P 3 ratio and proportion test. Relationships and proportions
P.1. Similarity of figures
Tests
Calculation and graphic work
Example of a title page
CHOU VPO Institute of Economics, Management and Law (Kazan)
Faculty of Management and Engineering Business
Department of Higher Mathematics
in the discipline "Financial Mathematics"
Option 1
Performer: 2 OZO SP gr. 112 at ______________ A.V. Petrov
Checked: Art. teacher ______________ E.A. Kasatkina
Naberezhnye Chelny
If there is no “Search for a solution...” item in the “Service” tab, you must execute the command “Service” / “Add-ons...”, and in the window that opens, select the “Search for a solution” add-on, after which the selected item will appear in the “Service” tab.
If the search for a solution fails to find a solution, then in the search for a solution window you need to click the “Options” button and set a higher value for the limiting number of iterations (for example, 1000) and/or a smaller value for the relative error (for example, 0.001).
Option 1
1. Similar geometric shapes have the same shape.
2. The coefficient of similarity of equal figures is equal to one.
3. The similarity coefficient of segments is equal to the quotient of their lengths.
4. The similarity coefficient of circles is equal to the quotient of the lengths of their radii.
5. The similarity coefficient of squares is equal to the quotient of the lengths of their diameters.
6. If the sides of the square are reduced by 5 times, then the perimeter of the resulting square will decrease by 25 times.
7. If the length of the rectangle is increased by k times, then its area will increase by k 2 times.
8. If the edge of a cube is doubled, then its volume of the new cube will be 4 times greater.
9. Any two squares are similar.
10. If the figures are equal, then their areas are equal.
Option 2
Write down a numerical code made up of the numbers of correct statements.
1. Equal geometric figures have the same shape and the same dimensions.
2. The similarity coefficient is a number that shows how many times one of the similar figures is larger or smaller than the other.
3. Similar triangles have equal corresponding angles.
4. The similarity coefficient of triangles is equal to the quotient of the lengths of their similar sides.
5. The similarity coefficient of circles is equal to the quotient of the lengths of their diameters.
6. If the sides of a rectangle are reduced by k times, then its perimeter will decrease by k once.
7. If the side of the square is increased by k times, then the area of the new square will be k 2 times more.
8. If the edge of a cube is reduced by 3 times, then the volume of the new cube will become 9 times smaller.
9. Any two rectangles are similar.
10. If the areas of the figures are equal, then the figures themselves are equal.
Option 1
1. The quotient of two quantities measured in the same units is called the ratio of these quantities.
2. The ratio of the number 150 to the number 250 is equal to .
3. The equality 2:5= 0.1:0.25 is a proportion.
4. In proportion A:b=c:d numbers b And c are called extreme terms of the proportion.
5. In proportion, the product of the extreme terms is equal to the product of the middle terms.
6. In a proportion, the unknown term is 2.4.
7. If triangles ABC And KLM are similar, then Sun:L.M.=A.C.:MK.
8. If the distance between settlements on the ground is 5 km, and on the map 0.5 cm, then the map scale is 1:100,000.
9. 1% of 55 is equal to 0.55.
10. A number of which 20% is the number 5 is 100.
Option 2
Write down a number made up of the numbers of correct statements.
1. True equality of two ratios is called proportion.
2. The ratio of the numbers 350 to 420 is equal to .
3. The equality 7:10=5:9 is a proportion.
4. In proportion to the number A And d are called extreme members.
5. If c:d=k:m, That cm=kd.
6. In a proportion, the unknown term is 4.5.
7. If triangles ABC And KLM are similar, then AB:KL=A.C.:KM.
8. If on the map the distance between villages is 2 cm, and the map scale is 1:100,000, then the distance on the ground is 2 km.
9. 1% of 2 is equal to 0.2.
10. A number of which 10% is 5 is 50.
Relations in mathematics 2 m were cut from a piece of matter 5 m long. What part of the piece of matter was cut off? 5 m 2 m Solution =0.4=40 0 / 0 The quotient of two numbers is called the ratio of these numbers. What does attitude show? The answer can also be written as a decimal or percentage. 2:5=
What does attitude show? The ratio shows how many times the first number is greater than the second 16 kg 8 kg 16: 8 = 2(r.) or what part the first number is from the second. 4 m 20 m 4: 20 = 0.2 (parts) If two quantities are measured by the same unit of measurement, then the ratio of their values is called the ratio of these quantities. Mass ratio Length ratio To dough
P R O P O R T I O N “Proportion is proportionality. 1) A certain relationship between the parts. Proportionality in nature, art, architecture means maintaining certain relationships between the sizes of individual parts of a plant, sculpture, building and is an indispensable condition for the correct and beautiful depiction of an object. 2) In mathematics: the equality of two relations.” Ozhegov S. I.
PROPORTIONS The ratios 3.6:1.2 and 6.3:2.1 are equal. Therefore, we can write the equality 3.6:1.2=6.3:2.1 or a: b = c:d The middle terms of the proportion The extreme terms of the proportion In the correct proportion, the product of the extreme terms is equal to the product of the middle terms. a * d = b * c How to check if the proportion is correct? To a question
PROPORTIONS Basic property of proportion: If the product of the extreme members is equal to the product of the middle members of the proportion, then the proportion is correct. Check if the proportion is correct? 20:16=5:
EXERCISES Make up, if possible, proportions from the following ratios: a) 20:4 and 60: Make up, if possible, proportions from the four given numbers: a) 100; 80; 4; Check in two ways whether the equality is true: a) 49:14=14: Make up a proportion from the following equalities: a) 40*30=20* Find the unknown term of the proportion: a) x:30=54:40
Test 1. Relationships. 1. Which of these ratios is equal? a)7:2; b) 4:14; c) 7:17.5; d)12:17;7:24:147:17,512:17 2. Find the ratio of 1.2 m to 10 cm. a) 12; b) 12 m; c)0.12; d) another answer. 1212 m 0.12 another answer 3. How does one third of an hour relate to eighteen minutes? a)1:54; b)10:8; c)1:6; d) another answer.1:5410:81:6 another answer. 4. The ratio a:b is 5:3. Find the ratio 3a:10c. a) 1:2; b)2; c) 9:30; d) another answer.1:229:30 another answer.
Test 2. Proportions. 1. Find the product of the middle terms of the proportion: a)9.8; b)0.98; c)80; d) another answer.9,80,9880 another answer. 2. Find the unknown member of the proportion: a)0.05; b)20; c)0.5; d) another answer 0.05200.5 another answer. 3. From the given proportions, choose the correct one: a)82:72=64:78; b)15:8=13:6;82:72=64:7815:8=13:6 c)17:2=34:4; d)22:23=81:82.17:2=34:422:23=81:82
Task 4 The distance on the map from the Earth to the Moon is 38.4 cm. Find the distance between them if the map scale is 1:
in exercises, problems and tests
Zheleznogorsk
sanatorium-forest school
§ 1 Ordinary fractions (repetition).
item 1. addition and subtraction of fractions with different denominators.
item 2. Joint actions with decimal and ordinary fractions.
§ 2 Relations and proportions
clause 3. relationships.
point 4. Proportions. The main property of proportion.
clause 6. Inverse proportionality of quantities.
§ 3 Positive and negative numbers
item 7. Coordinate line.
item 8. Positive numbers. The absolute value of a number.
paragraph 9. Comparison of numbers.
item 10. Addition of rational numbers.
item 11. Addition of numbers with different signs.
item 12. Laws of addition of rational numbers.
item 13. Subtraction.
item 14. Distance between points.
item 15. Multiplication of rational numbers.
item 16. Division.
item 17. Properties of actions with rational numbers.
§ 4 Solutions of equations
paragraph 18. Expanding parentheses.
item 19. Reduction of similar terms.
item 20. Solving equations.
§ 5 Problem solving
clause 21. Tasks.
paragraph 22. Repetition.
ChapterI. Common fractions (repetition).
§ 1 adding and subtracting fractions with different denominators.
Abstract
1. Comparison of fractions.
a) if the denominators are the same: that fraction > which has a larger numerator?
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c) if the numerators and denominators are different: reduce to a common denominator.
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3. Calculate:
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Withindependent work
4. Choose the correct answer.
https://pandia.ru/text/78/170/images/image035_0.png" align="left" width="100" height="45 src=">a) b)
https://pandia.ru/text/78/170/images/image037_0.png" align="left" width="92" height="45 src=">c) d)
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https://pandia.ru/text/78/170/images/image045.png" align="left" width="49" height="23 src=">c) The morning milk yield was 81/2 l, the evening - 63/10 l, and at lunchtime the milk yield was 3/5 l less than in the morning. What is the milk yield per day?
6. Compare the fractions and draw a conclusion.
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8. Arrange in descending order.
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https://pandia.ru/text/78/170/images/image065.png" align="left" width="67" height="41 src=">.png" align="left" width="100 " height="45 src=">.png" align="left" width="115" height="41 src=">v g)
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Png" align="left" height="17 src=">.png" align="left" width="16" height="41 src=">.png" align="left" height="17 src= ">.png" align="left" height="17 src=">.png" align="left" width="15" height="41 src=">.png" align="left" width=" 21" height="41 src=">.png" align="left" width="15" height="41 src=">a) b)
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Png" align="left" height="17 src=">2). The sum of the fractions is equal to:
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3). The value of the expression is:
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4). Add the fractions:
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5). Calculate:
https://pandia.ru/text/78/170/images/image085.png" align="left" width="99" height="45 src=">6). Follow these steps:
https://pandia.ru/text/78/170/images/image086.png" align="left" width="72" height="41 src=">.png" align="left" width="44 " height="41 src=">.png" align="left" width="85" height="41 src=">.png" align="left" width="140" height="41 src=" >.png" align="left" width="81" height="41 src="> Examples: a) b) c)
(reducible by 2) (fraction not reducible) (reducible by 25)
https://pandia.ru/text/78/170/images/image096.png" align="left" width="59" height="41 src=">.png" align="left" width="51 " height="41 src="> A)
, since the denominator has a divisor of 5 and 2: 5 = 0.4
https://pandia.ru/text/78/170/images/image100.png" align="left" width="31" height="41 src="> V)
- cannot be converted to decimal, because the denominator does not have divisors 2 and 5
13. Find fractions that can be written as decimals and unscramble the word.
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14. Convert a fraction to a decimal.
https://pandia.ru/text/78/170/images/image112.png" align="left" width="32" height="41 src=">.png" align="left" width="20 " height="41 src=">.png" align="left" width="21" height="41 src=">.png" align="left" width="55" height="41 src=" >.png" align="left" width="55" height="41 src=">.png" align="left" width="49" height="41 src=">.png" align="left " width="61" height="41 src=">.png" align="left" width="147" height="45 src=">.png" align="left" width="100" height= "41 src=">a) b) c)
19. Independent work.
1). Calculate:
https://pandia.ru/text/78/170/images/image130.png" align="left" width="55" height="41 src=">.png" align="left" width="55 " height="41 src=">a) b) c) d)
2). Find the meaning of the expression:
https://pandia.ru/text/78/170/images/image134.png" align="left" width="81" height="41 src=">a) b)
20. Find the meaning of the fractions.
https://pandia.ru/text/78/170/images/image136.png" align="left" width="35" height="44 src=">.png" align="left" width="28 " height="44 src=">a) b) c) d)
21. Independent work (test yourself).
Find the meaning:
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1). a B C D)
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4). a B C D)
23. Complete the actions.
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https://pandia.ru/text/78/170/images/image165.png" align="left" width="135" height="83 src=">
hProblems with finding a fraction of a number.
To find a fraction of a number, you need to multiply the number by that fraction.
24. Find the fraction of the number.
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https://pandia.ru/text/78/170/images/image173.png" align="left" width="97" height="45 src=">
https://pandia.ru/text/78/170/images/image175.png" align="left" width="92" height="45 src=">.png" align="left" width="100 " height="45 src=">.png" align="left" width="181" height="45 src=">.png" align="left" width="177" height="45 src=" >
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33. 3/7 of the meadow was mowed. Find the area of the meadow if you mowed 21 hectares.
34. In the first hour the car covered 5/7 of the entire distance. What is the entire distance if the car covered 70 km in the first hour?
35. 2/7 of all machines in the workshop were repaired. How many machines are in the workshop if 28 machines were repaired?
36. 5/6 of the roads have been repaired, which is 30 km. What is the length of the entire road?
37. In the first hour, the car covered 27% of the intended path, after which it had another 146 km to go. How many kilometers is the length of the intended route?
38. We sold 32% of the vegetables, after which there was another 136 tons left to sell. How many tons of vegetables were in the store?
39. I've read 29% of the book, leaving 142 more pages to read. How many pages are in the book?
40. Test No. 1.
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2). Compare
41. The field of 120 hectares was planted with potatoes, cabbage and carrots. 3/4 of this field was planted with potatoes, 80% of the remainder was planted with cabbage, and the rest of the field with carrots. How many hectares were planted with carrots?
42. Test No. 2.
1). Find the meaning of the expression:
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and if A > b , then shows how many times A > b
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b) if A < b , then shows what part is A from b
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https://pandia.ru/text/78/170/images/image204.png" align="left" width="191" height="45 src=">.png" align="left" width="193 " height="45 src=">
43. What relationships show.
https://pandia.ru/text/78/170/images/image208.png" align="left" width="351" height="45 src=">
44. There are 6 white and 12 red roses in the flowerbed. What the relationship shows:
a) 6: 12; b) 12: 6; c) 6: 18; d) 18:12 ?
45. Simplify relationships (i.e., reduce fractions).
https://pandia.ru/text/78/170/images/image210.png" align="left" width="60" height="44 src=">.png" align="left" width="29 " height="41 src=">
a) 4:5; b) c) d) 77: 28; d)
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47. The garden occupies 5.6 a, and the vegetable garden 3.2 a. How many times is the area of the garden larger than the area of the vegetable garden? What part of the entire plot is occupied by the vegetable garden?
48. Serzha walked 5.6 km and traveled 12.6 km by bus. How many times is the distance traveled on foot shorter than the distance traveled by bus? How much of the entire journey did Seryozha travel by bus?
49. There are 25 people in the brigade, 20 of them are men. What percentage of all people in the team are men?
50. out of 32 students in the class, 4 students were absent due to illness. What percentage of students attended?
51. Instead of the planned 75 parts, the worker produced 80 parts. What percentage of the plan has been completed?
52. To determine the germination of seeds, 300 seeds were planted. Of these, 273 germinated. What is the germination percentage of the seeds?
53. Independent work.
a) We bought vegetables for 2.6 rubles and fruits for 9.1 rubles. How many times more did you pay for fruits than for vegetables? What proportion of the total purchase were vegetables?
b) The length of the entire road is 360 km. 240 km were paved. this road. What part of the road is paved? How many times is the entire road longer than its paved part?
c) Out of 250 seeds, 200 germinated. Find the percentage of germination.
§ 4 Pproportions. The main property of proportion.
Abstract
1. Attitude = attitude
https://pandia.ru/text/78/170/images/image216.png" align="left" width="27" height="34 src=">.png" align="left" width="46 " height="3 src="> proportion
a : b = c : d or
https://pandia.ru/text/78/170/images/image219.png" align="left" width="139" height="41 src="> 3.
Test 13-16 "Ratios and proportions".
The proposed tests are designed to test the knowledge and skills of students in a section of the sixth grade mathematics course"Ratio and Proportion" . Using the presented tests, the assimilation of educational material on the following topics is checked: “Ratios”, “Proportions”, “direct and inverse proportional relationships”, “Scale”, “Circumference and area of a circle”, “Ball”. This selection of tests can be used in a class-lesson system for studying the designated section or at home - during independent or distance learning for the purpose of self-control.
The test has a time limit of ten minutes. At the end of this time period, the test finishes its work and offers to go to the results window. For ease of orientation in time, there is a countdown timer at the top right. This test program provides convenient navigation between questions, and it is also possible to make changes to a previously selected or recorded answer. The tests are presented in two equivalent versions, each of which contains seven questions formulated in the form of tasks of varying levels of difficulty. The first four questions are worth one point and require you to choose one correct answer from four options. Problems numbered five and six are of medium difficulty level and are worth two points each. The last, seventh, task corresponds to a high level of difficulty and for the correct solution the test taker receives three points.
After the test is completed, a results window with the scores is displayed. You can also view the details of the assessment, and, if necessary, you can return to the test tasks with subsequent analysis of the correct and selected (recorded) answers.
Let's make a short analysis of the proposed tests.
First And second tests test knowledge and skills on the topic "Relationship". While passing the tasks of the first test, the student must be able to write down the ratio of two numbers, determine what part one number is relative to another (how many times one number is greater than the other), find what percentage one number is of another, and write the inverse ratio for a given ratio. The seventh task is of particular interest. Here in the condition it is given what a given number of percentages of the percentages of a number are equal to and you need to find what this number is equal to.
Tasks second test Although they relate to the same topic as the tasks of the first test, they are no longer based on testing basic theoretical and practical knowledge and skills on this topic, but are aimed at applying relationships to solve problems. The first question contains a graphical drawing that shows two segments. The student should determine the ratio of the lengths of these segments. In the second task, two quantities are given in different units of measurement and you need to find their ratio. Task number three asks you to determine the percentage ratio of two given numbers. And in the fourth, given a given ratio (written as a mixed number), you need to find the inverse ratio. The fifth question contains a task in which you need to determine what percentage of one number is from another. In the problem, which is in the sixth task, you need to find what part one number is relative to another. In the seventh question, the problem statement contains the ratio of two numbers and you need to find the ratio of the larger number to the sum of the two numbers involved in the ratio.
Third test intended for monitoring by topic "Proportions" And “Direct and inverse proportional relationships”. To successfully pass the test, the student will need knowledge of the members of a proportion (which members of the proportion are extreme and which are average), using a given notation of a proportional relationship, find an unknown member of a proportion, and be able to compose proportional relationships (and solve them) to solve problems.
IN fourth test assignments test knowledge and ability to work with proportions, as well as on topics "Circumference and Area of a Circle" And "Scale". In the first two questions, you need to solve the proportion. Next, it is proposed to find the length of a circle of a given radius. Then, using the known radius, you need to calculate the area of the circle. The fifth and sixth tasks are essentially opposite to each other. In the fifth, using a known scale, you should determine what the distance will be on the map (on the ground), if this distance on the ground (on the map) is known. The sixth task, on the contrary, suggests finding the scale of the map using the known corresponding distances on the map and terrain. Answering the seventh question will require logical thinking and attention. You need to determine how many even (multiples of 5) two-digit numbers can be made from four given digits.
Khartsyzsk secondary school No. 25 “Intelligence” with in-depth study of individual subjects
Nakonechnaya Larisa Petrovna
mathematic teacher
Test work
Mathematics, 6th grade
Subject. Relationships and proportions
Textbook: Mathematics. 6th grade: textbook for educational institutions / S.M. Nikolsky, M.K. Potapov, N.I. Reshetnikov, A.V. Shevkin. -M.: Education, 2016.
In accordance with the Basic Curriculum for the 2017-2018 academic year, 4 hours per week are allocated for the study of mathematics in the 6th grade. 12 hours are provided for studying the topic “Relationships and Proportions”.
Planned results of studying this topic:
Students will learn to use the concepts of ratio, scale, and proportion when solving problems. Give examples of using these concepts in practice. Solve problems involving proportional division (including problems from real practice).
Use knowledge about dependencies (direct and inverse proportionality) between quantities (speed, time, distance; work, productivity, time, etc.) when solving word problems: comprehend the text of the problem, extract the necessary information, build a logical chain of reasoning, critically evaluate the answer received, perform simple practical calculations.
Results of mastering the topic content:
Personal
Formation of communicative competence in education and cooperation with peers;
The ability to accurately and competently express one’s thoughts when solving problems, understanding the meaning of the task, the ability to build an argument;
Creative thinking, initiative, resourcefulness, activity in solving arithmetic problems;
Formation of the ability for emotional perception of mathematical objects, problems, solutions, reasoning.
Metasubject
The ability to independently plan alternative ways to achieve goals, consciously choose the most effective ways to solve educational and cognitive problems;
Development of the ability to see a mathematical problem in other disciplines, in the surrounding life;
Understanding the essence of algorithmic instructions and the ability to act in accordance with the proposed algorithm.
Subject
Possession of a basic conceptual apparatus: have an idea of relationships, proportions, direct and inverse proportionality, scale, the formation of ideas about patterns in the real world;
The ability to apply learned concepts to solve problems of direct and inverse proportionality, dividing a number in a given ratio.
The proposed test covers the material of the entire studied topic “Ratios and Proportions” and consists of 12 tasks differing in the level of complexity and form of presentation, the content of which corresponds to the current mathematics program for the 6th grade of general education organizations.
The purpose of the work is to check the level of assimilation by sixth-graders of educational material on this topic with subsequent correction of knowledge and skills.
The first 9 tasks are tasks for choosing one correct answer. For each task there are four possible answers, of which only one is correct. The task is considered completed correctly if the student indicates in the answer table only one letter that indicates the correct answer. There is no need to provide any explanation. For each correct answer, the student receives 1 point. Maximum points - 9
The next 3 tasks (10 - 12) involve establishing correspondence between tasks (1 - 4) and their answers (A - D). For each of the four rows, indicated by numbers, you must select one answer, indicated by a letter. For each correct answer, the student receives 1 point. The maximum number of points scored for 10 - 12 tasks is 12. Total 21 points
Table for converting points to marks
| points | mark |
| 1 - 5 | "1" |
| 6 - 10 | "2" |
| 11 - 15 | "3" |
| 16 - 19 | "4" |
| 20 - 21 | "5" |
45 minutes are allowed to complete the work.
Test work
1. The ratio of 23 and 70 is:
A) B) C) 47; D) 93.
2. Which of the proposed ratios are equal?
A) 4:7 and 8:28; B) 30:5 and 65:13; B) 2:1 and 6:3; D) 3:9 and 13:39.
3. Which of these equalities are proportions?
A) 40: 8 = 4: 2; B) 6:13 = 7:12; B) 7: 2 = 21: 4; D) 36:9 = 16:4;
4. Find the ratio of 40 minutes to 2 hours
A) 1: 3; B) 20: 1; B) 1: 20; D) 3:1.
5.Which quantities are directly proportional?
A) Area of the square and its side;
B) The number of workers and the time during which they will complete the work;
C) The path traveled by the pedestrian and the time he was on the road;
D) The number of pipes filling the pool and the time it takes to fill the pool.
6. Which Russian proverb talks about inversely proportional quantities?
B) The spool is small, but expensive;
C) The higher the stump, the higher the shadow;
D) What is hello, is the answer.
7. What expressions are suitable for calculating the unknown term of the proportionat : 24 = 3: 7
A) 
.
8. Given proportion 13:X = 17: at. Which of the following equations is not a proportion?
A)x:y= 13:17; B) x: 13 = y: 17; IN)y: x= 17:13; G)x:y = 17: 13.
9. What is the ratio??
A) 8; B) ; IN) ; G).
10. Establish a correspondence between the relations (1 - 4) and the quantities (A - D) that these relations are.
1. ; A) number;
2. ; B) price;
3. ; B) concentration;
4. ; D) speed;
11. Establish a correspondence between the given equations (1 - 4) and the roots of each of them (A - D)
1. 7: 8 = X: 96; A) 2;
2. ; B) 6
3. T IN 1 ;
4.
To : 
D) 50;
D) 84.
12. Establish a correspondence between problems (1 - 4) and numbers (A - D), which are the answers to these problems.
| 1. In the book by Elena Molokhovets “A Gift for Young Housewives” there is prune pie recipe. For a pie for 10 people, use a pound of prunes. How many grams of prunes should I use for a pie for 3 people? Consider that 1 pound = 400 g. 2. Three tangerine trees together produced 240 fruits, and the number of fruits on them was in the ratio 1:3:4. How many fruits grew on that tree where the number of fruits was neither the largest nor the smallest? 3. To transport cargo by a machine with a carrying capacity of 6 tons, it is necessary to complete 10 trips. How many trips do you need to make to transport this cargo with a vehicle whose carrying capacity is 2 tons less?4. The distance between two cities on the map is 7 cm. Find the distance in kilometers between cities on the ground if the map scale is 1: 200,000. | A) 90; B) 15; AT 12; D) 120; D) 14. |
ANSWERS to tasks 1 - 9.
ANSWERS to tasks 10 - 12
Task 10
Task 11
Task 12
To correct knowledge, you can use the following table, which indicates the nature of possible errors
| p/p | Character errors | S.M. Nikolsky Mathematics, 5th grade M.: 2016 | S.M. Nikolsky Mathematics, 6th grade M.: 2016 |
||
| theory | practice | theory | practice |
||
| You don't know the definition of attitude. | clause 1.1 | № 4, №5 |
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| You don't know the properties of relationships. | clause 1.1 | №6, №7, №9 |
|||
| You do not know how to find the ratio of homogeneous quantities with different units of measurement. | clause 1.1 | №10, №11 |
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| You don’t know how to find the ratios of quantities of different names. | clause 1.1 | №12 - №16 №18, №19 |
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| Don't know the definition of scale | clause 1.2 | № 21 |
|||
| You do not know how to find the distance on the ground, knowing the scale and distance on the map. | clause 1.2 | №24, №28, №29 |
|||
| You do not know how to divide a number in a given ratio. | clause 1.3 | №36, №37, №39, №40 |
|||
| You don't know the definition of proportion. | clause 1.4 | №46 - №48, №50 |
|||
| You don't know the basic property of proportion. | clause 1.4 | №51, №52 |
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| You don't know how to find the unknown term of a proportion. | clause 1.4 | №53 - №55, №57, №58, №60, №61 |
|||
| 11. | You don't know the definition of directly proportional quantities. | clause 1.5 | №72 - №75 |
||
| 12. | You don't know the definition of inversely proportional quantities. | clause 1.5 | №76, №77, №79 |
||
| 13. | You don't know how to multiply fractions. | clause 4.9 | №892 - №900 | ||
| 14. | You don't know how to divide common fractions. | clause 4.11 | №925, №926, №927 | ||
| Don't know how to find a fraction of a number? | clause 4.12 | №941, №943, №945 | |||
List of used literature
1. Mathematics. 5th grade: textbook for educational institutions / S.M. Nikolsky, M.K. Potapov, N.I. Reshetnikov, A.V. Shevkin. -M.: Education, 2016.
2. Mathematics. 6th grade: textbook for educational institutions / S.M. Nikolsky, M.K. Potapov, N.I. Reshetnikov, A.V. Shevkin
3.Mathematics. Grade 6: Collection of tasks and assignments for thematic assessment / A.G. Merzlyak, V.B. Polonsky, E.M. Rabinovich, M.S. Yakir. - Kharkov “Gymnasium”, 2008
4. Didactic materials in mathematics for grade 5: independent and test work / A.S. Chesnokov, K.I. Neshkov. -M.: Education, 1981.
5. Mathematics 6th grade: independent and test work / A.P. Ershova, V.V. Goloborodko. . - Kharkov “Gymnasium”, 2007
