Mathematics (Answers to the MMA, IDO test)

Answers to the test Mathematics - MMA (Moscow International Academy)..
Pass result: 17/20 points.
The test was taken in 2024.

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Questions for the test:
Solve a system of equations using Cramer's formula

x1=2;x2=1;x3=−3|1=2; |2=1; |3=−3

x1=1;x2=0;x3=2|1=1; |2=0; |3=2

x1=3;x2=1;x3=−3|1=3; |2=1; |3=−3


Calculate limit

2

3

4


Calculate Derivative

3x+2ln[x−1x+1]+C3|+2|| [|−1|+1]+ |

x+2ln[x−1x+1]+C|+2|| [|−1|+1]+ |

3x+ln[x−1x+1]+C3|+| | [|−1|+1]+ |



Calculate Derivative

∫dx2−5x√∫||2−5|

−232−5x−−−−−√+C−232−5|+|

−152−5x−−−−−√+C−152−5|+|

−252−5x−−−−−√+C−252−5|+|



If a function is differentiable at a point a, then it

not defined at this point

is continuous at this point

is constant on the set R

equal to zero at this point


Finding the derivative of a given function is called

graphic illustration

simplification

root extraction

differentiation


The identity matrix is ​​a matrix for which

all elements of the first row are equal to one and the remaining elements are equal to zero

the main diagonal contains ones, and all other elements are equal to zero

all elements are equal to one

the sum of the elements of each line is equal to one



To solve a nonlinear equation, the method of second order convergence is

Gaussian

simple iteration

half division

Newton



Find the determinant of the matrix

92

101

80



Solve a system of equations using the inverse matrix method

x1=1;x2=2;x3=−3|1=1;|2=2;|3=−3

x1=5;x2=0;x3=−3|1=5;|2=0;|3=−3

x1=2;x2=4;x3=−3|1=2;|2=4;|3=−3






The Gaussian method consists in reducing the original matrix of the system to an equivalent form, where the matrix of the transformed system is

symmetric matrix

upper triangular matrix

diagonal matrix


When applying the Gauss method to calculate a definite integral, the integration nodes are located on the segment

unevenly, condensing towards the middle of the segment

unevenly, condensing towards the ends of the segment

unevenly, condensing towards the middle of the segment and towards its ends

evenly



The theory of "Analytical Geometry" was created by R. Descartes:

wrong

right



The area of ​​the triangle is

half the product of its two sides and the cosine of the angle between them

the product of its two sides and the sine of the angle between them

half the product of its two sides and the sine of the angle between them

the product of its two sides and the tangent of the angle between them





Calculate integral

∫x3dxx8−2∫38−2

182√ln[x3−2√x4+2√]+C182|3−2|4+2]+ |

182√ln[x5−2√x4+2√]+C182|5−2|4+2]+ |

182√ln[x4−2√x4+2√]+C182|| [|4−2|4+2]+ |





Calculate integral

∫ln2xdx∫||2|||

xln3x - 2xlnx + 2x + C

xln2x - 2xlnx + 2x + C

2xln3x - 2xlnx + 2x + C


Linear equation defines

uniform slow motion

uneven movement

uniform motion

uniformly accelerated motion



The value of the derivative of the function at point x_0

shows the acceleration of the function

always equal to zero

shows the rate of change of a function

always a positive number