test topic
Units of measurement of information (translation)
item
Computer science
class/group
used sources and literature
FIPI materials
Key words or supporting concepts separated by commas (at least 5 pieces):
information, units of measurement, translation, bit, byte
methodological abstract
Some topics in the computer science course are covered at the beginning of the tenth grade (if taken in middle school or earlier), and the skills are used when completing the entire course and passing the Unified State Exam.
I suggest a five-minute activity that can be done at the beginning or end of the lesson.
Option 1
How many MB of information does a message of 2 to the 28th bit contain?
(The answer is one number).
How many bits of information does a 16 KB message contain?
(The answer is degree 2).
How many Kbits of information does a message of 2 to the 23rd byte contain?
(The answer is degree 2).
How many bytes of information does a 512 Gbit message contain?
(The answer is degree 2).
How many bytes of information does a 0.25 KB message contain?
(The answer is one number).
Option 2
How many kilobytes of information does a message of 2 to the 21th power of bits contain?
(The answer is one number).
How many bits of information does an 8 GB message contain?
(The answer is degree 2).
(The answer is degree 2).
How many bytes of information does a 1 Mbit message contain?
(The answer is degree 2).
How many Mbits of information does a 0.25 Gbit message contain?
(The answer is one number).
Option 3
1. How many GB of information does a message of 2 to the 33rd bit contain?
(The answer is one number).
2. How many bits of information does a 512 MB message contain?
(The answer is degree 2).
3. How many Mbits of information does a message of 2 to the 27th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 4096 Kbit message contain?
(The answer is degree 2).
5. How many KB of information does a 0.25 MB message contain?
(The answer is one number).
Option 4
1. How many MB of information does a message of 2 to the 30th bit contain?
(The answer is one number).
2. How many bits of information does a 1024 KB message contain?
(The answer is degree 2).
3. How many Kbits of information does a message of 2 to the 21th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 32 Gbit message contain?
(The answer is degree 2).
5. How many bits of information does a 0.125 Kbit message contain?
(The answer is one number).
Option 5
1. How many KB of information does a message of 2 to the 24th power of bits contain?
(The answer is one number).
2. How many bits of information does a 32 GB message contain?
(The answer is degree 2).
3. How many Gbits of information does a message of 2 to the 35th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 128 Mbit message contain?
(The answer is degree 2).
5. How many MB of information does a 0.125 GB message contain?
(The answer is one number).
Option 6
1. How many GB of information does a message of 2 to the 39th power of bits contain?
(The answer is one number).
2. How many bits of information does a 64 MB message contain?
(The answer is degree 2).
3. How many Mbits of information does a message of 2 to the 26th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 512 Kbit message contain?
(The answer is degree 2).
5. How many Kbits of information does a 0.125 Mbit message contain?
(The answer is one number).
Option 7
1. How many MB of information does a message of 2 to the 33rd bit contain?
(The answer is one number).
2. How many bits of information does an 8192 KB message contain?
(The answer is degree 2).
3. How many Kbits of information does a message of 2 to the 18th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 16 Gbit message contain?
(The answer is degree 2).
5. How many bytes of information does a 0.5 KB message contain?
(The answer is one number).
Option 8
1. How many KB of information does a message of 2 to the 20th power of bits contain?
(The answer is one number).
2. How many bits of information does a 2 GB message contain?
(The answer is degree 2).
3. How many Gbits of information does a message of 2 to the 40th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does an 8192 Mbit message contain?
(The answer is degree 2).
5. How many Mbits of information does a 0.5 Gbit message contain?
(The answer is one number).
Option 9
1. How many GB of information does a message of 2 to the 37th bit contain?
(The answer is one number).
2. How many bits of information does an 8 MB message contain?
(The answer is degree 2).
3. How many Mbits of information does a message of 2 to the 24th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 4 Kbit message contain?
(The answer is degree 2).
5. How many KB of information does a 0.5 MB message contain?
(The answer is one number).
Option 10
How many MB of information does a message of 2 to the 25th bit contain?
(The answer is one number).
How many bits of information does a 4096 KB message contain?
(The answer is degree 2).
How many Kbits of information does a message of 2 to the 24th power of bytes contain?
(The answer is degree 2).
How many bytes of information does a 64 Gbit message contain?
(The answer is degree 2).
How many bits of information does a 0.25 Kbit message contain?
(The answer is one number).
Option 11
How many kilobytes of information does a message of 2 to the 25th bit contain?
(The answer is one number).
How many bits of information does a 16 GB message contain?
(The answer is degree 2).
How many Gbits of information does a message of 2 to the 39th power of bytes contain?
(The answer is degree 2).
How many bytes of information does a 2 Mbit message contain?
(The answer is degree 2).
How many MB of information does a 0.25 GB message contain?
(The answer is one number).
Option 12
1. How many GB of information does a message of 2 to the 34th bit contain?
(The answer is one number).
2. How many bits of information does a 4 MB message contain?
(The answer is degree 2).
3. How many Mbits of information does a message of 2 to the 36th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 2048 Kbit message contain?
(The answer is degree 2).
5. How many Kbits of information does a 0.25 Mbit message contain?
(The answer is one number).
Option 13
1. How many MB of information does a message of 2 to the 26th bit contain?
(The answer is one number).
2. How many bits of information does a 128 KB message contain?
(The answer is degree 2).
3. How many Kbits of information does a message of 2 to the 15th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 128 Gbit message contain?
(The answer is degree 2).
5. How many bytes of information does a 0.125 KB message contain?
(The answer is one number).
Option 14
1. How many KB of information does a message of 2 to the 26th power of bits contain?
(The answer is one number).
2. How many bits of information does a 64 GB message contain?
(The answer is degree 2).
3. How many Gbits of information does a message of 2 to the 37th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does an 8 Mbit message contain?
(The answer is degree 2).
5. How many Mbits of information does a 0.125 Gbit message contain?
(The answer is one number).
Option 15
1. How many GB of information does a message of 2 to the 38th bit contain?
(The answer is one number).
2. How many bits of information does a 1024 MB message contain?
(The answer is degree 2).
3. How many Mbits of information does a message of 2 to the 30th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 32 Kbit message contain?
(The answer is degree 2).
5. How many KB of information does a 0.125 MB message contain?
(The answer is one number).
Option 16
1. How many MB of information does a message of 2 to the 29th power of bits contain?
(The answer is one number).
2. How many bits of information does a 2048 KB message contain?
(The answer is degree 2).
3. How many Kbits of information does a message of 2 to the 22nd byte contain?
(The answer is degree 2).
4. How many bytes of information does a 4 Gbit message contain?
(The answer is degree 2).
5. How many bits of information does a 0.5 Kbit message contain?
(The answer is one number).
Option 17
1. How many KB of information does a message of 2 to the 23rd bit contain?
(The answer is one number).
2. How many bits of information does a 1 GB message contain?
(The answer is degree 2).
3. How many Gbits of information does a message of 2 to the 38th power of bytes contain?
(The answer is degree 2).
4. How many bytes of information does a 16 Mbit message contain?
(The answer is degree 2).
5. How many MB of information does a 0.5 GB message contain?
(The answer is one number).
Option 18
1. How many GB of information does a message of 2 to the 36th power of bits contain?
(The answer is one number).
2. How many bits of information does a 128 MB message contain?
(The answer is degree 2).
3. How many Mbits of information does a message of 2 to the 23rd byte contain?
(The answer is degree 2).
4. How many bytes of information does a 256 Kbit message contain?
(The answer is degree 2).
5. How many Kbits of information does a 0.5 Mbit message contain?
(The answer is one number).
1
2
3
4
5
6
7
8
9
1
256
128
2048
1024
128
2
3
4
5
256
256
256
128
128
128
512
512
512
10
11
12
13
14
15
16
17
18
1
4096
8192
1024
2
3
4
5
256
256
256
128
128
128
512
512
512
Math test
Topic: “Units of measurement of quantities” 4th grade
1. From the units you know, choose those that are suitable for measurement:
a) distances between cities__________ d) your height _____________________
B) duration of the lesson ___________ e) volume of the pan _________________
C) the mass of one apple ________________f) your weight_______________________
2. Which of the entries mean 400500 cm in other units of measurement:
a) 400km 50m c) 4km 5m d) 4005 m
B) 400m 50dm d) 4005 dm f) 40050 dm
3. Express in the following units of measurement:
10580 kg = ____ t _____t _____kg 378 s = _______ min ________ s
1637 cm = _____ m _____dm _____cm102 hours = _______ days. ________ h
5 m 6 dm = ____________ mm
17 kg 17 g = ___________ g
28 t 30 c = ____________ kg
4. Compare:
2 sq. cm...2 sq. dm 1000 sq. dm... 1 sq. m
18 sq. m... 1800 sq. dm 300 sq. cm...3 sq. m
5. Indicate the correct answer to the problem.
A small child sleeps 1/2 of the day, and an adult sleeps 1/3 of the day. For how many hours
Does a child sleep longer than an adult?
A) 6 hours b) 2 hours c) 4 hours d) 1 hour
6. Choose the right solution to the problem.
What is the side of a rectangle if its perimeter is 92 cm, and the other
Side – 28 cm?
A) (92 – 28): 2 = 32 (cm);
B) (92 + 28) x 2 = 240 (cm);
B) 92: 2 – 28 =18 (cm).
7. Solve a geometric problem.
The sum of the lengths of the sides of the square is 300 cm. What is the area of this square?
_____________________________________________________________________
8. Perform operations with quantities and express them in new units of measurement:
A) (5 t 6 c + 2 c 5 kg): 9 = ___________________________________________
Answer: ______ c _______ kg
B) (4 m 8 cm – 16 dm) x 2050 = _________________________________________
Answer: _______ km _______ m
B) (6 min 4 s + 8 min 56 s) x 208 = ____________________________________
________________________________________________________________
Answer: _______ days. _______h.
Performed): ___________________________________________________________
Number of points: ___________________ Rating: ___________________________
On the topic: methodological developments, presentations and notes
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1 British minim = 0.0160126656733981 drachma
Initial value
Converted value
cubic meter cubic kilometer cubic decimeter cubic centimeter cubic millimeter liter Exaliter DEMALITRITRITER GIGALITRITRE IMGALITRIR HEXTOLIRER DECALITRIRER MICHLILIRER Microlyliter picoliter picoliter Figoliter attoliator cube (oil) Barrel British gallon British USA Varta Quarter British Pinta Pint British glass American glass (metric) glass British fluid ounce US fluid ounce British tablespoon amer. tablespoon (meter) tablespoon brit. American dessert spoon Brit dessert spoon teaspoon Amer. teaspoon metric teaspoon brit. gill, gill American gill, gill British minim American minim British cubic mile cubic yard cubic foot cubic inch register ton 100 cubic feet 100-foot cube acre-foot acre-foot (US, geodetic) acre-inch decaster ster decister cord tan hogshead plank foot drachma kor (biblical unit) homer (biblical unit) baht (biblical unit) gin (biblical unit) kab (biblical unit) log (biblical unit) glass (Spanish) volume of the Earth Planck volume cubic astronomical unit cubic parsec cubic kiloparsec cubic megaparsec cubic gigaparsec barrel bucket damask quarter wine bottle vodka bottle glass charka shalik
Electric potential and voltage
Learn more about volume and units of measurement in recipes
General information
Volume is the space occupied by a substance or object. Volume can also refer to the free space inside a container. Volume is a three-dimensional quantity, unlike, for example, length, which is two-dimensional. Therefore, the volume of flat or two-dimensional objects is zero.
Volume units
Cubic meter
The SI unit of volume is the cubic meter. The standard definition of one cubic meter is the volume of a cube with edges one meter long. Derived units such as cubic centimeters are also widely used.
Liter
The liter is one of the most commonly used units in the metric system. It is equal to the volume of a cube with edges 10 cm long:
1 liter = 10 cm × 10 cm × 10 cm = 1000 cubic centimeters
This is the same as 0.001 cubic meters. The mass of one liter of water at a temperature of 4°C is approximately equal to one kilogram. Milliliters, equal to one cubic centimeter or 1/1000 of a liter, are also often used. Milliliter is usually denoted as ml.
Jill
Gills are units of volume used in the United States to measure alcoholic beverages. One jill is five fluid ounces in the British Imperial system or four in the American system. One American jill is equal to a quarter of a pint or half a cup. Irish pubs serve strong drinks in portions of a quarter jill, or 35.5 milliliters. In Scotland, portions are smaller - one fifth of a jill, or 28.4 milliliters. In England, until recently, portions were even smaller, just one-sixth of a jill or 23.7 milliliters. Now, it’s 25 or 35 milliliters, depending on the rules of the establishment. The owners can decide for themselves which of the two portions to serve.
Dram
Dram, or drachma, is a measure of volume, mass, and also a coin. In the past, this measure was used in pharmacy and was equal to one teaspoon. Later, the standard volume of a teaspoon changed, and one spoon became equal to 1 and 1/3 drachms.
Volumes in cooking
Liquids in cooking recipes are usually measured by volume. Bulk and dry products in the metric system, on the contrary, are measured by mass.
Tea spoon
The volume of a teaspoon is different in different measurement systems. Initially, one teaspoon was a quarter of a tablespoon, then - one third. It is the latter volume that is now used in the American measurement system. This is approximately 4.93 milliliters. In American dietetics, the size of a teaspoon is 5 milliliters. In the UK it is common to use 5.9 milliliters, but some diet guides and cookbooks use 5 milliliters. The size of a teaspoon used in cooking is usually standardized in each country, but different sizes of spoons are used for food.
Tablespoon
The volume of a tablespoon also varies depending on the geographic region. So, for example, in America, one tablespoon is three teaspoons, half an ounce, approximately 14.7 milliliters, or 1/16 of an American cup. Tablespoons in the UK, Canada, Japan, South Africa and New Zealand also contain three teaspoons. So, a metric tablespoon is 15 milliliters. A British tablespoon is 17.7 milliliters, if a teaspoon is 5.9, and 15 if a teaspoon is 5 milliliters. Australian tablespoon - ⅔ ounce, 4 teaspoons, or 20 milliliters.
Cup
As a measure of volume, cups are not defined as strictly as spoons. The volume of the cup can vary from 200 to 250 milliliters. A metric cup is 250 milliliters, and an American cup is slightly smaller, approximately 236.6 milliliters. In American dietetics, the volume of a cup is 240 milliliters. In Japan, cups are even smaller - only 200 milliliters.
Quarts and gallons
Gallons and quarts also have different sizes depending on the geographic region where they are used. In the Imperial system of measurement, one gallon is equal to 4.55 liters, and in the American system of measurements - 3.79 liters. Fuel is generally measured in gallons. A quart is equal to a quarter of a gallon and, accordingly, 1.1 liters in the American system, and approximately 1.14 liters in the Imperial system.
Pint
Pints are used to measure beer even in countries where the pint is not used to measure other liquids. In the UK, milk and cider are measured in pints. A pint is equal to one-eighth of a gallon. Some other countries in the Commonwealth of Nations and Europe also use pints, but since they depend on the definition of a gallon, and a gallon has a different volume depending on the country, pints are also not the same everywhere. An imperial pint is approximately 568.2 milliliters, and an American pint is 473.2 milliliters.
Fluid ounce
An imperial ounce is approximately equal to 0.96 US ounces. Thus, an imperial ounce contains approximately 28.4 milliliters, and an American ounce contains approximately 29.6 milliliters. One US ounce is also approximately equal to six teaspoons, two tablespoons, and one eighth cup.
Volume calculation
Liquid displacement method
The volume of an object can be calculated using the fluid displacement method. To do this, it is lowered into a liquid of a known volume, a new volume is geometrically calculated or measured, and the difference between these two quantities is the volume of the object being measured. For example, if when you lower an object into a cup with one liter of water, the volume of the liquid increases to two liters, then the volume of the object is one liter. In this way, you can only calculate the volume of objects that do not absorb liquid.
Formulas for calculating volume
The volume of geometric shapes can be calculated using the following formulas:
Prism: the product of the area of the base of the prism and the height.
Rectangular parallelepiped: product of length, width and height.
Cube: length of an edge to the third power.
Ellipsoid: product of semi-axes and 4/3π.
Pyramid: one third of the product of the area of the base of the pyramid and the height. Post a question in TCTerms and within a few minutes you will receive an answer.
Mathematics test, grade 5, on the topic “Measuring Quantities”
Instructions for performing the work
45 minutes are allotted to complete the work. The work consists of 11 tasks.
Answers to assignments are written down on the answer sheet. When recording them, the following is taken into account:
in multiple-choice tasks, the number of the correct answer is indicated;
in tasks with a short answer, the number resulting from the solution is indicated;
in matching tasks, the sequence of numbers from the answer table is indicated without using letters, spaces or other symbols (wrong: A-2, B-1, B-3; correct: 213).
If you find that you have written down an incorrect answer on the form, carefully cross it out and write the correct answer next to it.
All necessary calculations and transformations are made in draft form. Drafts are not reviewed and are not taken into account when grading.
The correct answer, depending on the complexity of each task, is awarded one or more points. The points you receive for all completed tasks are summed up. Try to complete as many tasks as possible and score as many points as possible.
| 1. What is the area of a rectangle with sides 5 cm and 8 cm? Give your answer in square centimeters |
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| Answer: ______________ |
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| 2. The radius of the circle is 6 cm. What is the diameter of this circle? Give your answer in centimeters. |
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| Answer: ______________ |
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| 3. Establish a correspondence between the degree measure of an angle and its type |
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| 4) expanded |
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| |
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| 4. Choose the correct statements |
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| 1) If the triangles are equal, then their perimeters are equal |
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| 2) If the perimeters of the triangles are equal, then the triangles are equal |
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| 3) If the areas of the triangles are equal, then the triangles are equal |
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| 4) If the triangles are equal, then their areas are equal |
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| 5. Match the triangle with its description |
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| 1) equilateral rectangular |
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| 2) isosceles acute-angled |
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|
| 3) isosceles rectangular |
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| 4) scalene obtuse |
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| 5) versatile acute-angled |
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|
| 6) equilateral acute-angled |
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| 7) isosceles obtuse |
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| |
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| 6. Choose the correct statements |
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| 1) Any isosceles triangle is equilateral |
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| 2) Any equilateral triangle is isosceles |
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| 3) Any square is a rectangle |
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| 4) Any rectangle is a square |
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| 7. The length of the rectangle was increased by 8 times, and its width was reduced by 2 times. How did the area of this rectangle change? |
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| 1) Increased 4 times | 2) Decreased by 4 times |
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| 3) Increased 16 times | 4) Decreased by 16 times |
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| 8. Choose the correct statement. |
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| 1) 2 dm2< 80 см2 | 2) 470 cm2 > 4 m2 |
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| 3) 7 ha > 60,000 m2 | 4) 600 m2< 6 а |
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| 9. Select the statement that has an error |
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| 1) 3 hours = 10,800 s | 2) 2 days 5 hours 30 minutes = 3,230 minutes |
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| 3) 6 t 15 c 2 kg = 7,502 kg | 4) 9 kg 75 g = 9,075 g |
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| 10. One side of the triangle is 18 cm, the second is 10 cm larger, and the third is 2 times larger than the first side. What is the perimeter of this triangle? |
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| Answer: _________________________________ |
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| 11. Calculate the volume of a figure made up of identical cubes whose edge is 3 cm. |
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|
|
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| Solution: _____________________________________________________________________ |
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| Answer: ___________________________ |
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Answer form for the test “Measuring quantities”
| Last name, first name_______________________________________________ | Class _____________ |
|
| Points (set by teacher) |
||
Task 10
Task 11
Keys and criteria for assessing test items
| Job No. | Criteria for evaluation | ||
| 0.5 points if point 1 is written down and point 2 is not written down 0.5 points if point 4 is written down and point 3 is not written down (for example, answer 124 is worth 0.5 points) | |||
| 1.5 points if all the symbols are written correctly, 1 point if the wrong symbol is written at any one position in the answer; 0.5 points if any two positions of the answer contain characters other than those presented in the answer standard, and 0 points in all other cases | |||
| 0.5 points if point 2 is written down and point 1 is not written down 0.5 points if point 3 is written down and point 4 is not written down (for example, answer 13 is worth 0.5 points) | |||
| 1 point if the problem as a whole was solved correctly, but 1 typo or computational error was made | |||
| 2 points, if the problem is solved correctly, the correct answer is obtained 1 point if the volume of one cube is found, but the volume of the entire figure is not found, or the problem is solved completely, but 1 typo or 1 computational error is made | |||
| Maximum points | |||
Description of the test work
The test is focused on working on the teaching methods of S.M. Nikolsky (Textbook Mathematics. 5th grade: textbook for general education institutions / [S.M. Nikolsky, M.K. Potapov, N.N. Reshetnikov, A.V. Shevkin] - M.: Education, 2015). The purpose of the test is to check the level of mastery of the educational material in Chapter 2 “Measuring Quantities”, paragraphs 2.5 - 2.13.
The test consists of two parts and contains 11 tasks. Of these, 6 tasks are of a basic level, 4 tasks are of an advanced level and 1 task is of a high level of complexity. Tasks 1-9 provide three forms of answer:
. with a choice of answers from four proposed - 5 tasks,
. with a short answer - 2 tasks,
. for compliance - 2 tasks.
Students must demonstrate: mastery of basic algorithms; knowledge and understanding of such mathematical concepts as circle, angle, triangle, quadrilateral, their properties, knowledge of mathematical quantities, their units of measurement, knowledge of problem solving techniques.
Also testcontains 2 tasks with detailed answers, which are aimed at testing mastery of the material at an advanced and high level. When completing these tasks, students must demonstrate the ability to write a solution mathematically correctly, while providing the necessary explanations and justifications.
The tasks are arranged in order of increasing difficulty - from relatively simple to complex, assuming fluency in the material and a good level of mathematical culture.
Characteristics of tasks
| Job No. | Job type | Difficulty level |
| With a short answer | ||
| With a short answer | ||
| For compliance | ||
| Multiple choice | ||
| For compliance | ||
| Multiple choice | ||
| Multiple choice | Elevated |
|
| Multiple choice | Elevated |
|
| Multiple choice | Elevated |
|
| With a detailed answer | Elevated |
|
| With a detailed answer |
Distribution of tasks by type
| Job type | Number of tasks | Maximum score | The percentage of the maximum score for this type from the maximum for the entire work |
|
| Multiple choice | ||||
| With a short answer | ||||
| For compliance | ||||
| With a detailed answer |
Distribution of tasks by difficulty level
| Difficulty level | Number of tasks | Maximum score | The percentage of the maximum score for this level from the maximum for the entire work |
|
| Elevated | ||||
At the beginning of the lesson, students are given the full text of the work and answer forms. Answers and solutions to test problems are written down on forms. The wording of the assignments is not rewritten, the drawings are not redrawn.
After solving the task, the answer is written down. When recording a response, the following is taken into account:
In multiple-choice tasks, the number of the correct answer is indicated;
In tasks with a short answer, the number resulting from the solution is indicated;
In the matching task, a sequence of numbers from the answer table is indicated without using letters, spaces or other symbols (wrong: A-2, B-1, B-3; correct: 213).
Students can make all necessary calculations, transformations and drawings in a draft. Drafts are not reviewed and are not taken into account when grading.
Tasks No. 1, 2, 7, 8, 9 are considered completed correctly if the number of the correct answer is indicated (in tasks with a choice of answers), or the correct answer is entered (in tasks with a short answer).
For the answer to tasks No. 3, No. 5, 1.5 points are awarded if all symbols are written correctly; 1 point if at any one position of the answer the symbol written is not the one presented in the answer standard; 0.5 points if any two positions of the answer contain characters other than those presented in the answer standard, and 0 points in all other cases.
For the answer to task No. 4, 1 point is awarded if the answer is given correctly; 0.5 points if recorded point 1, and point 2 is not recorded; 0.5 points if item 4 is written down and item 3 is not written down (for example, answer 124 is worth 0.5 points).
For the answer to task No. 6, 1 point is awarded if the answer is given correctly; 0.5 points if point 2 is written down and point 1 is not written down; 0.5 points if item 3 is written down and item 4 is not written down (for example, answer 13 is worth 0.5 points).
For task No. 10, 2 points are awarded, if the problem is solved correctly, the correct answer is received; 1 point if the problem as a whole was solved correctly, but 1 typo or computational error was made.
For task No. 11, 2 points are awarded, if the problem is solved correctly, the correct answer is received; 1 point if the volume of one cube is found, but the volume of the entire figure is not found, or the problem is solved completely, but 1 typo or 1 computational error was made.
The overall score is formed by summing the points received for each task.
Scale for converting total score to school grade
| Mark on a five-point scale | "2" | "3" | "4" | "5" |
| Total score | 0 - 3,5 | 4 - 7 | 7,5 - 10,5 | 11 - 14 |
Test plan
| Job No. | Testable skill or knowledge |
| Knowledge of the formula for the area of a rectangle; ability to find the area of a rectangle |
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| Knowledge of the relationship between radius and diameter; ability to calculate the diameter of a circle from its radius |
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| Knowledge of types of angles; the ability to determine the type of angle by its degree measure |
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| Understanding the fact that equal figures always have equal perimeters and areas, but equality of perimeters or areas is not a sign of equality of figures |
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| Knowledge of different types of triangles, the ability to classify triangles by sides and angles; ability to determine the type of triangle from a drawing |
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| Knowledge of the classification of triangles by sides, understanding of the fact that equilateral triangles are included in the class of isosceles triangles. Knowledge of different types of quadrilaterals, understanding the fact that squares are included in the class of rectangles. |
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| Knowledge of the formula for the area of a rectangle, the ability to analyze the change in area when the sides of a rectangle change. |
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| Knowledge of area units, ability to convert units |
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| Knowledge of units of measurement of mass and time, ability to convert units |
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| Knowledge of the concept of the perimeter of a figure, the ability to solve simple word problems |
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| Knowledge of the formula for the volume of a cube, the ability to calculate the volume of a cube, understanding of the additivity of volume, the level of development of spatial thinking. |
When developing the test, materials (specifications) of regional exams in mathematics in general education organizations of the Orenburg region were used as a sample for analyzing the content of the test
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