College mathematics-100 test question
1. To Calculate differential of function y=3/5x5+10x
A. * dy=( 3x4+10)dx
B. dy=15x4dx
C. dy=15x4
D. dy=(5x4+10)dx
E. dy=( 15x6+10x)dx
2. To Calculate differential of function y=( x3+x2+10x)
A. dy=( 6x2+x2-3)dx
B. dy=(6x+2x-3)dx
C. * dy=( 3x2+2x+10)dx
D. dy=( 2x3+x2+10)dx
E. dy=(6x2+2x-13)dx
3. To Calculate differential of function y=1-x2
A. dy=( 1-2x)dx
B. * dy=( -2x)dx
C. dy=(-x+x3)dx
D. dy=(2-x2)dx
E. dy=2xdx
4. To Calculate differential of function y=1+x2
A. dy=( 1-2x)dx
B. dy=( -2x)dx
C. dy=(-x+x3)dx
D. dy=(2-x2)dx
E. * dy=2xdx
5. To Calculate differential of function y=2sin2x
A. dy=3sin2xcosxdx
B. * dy=4sinxcosxdx
C. dy=2cosxdx
D. dy=2sinxcosxdx
E. dy=( 3sin2xcosx+4)
6. To Calculate differential of function y=2x3+x3-3x
A. * dy=( 6x2+3x2-3)dx
B. dy=(6x+2x-3)dx
C. dy=( 3x2+2x+10)dx
D. dy=( 2x3+x2+10)dx
E. dy=(6x2+2x-13)dx
7. To Calculate differential of function y=2x3+x2-13x+10
A. dy=( 6x2+x2-3)dx
B. dy=(6x+2x-3)dx
C. dy=( 3x2+2x+10)dx
D. dy=( 2x3+x2+10)dx
E. * dy=(6x2+2x-13)dx
8. To find the derivate of function y = - cos 10x
A. y’ = 6 sin x
B. y’ = 7 sin x
C. y’ = 8 sin x
D. y’ = 9 sin x
E. * y’ = 10 sin x
9. To find the derivate of function : y = sin 7x
A. y' = 2 cos 2 x
B. y' = 3 cos 3 x
C. y' = 4 cos 4 x
D. * y' = 7 cos 7x
E. y' = 5 cos 5 x
10. To find integral 3cos x dx:
A. * 3sin x + C
B. 4sin x + C
C. 5sin x + C
D. 6sin x + C
E. 7sin x + C
11. Choose the correct record of law of reproduction of bacteria, through t=17, if initial
amount them is evened 2070, and coefficient of reproduction of k=2.
A. N=2050 е30
B. N=2060 е32
C. * N=2070 е34
D. N=2080 е36
E. N=2090 е38
12. Choose the correct record of law of reproduction of bacteria, through t=18, if initial
amount them is evened 2080, and coefficient of reproduction of k=2.
A. N=2050 е30
B. N=2060 е32
C. N=2070 е34
D. * N=2080 е36
E. N=2090 е38
13. Law of division of casual size is this:
A. * Accordance between the values of casual sizes and their probabilities.
B. Probability of casual sizes.
C. Value of casual size.
D. Discreteness of casual size.
E. Continuity of casual size.
14. Probability of sure event is equal:
A. 0
B. * 1
C. 0,5
D. 0,2
E. 0,6
15. Specify the correct formula of differentiation dsin u=...
A. dsin u=sin udu
B. dsin u=-cos udu
C. dsin u=-sin udu
D. * dsin u=cos udu
E. dsin u=ctg udu
16. Specify the correct formula of differentiation: (cos u) = …
A. * (cos u)' = -sin u u'
B. (cos u)' = sin uu'
C. (cos u)' = -sin u'
D. (cos u)' = cos uu'
E. (cos u)' = -cos uu'
17. The trained nurse looks after after two patients. Probability of that the first patient will
call the trained nurse - Р=0,45, and second - Р= 0,1. To find probability of that during a
hour the trained nurse will be called by both the patients.
A. 0,015
B. 0,025
C. 0,035
D. * 0,045
E. 0,055
18. The trained nurse looks after after two patients. Probability of that the first patient will
call the trained nurse -Р=0,25, and second - Р= 0,1. To find probability of that during a
hour the trained nurse will be called by both the patients.
A. 0,015
B. 0,025
C. * 0,035
D. 0,045
E. 0,055
19. The trained nurse looks after after two patients. Probability of that the first patient will
call the trained nurse -Р=0,6, and second - Р= 0,1. To find probability of that during a
hour the trained nurse will be called by both the patients.
A. 0,07
B. 0,08
C. 0,09
D. * 0,06
E. 0,05
20. The trained nurse looks after after two patients. Probability of that the first patient will
call the trained nurse -Р=0,5, and second - Р= 0,1. To find probability of that during a
hour the trained nurse will be called by both the patients.
A. 0,07
B. 0,08
C. 0,09
D. 0,06
E. * 0,05
21. The trained nurse looks after after two patients. Probability of that the first patient will
call the trained nurse -Р=0,2, and second - Р= 0,3. To find probability of that during a
hour the trained nurse will be called by both the patients.
A. * 0,06
B. 0,08
C. 0,04
D. 0,02
E. 0,01
22. To find standard deviation, if dispersion is evened 4.
A. 1
B. * 2
C. 3
D. 4
E. 5
23. To find standard deviation, if dispersion is evened 9.
A. 1
B. 2
C. * 3
D. 4
E. 5
24. To find standard deviation, if dispersion is evened 16.
A. 1
B. 2
C. 3
D. * 4
E. 5
25. To find standard deviation, if dispersion is evened 25.
A. 1
B. 2
C. 3
D. 4
E. * 5
26. To know selective middle.
xi 1 2 3
ni 1 3 2
A. 10/5
B. * 13/6
C. 15/7
D. 18/8
E. 15/5
27. To know selective middle.
xi 1 2 3
ni 2 2 3
A. 10/5
B. * 13/6
C. 15/7
D. 18/8
E. 15/5
28. To know selective middle.
xi 1 2 3
ni 2 2 4
A. 10/5
B. 13/6
C. 15/7
D. * 18/8
E. 15/5
29. To know selective middle.
xi 1 2 4
ni 1 1 3
A. 10/5
B. 13/6
C. 15/7
D. 18/8
E. * 15/5
30. To know selective middle.
xi 1 2 4
ni 1 2 1
A. * 11/4
B. 12/5
C. 17/7
D. 14/7
E. 12/4
31. To know selective middle.
xi 1 3 4
ni 2 2 1
A. 11/4
B. * 12/5
C. 17/7
D. 14/7
E. 12/4
32. To know selective middle.
xi 1 3 4
ni 3 2 2
A. 11/4
B. 12/5
C. * 17/7
D. 14/7
E. 12/4
33. To know selective middle.
xi 1 3 4
ni 4 2 1
A. 11/4
B. 12/5
C. 17/7
D. * 14/7
E. 12/4
34. To know selective middle.
xi 1 3 5
ni 1 2 1
A. 11/4
B. 12/5
C. 17/7
D. 14/7
E. * 12/4
35. To know selective middle.
xi 1 3 5
ni 2 2 1
A. * 13/5
B. 19/7
C. 15/7
D. 13/4
E. 15/5
36. To of find mean value of selection: 3, 5, 7
A. 3
B. * 5
C. 7
D. 0
E. 1
37. To of find mean value of selection: 0, 7, 14
A. 0
B. 9
C. * 7
D. 14
E. 21
38. To of find mean value of selection: 1, 3, 5
A. 10
B. 20
C. * 3
D. 7
E. 9
39. To of find mean value of selection: 10, 20, 30
A. 10
B. 30
C. * 20
D. 0
E. 60
40. To of find mean value of selection: 2, 7, 9
A. 2
B. * 7
C. 9
D. 6
E. 0
41. To of find mean value of selection: 30, 45, 60
A. 15
B. * 45
C. 90
D. 35
E. 30
42. To of find mean value of selection: 4, 8, 12
A. 4
B. * 8
C. 12
D. 24
E. 0
43. To of find mean value of selection: 5, 10, 15
A. * 10
B. 5
C. 15
D. 30
E. 20
44. To of find mean value of selection: 6, 12, 18
A. 24
B. 36
C. 17
D. * 12
E. 18
45. To solve differential equation y’=14x13.
A. y=x12+C
B. y=x13+C
C. * y=x14+C
D. y=x15+C
E. y=x16+C
46. To solve differential equation y’=15x14.
A. y=x12+C
B. y=x13+C
C. y=x14+C
D. * y=x15+C
E. y=x16+C
47. To solve differential equation y’=2x.
A. * y=x2+C
B. y=x3+C
C. y=x4+C
D. y=x5+C
E. y=x6+C
48. To solve differential equation y’=3x2.
A. y=x2+C
B. * y=x3+C
C. y=x4+C
D. y=x5+C
E. y=x6+C
49. To solve differential equation y’=4x3.
A. y=x2+C
B. y=x3+C
C. * y=x4+C
D. y=x5+C
E. y=x6+C
50. What does the order of differential equation concerne by?
A. Order of derivate.
B. * By the greatest order of derivate.
C. By the lowest order of derivate.
D. By the order of function.
E. By the order of argument.
51.
A. *
B.
C.
D.
E.
52.
A. *
Find the derivative y of the function y given by: y=2cos(2x)
у=-4sin(2x)
у=4sin(2x)
у=4cos(2x)
y=2sin(2x)
у=-4cos(2x)
Find the derivative y of the function y given by: y=3cos(3x)
у=-9sin(3x)
B.
у=9sin(3x)
C.
у=9cos(3x)
D.
y=3sin(3x)
E.
у=-9cos(3x)
53.
Find the derivative y of the function y given by: y=4cos(4x)
A. *
у=-16sin(4x)
B.
у=4sin(4x)
C.
у=16cos(4x)
D.
y=4sin(4x)
E.
у=-4cos(4x)
54.
Find the derivative y of the function y given by: y=6cos(6x)
A.
у=-36cos(6x)
B.
у=36sin(6x)
C.
у=36cos(6x)
D.
y=sin(6x)
E. *
у=-36sin(6x)
55 Find the derivative y of the function y given by: y=sin(2x)*ln(2x)
у=-2cos(2x)*ln(2x)-sin(2x)*1/x
у=-2cos(2x)*ln(2x)+sin(2x)*1/x
у=2sin(2x)*ln(2x)+sin(2x)*1/x
y=2cos(2x)*ln(2x)-sin(2x)*1/x
у=2cos(2x)*ln(2x)+sin(2x)*1/x
56 Find the derivative y of the function y given by: y=sin(3x)*ln(3x)
у=-3cos(3x)*ln(3x)-sin(3x)*1/x
у=-3cos(3x)*ln(3x)+sin(3x)*1/x
у=3sin(3x)*ln(3x)+sin(3x)*1/x
y=3cos(3x)*ln(3x)-sin(3x)*1/x
у=3cos(3x)*ln(3x)+sin(3x)*1/x
57 Find the derivative y of the function y given by: y=sin(4x)*ln(4x)
у=-4cos(4x)*ln(4x)-sin(4x)*1/x
у=-4cos(4x)*ln(4x)+sin(4x)*1/x
у=4sin(4x)*ln(4x)+sin(4x)*1/x
y=4cos(4x)*ln(4x)-sin(4x)*1/x
у=4cos(4x)*ln(4x)+sin(4x)*1/x
58 Find the derivative y of the function y given by: y=8x*exp(8x)
у=exp(8x)+exp(8x)
у=8*exp(8x)-8x*exp(8x)
у=8x*exp(8x)+64x*exp(8x)
y=8*exp(8x)+64x*exp(8x)
у=8x*exp(8x)-8x*exp(8x)
59 Find the derivative y of the function y given by: y=9x*exp(9x)
у=exp(9x)+exp(9x)
у=9*exp(9x)-9x*exp(9x)
у=9x*exp(9x)+81x*exp(9x)
y=9*exp(9x)+81x*exp(9x)
у=9x*exp(9x)-9x*exp(9x)
60.
The dependence of the amount of the substance x, received in the reaction and the time t is describe
with the equation x=3t+3exp(-3t). Determine the speed of the reaction.
A. *
B.
C.
D.
E.
61.
dx/dt=3-9exp(-3t)
dx/dt=3+9exp(-3t)
dx/dt=3-3exp(-3t)
dx/dt=9exp(-3t)
dx/dt=3+3exp(-3t)
The dependence of the amount of the substance x, received in the reaction and the time t is describe
with the equation x=4t+4exp(-4t). Determine the speed of the reaction.
A. * dx/dt=4-16exp(-4t)
B.
dx/dt=4+16exp(-4t)
C.
dx/dt=4-4exp(-4t)
D.
dx/dt=16exp(-4t)
E.
dx/dt=4+4exp(-4t)
62 The number of bacteria in a culture increases according to the law x=2000*exp(2t). Calculate the
growth rate of bacteria.
dx/dt=2000*exp(2t)
dx/dt=4000*exp(2t)
dx/dt=1000*exp(2t)
dx/dt=4000*exp(4t)
dx/dt=4000*exp(t)
63 The displacement as the response for the muscle stimulus (single nerve impulse) is estimated with
the
equation – y=3t+exp(-3t). Calculate the relationship between velocity and time.
dy/dt=3-3exp(-3t)
dy/dt=3+3exp(-2t)
dy/dt=3-3exp(8t)
dy/dt=3-3exp(-4t)
dy/dt=3+exp(-5t)
64 The displacement as the response for the muscle stimulus (single nerve impulse) is estimated with
the
equation – y=5t+exp(-5t). Calculate the relationship between velocity and time.
dy/dt=5-5exp(-5t)
dy/dt=5+5exp(-5t)
dy/dt=5-5exp(5t)
dy/dt=5-exp(-5t)
dy/dt=5+exp(-5t)
65 The displacement as the response for the muscle stimulus (single nerve impulse) is estimated with
the
equation – y=6t+exp(-6t). Calculate the relationship between velocity and time.
dy/dt=6-6exp(-6t)
dy/dt=6+6exp(-6t)
dy/dt=6-6exp(6t)
dy/dt=6-6exp(-6t)
dy/dt=6+exp(-6t)
66 The complex of potentials that appear during the massed electrical response of the retina to brief
flashes
of light (electroretinogram) is estimated by the equation : N=2exp(-2t), where “t” stands for
dN/dt=-4exp(-2t)
time.
Determine the speed of the cell destruction.
dN/dt=4exp(-2t)
dN/dt=-4exp(2t)
dN/dt=-4exp(-4)
dN/dt=4exp(2t)
67 The complex of potentials that appear during the massed electrical response of the retina to brief
flashes
of light (electroretinogram) is estimated by the equation N=3exp(-3t), where “t” stands for
dN/dt=-9exp(-3t)
time.
Determine
dN/dt=9exp(-3t)the speed of the cell destruction.
dN/dt=-9exp(3t)
dN/dt=-9exp(-9t)
dN/dt=9exp(3t)
68 What determines the order of a differential equation?
The order of the derivative.
The order of the highest derivative included in the equation.
The order of the lowest derivative included in the equation.
The order of the function.
The order of the argument.
69 Find the fromula for the approximate calculation:
f ( x  x)  f ( x)  f ( x)x
f ( x  x)  f ( x)  fx
f ( x  x)  f ( x)x
f ( x  x)  f ( y)x
f ( x  x)  f ( x)x  f ( x)
70 Choose the correct option for finding the amount of the drug substance dissolved from the tablet
with
m
= ethe
-10tablet mass m0 = 2 mg, the dissolution coefficient k = 2 after the time t= 6 sec.
m = e -12
m = e -14
m = e -16
m = e -18
71 Find the general solution for the following differential equation: у′=5ех
ех+с
2ех+с
3ех+с
4ех+с
5ех+с
72. 1
Sinxdx
1
Choose
the most common integration formula 
6
A.
. SinxdxCosx  c
B.
Sinxdx  Sinx c
C. *
D.
E.
73
A.
B.
C. *
D.
E.
74.
A. *

 Sinxdx  Cosx  c
 Sinxdx   xCosx  c
 Sinxdx  2 xCosx  c
x dx ...
Choose the most common integration formula: 
n
n
 x dx 
x n1
 c, (n  1)
n 1
n
 x dx 
x n1
 c, (n  1)
n 1
n
 x dx 
x n1
 c, (n  1)
n 1
n
 x dx 
x n1
, (n  1)
n 1
x n1
 c, (n  1)
n 1
Calculate the following integral  3cos x dx:
3sin x  C
n
 x dx 
B.
C.
D.
E.
75.
A. *
B.
4sin x  C
5sin x  C
6sin x  C
7sin x  C
Find the derivative y of the function y given by: y=5x3-3x2+6
y=15x2-6x
0,1
y' 
4
x3
C.
D.
E.
76.
y=12x(3+2x2)2
y=12x2+3x
y=8x-6
A.
B.
C. *
D.
E.
77.
A.
B.
C.
D.
1
 x dx
5
Find integral 0
1
2
1/6
4
5
Find the derivative y of the function y given by: y′=10ln10x
y′=6/x
y′=7/x
8
y′= x
9
y′= x
E. *
10
y′= x
78.
A. *
B.
C.
D.
E.
Find integral
lnx+C
x-1+C
x-2+C
ln2x+C
ex+C

dx
x
79 Probability of eventА:
n
P A  lim
n  m
m2
P A  lim
n n
m3
n n
m
P A  lim 2
n n
P A  lim
P A  lim
m
n
Inspected 350 people with the help of photofluorograph. In 7 people a tumour is is lungs, in 10
n 
80.
lungs fever. What probability of exposure of tumour:
A.
81.
1
350
10
350
17
350
30
350
7
350
Law of division of casual size is this:
A.
Probability of casual sizes.
B.
Value of casual size.
C.
Discreteness of casual size.
D.
Continuity of casual size.
E. *
Accordance between the values of casual sizes and their probabilities.
82.
Casual sizes are divided on:
A.
B.
Discrete
Continuous.
C.
D.
E. *
83.
A.
B.
C.
D.
E. *
84.
A.
B.
C.
D.
E. *
85.
Positive
Negative
Discrete and continuous.
By|by means of| flurography| it is inspected 100 persons. At three persons it was
found|exposed,shown,displayed|
out the lungs fever|lighting|, in four is bronchitis, in two is pleuris
3
What
probability
of
exposure|discovery|
of illness?
4
100
2
100
91
100
9
100
By|by
100 means of| flurography| it is inspected 100 persons. At three persons it was
found|exposed,shown,displayed|
out the lungs fever|lighting|, in four is bronchitis, in two is pleuris
9
What
probability
of
exposure|discovery|
of lungs fever|lighting|?
4
100
2
100
91
100
3
100
There
100 were 15 ampoules of analgin in a pharmacy, 20 - dimedrol|, 30 - novocaine, 40 - noshpa|, 25
subazol|. At random fished out one ampoule. To find probability of that fished out the ampoule of
analgin.
B.
C.
D.
E. *
A.
B.
C.
D.
E. *
86.
A.
B.
C.
D.
E. *
87.
A.
B.
C.
D.
E. *
88.
A.
B.
C.
D.
E. *
89.
A.
B.
C.
D.
E. *
90.
A.
B.
C.
D.
E. *
91.
A.
B.
C.
D.
E. *
92.
A.
B.
C.
D.
E. *
93.
20
30
130
40
130
25
130
15
130
There
130 were 15 ampoules of analgin in a pharmacy, 20 - dimedrol|, 30 - novocaine, 40 - noshpa, 25
subazol|.
At random fished out one ampoule. To find probability of that fished out the ampoule of
15
dimedrol|.
30
130
40
130
25
130
20
130
To
130specify the correct record of law of distribution:
To specify the correct record of law of distribution:
To specify the correct record of law of distribution:
Specify|indicates| a correct formula for the corrected dispersion selective|electoral| middle:
S x2В  S 2  n
n
S xx2В nS 2 2
В =
S
S2
S x2В S 2n
=
S x2В
Specify|indicates|
correctly the record confidence interval of estimation|appraisal| of mathematical
= n

hope
on middle
selective
n
  n   В :
В 
;


 В     nВ;  В    n


 



  В ;
  В 
 
n n
 n n

    В;      В  
  В  
;В 
  of selection: 1, 3, 5
To
of
find
mean
value
n
n

10
20
7
9
3
To of find mean value of selection: 0, 7, 14


A.
B.
C.
D.
E. *
94.
A.
B.
C.
D.
E. *
95.
A.
B.
C.
D.
E. *
96.
A.
B.
C.
D.
E. *
97.
A.
B.
C.
D.
E. *
0
9
14
21
7
The complex of potentials that appear during the massed electrical response of the retina to brief
flashes
of light (electroretinogram) is estimated by the equation N=8exp(-8t), where “t” stands for
dN/dt=64exp(8t)
time.
Determine
the speed of the cell destruction.
dN/dt=64exp(-8t)
dN/dt=-64exp(8t)
dN/dt=-64exp(-64t)
dN/dt=-64exp(-8t)
The complex of potentials that appear during the massed electrical response of the retina to brief
flashes
of light (electroretinogram) is estimated by the equation N=2exp(-2t), where “t” stands for
dN/dt=81exp(9t)
time.
Determine
the speed of the cell destruction.
dN/dt=81exp(-9t)
dN/dt=-81exp(9t)
dN/dt=-81exp(-81t)
dN/dt=-81exp(-9t)
What determines the order of a differential equation?
The order of the derivative.
The order of the lowest derivative included in the equation.
The order of the function.
The order of the argument.
The order of the highest derivative included in the equation.
Choose the most common integration formula: 
n
 x dx 
x n1
 c, (n  1)
n 1
n
 x dx 
x n1
 c, (n  1)
n 1
n
 x dx 
x n1
, (n  1)
n 1
n
 x dx 
x n1
 c, (n  1)
n 1
n
 x dx 
x n1
 c, (n  1)
n 1
98.
Find the probability of the event A:
A.
P  A  lim
n
n
m
B.
m2
P A  lim
n n
C.
P A  lim
m3
n n
x n dx ...
D.
P  A  lim
n
m
n2
E. *
P  A   lim
99.
Choose the valid formula for the corrected discreteness of the random average:
A.
S x2В  S 2  n
m
n n
B.
S x2В
C.
S x2В
n
2
= S
= n S
D.
S2
S x2В
E. *
2
=
n
S2
S
= n
2
xВ
100.
Calculate the mean squared error if the variance is equal to 49.
A.
6
B.
8
C.
9
D.
10
E. *
7