The author of the assignments is a leading specialist who is directly involved in the development of control measuring materials for the Unified State Examination.
Typical test tasks in computer science contain 14 variants of sets of tasks, compiled taking into account all the features and requirements of the Unified State Exam in 2019. The purpose of the manual is to provide readers with information about the structure and content of the 2019 KIM in computer science, the degree of difficulty of the tasks.
The collection contains answers to all test options, provides solutions to all tasks of one of the options, as well as solutions to problems in part 2.
The manual is intended for teachers to prepare students for the computer science exam, as well as for high school students for self-preparation and self-control.

Examples.
The automatic camera produces raster images measuring 640 x 480 pixels. In this case, the size of the image file cannot exceed 170 KB, and no data packaging is performed. What is the maximum number of colors that can be used in a palette?

Performer A16 converts the number written on the screen.
The performer has three teams, which are assigned numbers:
1. Add 1
2. Add 2
3. Multiply by 2
The first of them increases the number on the screen by 1, the second increases it by 2, the third multiplies it by 2.
A program for performer A16 is a sequence of commands.
How many programs are there that convert the original number 3 into the number 12 and at the same time the program's computation path contains the number 10?
A program's computation trajectory is a sequence of results from the execution of all program commands. For example, for program 132 with the initial number 7, the trajectory will consist of the numbers 8, 16, 18.

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• I will pass the Unified State Exam, Computer Science, Typical tasks, Leshchiner V.R., Krylov S.S., Ushakov D.M., 2019
• Unified State Examination, Computer Science, grade 11, Preparing for the final certification, Leshchiner V.R., Krylov S.S., Yakushkin A.P., 2020
• Unified State Exam 2020, Computer Science, 16 options, Typical versions of exam tasks from Unified State Exam developers, Leshchiner V.R.
• Computer Science, Unified State Exam, Preparing for the final certification, Leshchiner V.R., Krylov S.S., Yakushkin A.P., 2020

The following textbooks and books.

. Information coding, volume and transmission of information: Demo version Unified State Exam in Computer Science 2018; State final exam 2018; training Unified State Exam options in computer science, thematic test tasks and tasks from the computer science simulator 2018

✍ Show solution:

• Using the formula for image file volume, we have:

Where N is the total number of pixels or resolution, and i— color coding depth (number of bits allocated per 1 pixel)

• Let's see what we have already been given from the formula:

I= 320 KB, N= 640 * 420 = 307200 = 75 * 2 12 total pixels, i - ?

The number of colors in the image depends on the parameter i, which is unknown. Let's remember the formula:

number of colors = 2 i

Since color depth is measured in bits, it is necessary to convert the volume from Kilobytes to bits:

320 KB = 320 * 2 10 * 2 3 bits = 320 * 2 13 bits

We'll find i:

\[ i = \frac (I)(N) = \frac (320 * 2^(13))(75 * 2^(12)) \approx 8.5 bits \]

Let's find the number of colors:

2 i = 2 8 = 256

Result: 256

State final exam GVE 2018 (informatics GVE FIPI, task 7):

Produced two-channel(stereo) digital sound recording. The signal value is fixed 48,000 times per second, to record each value is used 32 bit. Recording lasts 5 minutes, its results are written to a file, data compression is not performed.

Which of the following values ​​is closest to the size of the resulting file?

1) 14 MB
2) 28 MB
3) 55 MB
4) 110 MB

✍ Show solution:

I = β * ƒ * t * S

Let's substitute the available values ​​into the formula:

I = 48000 * 32 * 300 * 2

Since the values ​​are large, numbers are needed 48000 And 300 express in powers of two:

48000 | 2 24000 | 2 12000 | 2 6000 | 2 = 375 * 2 7 3000 | 2 1500 | 2 750 | 2 375 | 2 - no longer divisible 187.5 300 | 2 = 75 * 2 2 150 | 2 75 | 2 - no longer divisible 37.5

We get:

I = 375 * 75 * 2 15

In the proposed answer options we see that the result is everywhere in MB. This means that we need to divide our result by 2 23 (2 3 * 2 10 * 2 10):

I = 375 * 75 * 2 15 / 2 23 = 28125 / 2 8

Let's find something close to the number 28125 value to the power of two:

2 10 = 1024 1024 * 2 2048 * 2 4096 * 2 8192 * 2 16384 * 2 32768

We get:

2 10 * 2 5 = 2 15 = 32768 2 10 * 2 4 = 2 14 = 16384

Number 28125 lies between these values, so we take them:

2 15 / 2 8 = 2 7 = 128 2 14 / 2 8 = 2 6 = 64

We choose the answer whose value is between these two numbers: option 4 (110 MB)

Result: 4

Solution 9 of the Unified State Examination task in computer science (diagnostic version of the 2018 exam paper, S.S. Krylov, D.M. Ushakov):

Produced two-channel(stereo) sound recording with sampling rate 4 kHz And 64-bit resolution. Recording lasts 1 minute, its results are written to a file, data compression is not performed.

Approximately determine size of the resulting file (in MB). As an answer, indicate the integer multiple of the file size that is closest to 2 .

✍ Show solution:

• According to the volume formula sound file we have:

I = β * ƒ * t * S

I - volume β - encoding depth = 32 bits ƒ - sampling frequency = 48000 Hz t - time = 5 min = 300 s S - number of channels = 2

Let's substitute the existing values ​​into the formula. For convenience, we will use powers of two:

ƒ = 4 kHz = 4 * 1000 Hz ~ 2 2 * 2 10 B = 64 bits = 2 6 / 2 23 MB t = 1 min = 60 s = 15 * 2 2 s S = 2

Let's substitute the values ​​into the sound file volume formula:

I = 2 6 * 2 2 * 2 10 * 15 * 2 2 * 2 1 / 2 23 = 15/4 ~ 3.75

The nearest integer multiple of two is a number 4

Result: 4

Solution 9 of the Unified State Examination in computer science, option 1 (FIPI, “Unified State Examination Informatics and ICT, standard exam options 2018”, S.S. Krylov, T.E. Churkina):

The musical fragment was recorded in the format quad(four-channel recording), digitized and saved as a file without using data compression. Received file size 48 MB. Then the same piece of music was recorded again in the format mono with sampling rate 2 times less than the first time. Moreover, when recording again, the tempo of music playback was reduced by 2.5 times. No data compression was performed.

Specify file size in MB, received during re-recording. In your answer, write down only an integer; there is no need to write a unit of measurement.

✍ Show solution:

• Let's write down the known data about the two states of the file - before and after conversion:

S 1 = 4 channels I 1 = 48 MB S 2 = 1 channel ƒ 2 = 1/2 ƒ 1 (half the size) t 2 = 2.5 t 1 (tempo decreased by 2.5 times)

Since the volume of the file changes in the same way as the time and sampling frequency, we will find the volume for the converted file (taking into account the number of channels):

I 2 = I 1 / 2 * 2.5 / 4; I 2 = 48 / 2 * 2.5 / 4 = 15

Result: 15

All categories of the task Finding volume graphic file Finding the volume of an audio file Bit rate

1) To store an arbitrary raster image of 128×320 pixels, 40 KB of memory is allocated, excluding the size of the file header. The same number of bits are used to encode the color of each pixel, and the pixel codes are written to the file one after the other without gaps. What is the maximum number of colors that can be used in an image?

2) The automatic camera produces raster images of 200x256 pixels. The same number of bits are used to encode the color of each pixel, and the pixel codes are written to the file one after the other without gaps. The size of the image file cannot exceed 65 KB without taking into account the size of the file header. What is the maximum number of colors that can be used in a palette?

3) A 40 MB document can be transferred from one computer to another in two ways.

A. Compress with an archiver, transfer the archive via a communication channel, unpack.

B. Transmit over a communication channel without using an archiver.

Which method is faster and by how much, if:  the average data transfer speed over the communication channel is 223 bits per second;  the volume of the document compressed by the archiver is 90% of the original;  time required to compress a document – ​​16 seconds, to decompress – 2 seconds?

In your answer, write the letter A if method A is faster, or B if method B is faster. Immediately after the letter, write a number indicating how many seconds one method is faster than the other. So, for example, if method B faster way And for 23 seconds, you need to write B23 in your answer.

The units of measurement “seconds”, “sec.”, “s” do not need to be added to the answer.

4) Two-channel (stereo) sound recording was made with a sampling frequency of 64 kHz and 24-bit resolution. The result was a file of 120 MB in size; no data compression was performed. Determine approximately how long (in minutes) the recording took place. As an answer, indicate the integer closest to the time of recording, a multiple of 5.

5) What is the minimum amount of memory (in KB) that must be reserved to be able to store any 64x64 pixel bitmap image, assuming that the image can contain 256 different colors? In your answer, write down only an integer; there is no need to write a unit of measurement.

6) To store an arbitrary raster image of 1024×1024 pixels in size, 512 KB of memory are allocated, and for each pixel it is stored binary number– color code of this pixel. For each pixel, the same number of bits are allocated to store the code. Data compression is not performed. What is the maximum number of colors that can be used in an image?

7) The piece of music was digitized and recorded as a file without using data compression. The resulting file was transmitted to city A via a communication channel in 15 seconds. Then the same piece of music was re-digitized with a resolution 2 times higher and a sampling rate 1.5 times lower than the first time. No data compression was performed. The resulting file was transferred to city B; The bandwidth of the communication channel with city B is 2 times higher than the communication channel with city A. How many seconds did the file transfer to city B last? In your answer, write down only an integer; there is no need to write a unit of measurement.

8) An automatic camera produces raster images of 640x480 pixels. In this case, the size of the image file cannot exceed 320 KB, and no data packaging is performed. What is the maximum number of colors that can be used in a palette?

9) The musical fragment was recorded in mono format, digitized and saved as a file without using data compression. The size of the resulting file is 24 MB. Then the same piece of music was recorded again in stereo format (two-channel recording) and digitized with a resolution 4 times higher and a sampling rate 1.5 times lower than the first time. No data compression was performed. Specify the file size in MB of the resulting rewrite.

10) The piece of music was digitized and recorded as a file without using data compression. The resulting file was transmitted to city A via a communication channel in 96 seconds. The same piece of music was then re-digitized at a resolution 4 times higher and a sampling rate 3 times lower than the first time. No data compression was performed. The resulting file was transferred to city B in 16 seconds. How many times is the speed of the channel to city B greater? bandwidth channel to city A?

11) The piece of music was digitized and recorded as a file without using data compression. The resulting file was transmitted to city A via a communication channel in 45 seconds. The same piece of music was then re-digitized at a resolution 4 times lower and a sampling rate 12 times higher than the first time. No data compression was performed. The resulting file was transferred to city B in 15 seconds. How many times is the speed of the channel to city B greater than the speed of the channel to city A?

| Computer Science and Information and Communication Technologies | Preparation for the Unified State Exam | Control training tasks

Control training tasks

Part 1

Task 9

The answers to tasks 1 – 23 are a number, a sequence of letters or numbers that should be written in ANSWER FORM No. 1 to the right of the number of the corresponding task, starting from the first cell, without spaces, commas and other additional characters. Write each character in a separate box in accordance with the samples given in the form.

Example 1

What is the minimum amount of memory (in KB) that must be reserved to be able to store any 64x64 pixel bitmap image, assuming that the image can contain 256 different colors? In your answer, write down only an integer; there is no need to write a unit of measurement.

Example 2

To store an arbitrary raster image of 1024x1024 pixels in size, 512 KB of memory is allocated, and for each pixel a binary number is stored - the color code of this pixel. For each pixel, the same number of bits are allocated to store the code. Data compression is not performed. What is the maximum number of colors that can be used in an image?

Answer: ___________________________.

Example 3

The automatic camera produces raster images of 640x480 pixels. In this case, the size of the image file cannot exceed 320 KB, and no data packaging is performed. What is the maximum number of colors that can be used in a palette?