Free Printable Differentiation and it's Application: ( Prepared by :NMK)

1.

$\frac{\text{d}}{\text{d}y}\left(2x^2+5x+7\right)$

a)

5x+2

b)

$2x^3+5$

c)

4x+5

d)

5+4x

2.

$find\ \frac{\text{d}y}{\text{d}x}\ for:\ \ y=\left(x+1\right)^2$

a)

2x+2

b)

2x+1

c)

1+2x

d)

2x+4

3.

$Given\ that\ y=5x+\frac{1}{x^2}calulate\ the\ gradient\ of\ the\ curve\ at\ x=3$

a)

$\frac{145}{23}$

b)

$\frac{27}{133}$

c)

$\frac{55}{27}$

d)

$\frac{133}{27}$

4.

$Given\ that\ PV=3600,\ find\ the\ value\ of\ \frac{\text{d}P}{\text{d}V}\ when\ P=40\$

a)

$-\frac{9}{4}$

b)

$-\frac{4}{9}$

c)

Answer option 3

-

-\frac{8}{5}

d)

$\frac{9}{4}$

5.

$differentiate\ with\ respect\ to\ x:\ \frac{\text{d}}{\text{d}x}\left(2x^3+7\right)^6$

a)

$6x^2\left(2x^3+7\right)^5$

b)

$36x^2\left(2x^2+7\right)^5$

c)

$36x\left(2x^3+7\right)^{5^{ }}$

d)

$36x^2\left(2x^3+7\right)^5$

6.

calculate the coordinates of the points on the curve

\sqrt{x^2-4x+8}

at which

\frac{\text{d}y}{\text{d}x}=0

a)

(2,3)

b)

(2,2)

c)

(2,1)

d)

(3,2)

7.

$\ \ \ \ \ Differentiate\ with\ respect\ to\ x:\ \left(x+7\right)^{10}\left(x^2+2\right)^7$

a)

$2\left(x+7\right)^9\left(x^2+2\right)^6\left(12x^2+49x+10\right)$

b)

$2\left(x+7\right)^8\left(x^2+2\right)^5\left(12x^2+49x+10\right)$

c)

$2\left(x+7\right)^{10}\left(x^2+2\right)^6\left(24x^2+49x+10\right)$

d)

$6\left(x+7\right)^9\left(x^{ }+2\right)^6\left(12x^2+49x+10\right)$

8.

$Differentiate\ with\ respect\ to\ x:\ \ \frac{\text{d}}{\text{d}x}\left(\frac{2x+5}{3x-4}\right)$

a)

$-\frac{23}{\left(3x-4\right)^3}$

b)

$-\frac{32}{\left(3x-4\right)^2}$

c)

$\frac{23}{\left(3x-4\right)^2}$

d)

$-\frac{23}{\left(3x-4\right)^2}$

9.

$If\ v=t^3+2t^2+3t+1,\ calculate\ the\ value\ of\ \frac{\text{d}^2v}{\text{d}t^2}\ \ \ when\ t=\frac{2}{3}$

a)

$\frac{\text{d}^2v}{\text{d}t^2}=100$

b)

$\frac{\text{d}^2v}{\text{d}t^2}=-20$

c)

$\frac{\text{d}^2v}{\text{d}t^2}=-10$

d)

$\frac{\text{d}^2v}{\text{d}t^2}=10$

10.

if

y=ax^{\frac{5}{4}},\

where a is a constant , find the approximate percentage change in x when there is a 5% change in y.

a)

4%

b)

5%

c)

-4%

d)

6%

11.

The volume of the sphere is given by $v=\frac{4}{3}\pi r^3$ ,where r is the radius. If there is 1.5% change in it's radius find the corresponding percentage change in it's volume.

a)

4%

b)

5%

c)

4.5%

d)

5.5%

12.

Find the equation of the normal to the curve $y=x^3-2x^2+3$ at the point x=2

a)

4y+x=14

b)

4y+3x=14

c)

y+x=14

d)

4y+x=41

13.

$\ \ \ \ \ \ Given\ that\ \ y=x^2-6x+15$ , find the gradient of the normal (m) to the curve at (4,7)

a)

m=-2

b)

m= $-\frac{1}{2}$

c)

$m=\frac{1}{2}$

d)

$m=-\frac{1}{3}$

14.

Calculate the gradient of the curve

y=x\sqrt{x+1}

at the point where x=3.

a)

$2\ \frac{7}{9}$

b)

$2\ \frac{3}{5}$

c)

$3\ \frac{3}{4}$

d)

$2\ \frac{3}{4}$

15.

A spherical ball is being inflated at a rate of 20 $\frac{cm^3}{s}$ . Find the rate of increase of its radius when it's surface area is $100\pi\ cm^2$

a)

$\frac{1}{6\pi}$ cm/s

b)

$\frac{1}{4\pi}$ cm/s

c)

$\frac{1}{5\pi}$ cm/s

d)

$\frac{2}{5\pi}$ cm/s

16.

find the coordinates of the stationary points of $y=x^3-3x^2+7$ and determine the nature of the stationary points.

a)

(0,7) max and (2,3)min

b)

(0,2) max and (2,3)min

c)

(2,3) max and (0,7)min

d)

(0,7) min and (2,3)max

Differentiation and it's Application: ( Prepared by :NMK)

Total questions: 16

Worksheet time: 2hrs 36mins

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