Free Printable Chap 6 to 9

1.

a)

a

b)

b

c)

c

d)

d

2.

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

a)

38 m/s/s

b)

27 m/s/s

c)

16 m/s/s

d)

49 m/s/s

3.

The maximum and minimum value of 3 sin x + 4 cos x +10 is

a)

17 and 3

b)

15 and 5

c)

12 and 10

d)

None of these

4.

Let f (x) = x³ – 6x² + 9x + 18, then f (x) is strictly decreasing in

a)

(–∞, 1]

b)

[3, ∞)

c)

(–∞, 1] U [3, ∞)

d)

[1, 3]

5.

The logarithmic function is increasing on

a)

$\left(0,\ 1\right)$

b)

$\left(0,\ \infty\right)$

c)

$\left(1,\ \infty\right)$

d)

$\left(-\infty,\ \infty\right)$

6.

Determine the point on the curve f(x)=(2x-1)² where the tangent is parallel to the line y=4x-2

a)

(0 , 1)

b)

(1 , 9)

c)

(1/2 , 0)

d)

(1 , 1)

7.

$\int\tan x_{ }dx\$

a)

$\ln\left|\cos\right|+C$

b)

$-\ln\left|\cos x\right|+C$

c)

$\ln\left|\sin x\right|+c$

d)

$\frac{\tan^2x}{2}+c$

8.

a)

A

b)

B

c)

C

d)

D

9.

a)

A

b)

B

c)

C

d)

D

10.

∫3x²(x³-9)^2/3 dx

a)

(3x²)^4/3

b)

(2/3)(x³-9)^5/3

c)

3(x³-9)^-1/3

d)

-3(x³-9)^-1/3

11.

Which of the following is TRUE ?

a)

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

b)

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

c)

$\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

d)

$\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

12.

Using integration by part, if given that u = (x + 1) then find integration of v for $\int\left(x\ +1\right)\ e^{2x}\ dx$

a)

$\frac{x^2}{2}+x$

b)

$e^{2x}$

c)

$2e^{2x}$

d)

$\frac{e^{2x}}{2}$

13.

Find the area of the region bounded by the graphs of y = x² and y = 4x.

a)

32/3

b)

64/3

c)

32

d)

64

e)

32/5

14.

Write the integral that would be used to find the area of the region bounded by x = 1, y = √x and y = -x + 6.

a)

b)

c)

d)

e)

15.

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

a)

B

b)

C

c)

D

d)

E

16.

Solution of a linear differential equation of first order can be obtain by

a)

multiplying on both the sides by its integrating factor.

b)

adding on both the sides by integrating factor.

c)

subtracting integrating factor from both sides

d)

None of the above

17.

What is the order and degree of the differential equation?

a)

1, 2

b)

2, 1

c)

3, 2

d)

2, 3

18.

What is the integrating factor for the differential equation: $\frac{1}{x}\frac{\text{d}x}{\text{d}y}-\frac{1}{1+x^2}y=x^3$

a)

$\ln\left(x^2\right)$

b)

$-\frac{1}{x^2}$

c)

$-\frac{1}{\sqrt{x}}$

d)

$\frac{1}{\sqrt{x}}$

19.

Number of arbitrary constant in the general solution of a differential equation of degree 3 and order 4 is

a)

3

b)

4

c)

0

d)

4³

20.

A differential equation dy/dx = f(x, y) is called homogeneous if f(λx, λy) = λf(x, y). True or false?

a)

True

b)

False

Chap 6 to 9

Total questions: 20

Worksheet time: 30mins

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