\right)=3x-x^3$  

•  $f'\left(3\right)=0$  

•  $f'\left(3\right)=9$  

•  $f'\left(3\right)=-18$  

•  $f'\left(3\right)=-24$  

What is the value of  $\frac{dy}{dx}$  if  $y=\left(2x-3\right)^8$  ?

•  $\frac{dy}{dx}=8\left(2x-3\right)^7$  

•  $\frac{dy}{dx}=16\left(2x-3\right)^7$  

•  $\frac{dy}{dx}=8\left(2x-3\right)^8$  

•  $\frac{dy}{dx}=16\left(2x-3\right)^8$  

What is the value of  $f'\left(x\right)$  if  $f\left(x\right)=\sqrt{3-x}$  

•  $f'\left(x\right)=\frac{-1}{2\sqrt{3-x}}$  

•  $f'\left(x\right)=\frac{-2}{\sqrt{3-x}}$  

•  $f'\left(x\right)=\frac{1}{2\sqrt{3-x}}$  

•  $f'\left(x\right)=\frac{2}{\sqrt{3-x}}$  

What is the gradient of the curve  $y=x^2-x-6$  at (6,24)?

• 24

• 23

• 12

• 11

What is the equation of the tangent to the curve   $y=x^2-2x$  at the point (1.-1)

•  $y=1$  

•  $y=-1$  

•  $y=x+2$  

•  $y=x-2$  

What is the equation of the normal to the curve  $f\left(x\right)=x^2-4x$  at (1,-3)

•  $x-2y-7=0$  

•  $x+2y-7=0$  

•  $2x-y-5=0$  

•  $2x+y+5=0$  

For what value of x is the gradient of the tangent to the curve  $f\left(x\right)=1-x^2$  equal to -6

•  $x=12$  

•  $x=3$  

•  $x=-3$  

•  $x=-12$