# Grade 10 mathematics: System and synthesis of basic knowledge – Exercise

## i, the algebraic part of math formulas grade 10

** 1. inequality formula: **

** + Property 1 (connecting property): **a > b and b > ca > c

** + attribute 2: **sebuah & gt; b a + c & gt; b + c

that is: if we add both sides of the equation by the same number, we get an inequality that has the same direction and is equivalent to the given inequality.

Consequence (Transition rule): a > b + ca – c > b

** + attribute 3: **

** + attribute 4: **

sebuah & gt; bc & gt; b.c if c & gt; 0

or > b & aacute; c c & spin; ng l & agrave; b.c if c & lt; 0

** + attribute 5: **

If we multiply the sides of each of the two inequalities in the same direction, we get the inequality in the same direction. Note: There is no rule for dividing both sides of two inequalities in the same direction.

** + attribute 6: **

to > b> 0 to > bn (n nguyen yang)

** + attribute 7: **

(n is a positive integer)

** + Cauchy inequality (co-si): **

If andThen . The sign = occurs if and only if: a = b

that is: the average of two non-negative numbers is greater than or equal to the average of their multiplication.

Consequence 1: If two positive numbers have a constant sum, the product of slack is greater when the two numbers are equal.

geometrical significance: of all the rectangles with the same perimeter, the square has the largest area.

Consequence 2: If two positive numbers have a constant product, the sum of the numbers is less than when the two numbers are equal.

geometric sense: of all the rectangles with the same area, the square has the smallest perimeter.

** + inequality in absolute value: **

From the definition concludes: for everyWe have:

A. | x | 0

B. | x | 2 = x2

C. X|x| and -x |x|

theorem: for all real numbers a and b, we have:

|a + b||a| + |b| (1)

|a – b||a| + |b| (2)

|a + b| = |a| + |b| if and only if a.b0

| a-b | = | a | + | b| if and only if a.b 0

** 2. Quadratic equation formula: **** A. quadratic equation: **

: The equation has no solution. : Equation with multiple solutions:

: The equation has 2 different solutions:

;

** B. Reduced solution of the quadratic equation: **

If “b is even” (eg) we use the reduced solution formula.

: The equation has no solution.: Equation with multiple solutions:: The equation has two different solutions:

;

Attention: withare two solutions of the quadratic equation:

** C. Viet’s theorem: **

If the quadratic equationThen there are 2 solutions:

D. special cases of quadratic equations:

– If then the equation has a solution:– If then the equation has a solution:

** P. sign of solution: **

– The equation has 2 solutions** opposite sign: **

– The equation has 2 solutions** positive discrimination: **

– The equation has 2 solutions** distinguishing sound **

** 3. polynomial sign formula: **

A. First degree binomial sign:

See More: ✅ Inequality formula ⭐️⭐️⭐️⭐️⭐

the reciprocal of 0 and a

“right, left left”

B. quadratic trigonometry sign:

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Watch now: The formula for calculating the amplitude of a simple pendulum and practice with the solution

& lt; 0: f(x) has the same sign as the coefficient a

= 0: f(x) has the same sign as the coefficient a for all

= 0: f(x) has 2 solutions x1, x2

x1 x2

f (x)

sign equal to 0 opposite sign to 0 equal sign to

C. polynomial degree ≥ 3: starting from the right cell with the same sign as the coefficient a of the largest exponent, through the simple solution of the sign change, through the constant double root.

** 4. The trinomial conditional formula does not change the sign of r **** . **

for quadratic trigonometry:

** 5. Grade 10 math formulas about equations, inequalities contain absolute value **

** A. equation: **

Watch now: Industrial Revolution 4.0: opportunities, challenges and solutions for Vietnam’s Culture and Arts industry

Watch now: The formula for calculating the amplitude of a simple pendulum and practice with the solution

Watch now: Industrial Revolution 4.0: opportunities, challenges and solutions for Vietnam’s Culture and Arts industry

Watch now: The formula for calculating the amplitude of a simple pendulum and practice with the solution

** B. Dissimilarity: **

** 6. Grade 10 math formulas about equations, inequalities hidden under the square root **

** A. equation: **

** B. Dissimilarity: **

** 7. class 10. trigonometry formulas **

** A. definition of trigonometry values: **

** **

** B. Basic trigonometry formulas: **

** C. special trigonometry values: **

** D. sum formula: **

** e. double formula: **

** F. declining formula: **

** G. formula three: **

** H. the formula for converting the product into a sum: **

** I. The formula for converting the total performance: **

** k. Supply Link: **Sin – compensation; cos – for; sub-cross; less than– tan, couch.

– Two complementary signs: and

– Two opposite signs:And

– Two sub-signs: and

– Two more and less signs: And

– Two more and less signs: And

** l. Calculation formulateo: **

If setThen:

** M. Some other formulas: **

## ii. Grade 10 math formulas in the geometry section

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** **

give, symbol

– a, b, c: length of 3 sides – r: radius of circumference

Cosine theorem:

sine theorem:

The formula for calculating the median length:

regular triangle:

(: length 3 lines high)

(r: the radius of the inscribed circle,: half circle)

(hero formula)

Right triangle:** x multiply 2 sides of a right angle **

isosceles triangle with side a:

Square side a:

rectangle:

Parallelogram:or

Cut a rhombus:or or

** x multiplication of 2 diagonals **

Connected loop:

** **

** A. application of dot multiplication of two vectors **

returns three dots:. we have:

– Coordinate vector

The coordinates of the midpoint of I AB are: .

– The coordinates of the center of gravity G are:.

For vectors and points:

** B. the equation of the line: **

Givingis the VTCP of d., is the VTPT of d .

Point M(Belongs to d.

– PT parameter d: =

– PT canonis d:

– General PT d: or:

** C.distance: **

+ distance from point m (x0, y0) to line (d): ax + by + c = 0

+ distance between two parallel lines: ax + by + c1 = 0 and ax + by + c2 = 0

** D. relative position of 2 lines: **

(d1): a1 x + b1 y + c1 = 0, (d2): a2 x + b2 y + c2 = 0

** e. angle between two lines: **

(d1) : A1 x + B1 y + C1 = 0, (d2) : A2 x + B2 y + C2 = 0,

** D. Line equation of the angle formed by two lines (d1) and (d2): **

(sharp angles are marked with – , obtuse angles are marked with + )

** e. circle equation: **

a circle with center i (a; b) and radius r has the equation:

form 1:

Form 2:

, condition :

Here is the summary** Grade 10 Math Formulas **synthesize the knowledge learned in the Mathematics 10 program. Formulas are specially developed for each chapter and each lesson. very suitable for students to easily memorize it. With this set of concise formulas, we hope to help them study effectively, pass their upcoming exams successfully, and serve as a companion throughout their high school years.

Source: https://truongxaydunghcm.edu.vn

Category: Recipes

## How to learn good 10th grade math effectively

High school to high school math programs are a big leap for students. Because they have just experienced a complete change in environment, teaching methods, friends, etc. Especially the fierce and competitive class 10 entrance exam. Often, when starting a new curriculum at a new level, students often have the mentality of getting used to and wanting to play with the new environment. However, time did not allow them to do that. If you don’t adapt quickly and make efforts from day one, student learning outcomes will be affected. A few notes on how to learn 10th grade math will help parents and students take certain steps from day one of high school.

1. For Parents

Starting from 10th grade Math problems, it creates a lot of difficulties for kids with new concepts and symbols. However, this is fundamental knowledge that children should not take lightly and easily learn through speakers.

Parents need to pay attention, care, ask questions and follow the learning process of their children. Checking the school situation on a regular basis helps parents accurately assess their child’s learning abilities, so that they always know what knowledge their child’s weaknesses are and are more nurturing.

Ask your child to research new material at home before coming to class. This will help your child quickly understand the teacher’s lecture in class.

If there is time, parents must actively learn and solve math problems with their children. This helps your child forget the feeling of dealing with numbers and formulas alone.

If you want your child to be a good student and solve 10th grade math problems and get 9th and 10th grades on the final exam, he/she needs to master not only 10th grade math textbook knowledge, but also advanced knowledge. The goal is towards good students, students only need to master core knowledge.

Therefore, depending on each specific goal, parents set their resolve to revisit their children. At the same time, set a clear learning path for them.

2. For students

In order to solve math problem 10 correctly, students need to prepare well in the lower grades. If knowledge is empty, students need to add it immediately. Because if you study mathematics in a state of root loss it is really difficult and you don’t understand the main problem.

Limit the use of sample books to solve Math 10. Referring to many sample booklets of problem solving will make the brain unable to train its ability to think mathematically and become more dependent on how to solve them.

Students can become familiar with how to use a calculator to help with problem solving. However, it should not be overused.

When listening to lectures in class, if there are parts of science that you don’t understand or are unclear, you need to actively ask the teacher directly. Always make sure to remember, understand and master the basics from the start.

Dynamically solve problems in various ways and methods. However, not at all lethal. It is recommended to complete each step carefully to master the solution process.

Apart from focusing on studying knowledge, students also need to invest time in sports activities. Not making sure of health and review in a tired state will not lead to anything. Sometimes, it will bring negative results.

Students can improve their knowledge and problem solving abilities through refresher courses. Toppy’s Class 10 Mathematics tutor course helps students easily master key knowledge.

3. Learn 10th grade math online

Online learning programs are an easy method to help increase children’s enthusiasm and learning abilities effectively, which many parents apply.

Online learning programs bring lots of great benefits and features. Viewing and learning on new platforms and teaching methods that are engaging and engaging for all ages will keep students interested and engaged in the lesson. At the same time, parents can easily be by his side to closely monitor and understand their children’s learning process.

During a complicated epidemic period, online learning helped children limit their exposure to pathogens. In particular, the prices for online learning programs are much more reasonable than hiring a home tutor.

Enroll your child to learn 10th grade math online at Toppy (100% free)

## English lessons

- English 10 – Global Success
- English 10 – Global Friends
- English 10 – Smart World iLearn
- English 10 – Discovery of English
- English 10 – Sunny
- English 10 – Explore the New World
- SBT English 10 – Global Success (Connecting knowledge)
- SBT English 10 – Global Friends (Creative Horizon)
- SBT English 10 – Smart World iLearn
- SBT English 10 – Sunny
- SBT English 10 – Discovery of English
- English Quiz 10 – Global Success
- English 10 multiple choice exercises – Global Success
- English Quiz 10 – Global Friends
- English 10 multiple choice exercises – Friends Global
- English Quiz 10 – iLearn Smart World
- English 10 multiple choice exercises – iLearn Smart World
- Grade 10 English questions and tests – Global Success
- Class 10 English questions and tests – Friends Global
- Class 10 English exam questions and exam questions – iLearn Smart World
- Grade 10 English exam questions and exam questions – Sunny
- Grade 10 English exam questions and test questions – English Discovery
- Theory of English 10

## Biology

- Class 10 Textbook – Linking knowledge
- 10th Birth Textbook – Creative horizon
- Class 10 Textbook – Kites
- SBT class 10 – Linking knowledge
- SBT grade 10 students – Creative horizon
- SBT class 10 – Kites
- Class 10 student learning topic – Connection of knowledge
- Class 10 learning topics – Creative horizon
- Birth Quiz 10 – Connecting knowledge
- Birth Quiz Practice 10 – Linking knowledge
- Birth Quiz 10 – Creative horizon
- Birth of 10 multiple choice exercises – Creative horizons
- Birth Quiz 10 – Kites
- Birth Quiz Practice 10 – Kites
- Exam questions, exam questions for grade 10 students – Connecting knowledge
- test questions and test questions for grade 10 students
- Exam questions, test questions for grade 10 are born – Creative horizon
- Exam questions, exam questions 10th grade students – Kites
- Theory of Birth 10

## literature

- Write 10 essays – Connection of knowledge – very short
- Write 10 essays – Linking knowledge – details
- Composition 10 – Creative horizon – super short
- Writing 10 – Creative horizon – details
- Composer 10 – Kites – super short
- Komposer 10 – The Kite – detail
- Class 10 assignment writer
- Example document 10 – Linking knowledge
- Literary Examples 10 – Creative horizon
- Literary Example 10 – Kites
- SBT Van 10 – Linking knowledge
- SBT Van 10 – Creative horizon
- SBT Van 10 – Kite
- Literature 10 learning topics – Knowledge connections
- Literature learning topic 10 – Creative horizons
- Literature study topic 10 – Kites
- Literature Quiz 10 – Knowledge connection
- Literature Quiz 10 – Kites
- Literature Quiz 10 – Creative horizons
- Literature 10 questions and exam test – Knowledge connection
- Literature 10 exam questions and exam questions – Kites
- Literature 10 exam questions and tests – Creative horizons
- Literary Theory 10
- Literature 10 multiple choice exercises – Linking knowledge
- Literature 10 – Kite multiple choice exercise
- Literature 10 multiple choice exercises – Creative horizons

## Some reference books for Algebraic Mathematics 10

Algebraic Thematic Mathematical Solution Method 10** This book consists of six chapters: **

Chapter 1. Propositions and sets.

Chapter 2: First functions and squaring.

Chapter 3: Equations and systems of equations.

Chapter 4: Unconsciousness, inequality.

Chapter 5. Statistics.

Chapter 6: Trigonometry angles and arcs, trigonometry formulas.

From the knowledge content that is built will help students master the knowledge to properly practice basic skills (such as solving equations, solving systems of equations and solving inequalities). At the same time, the two most difficult questions in the national exam are also included in this section, so starting in grade 10, we need to practice math problems to be able to solve the questions that classify candidates in the exam questions. high school national exam Carefully study the examples and apply them to complete each exercise. Then review the solutions, to adapt your own thinking. It is important to know how to infer for yourself how to solve and how to present the solution in each mathematical form.

The current integration process demands high self-learning from each individual. In my opinion, besides the guidance of teachers and teachers in class, this book will be a good companion for students in facing upcoming exams.

Geometry Thematic Mathematical Solution Method 10

By presenting a method of solving grade 10 geometry problems, students will be more confident in solving grade 10 geometry problems.** This book consists of 3 chapters: **

Chapter 1: Vectors

Chapter 2: The dot product of two vectors

Students need to pay special attention to chapters 2 and 3 which need to be mastered to practice good basic skills (such as solving triangles, calculating line lengths). Questions that are difficult to classify in the national exam are also in chapter 3, so starting in grade 10 we need to practice math questions to be able to solve questions that classify candidates in the exam questions for the high school national exam. .

With 9 topics and exam questions spread across 38 main knowledge topics. This book will provide a wide range of math for eliminating knowledge in grade 10.

Every grade 10 student must have a Class 10 BREAKOUT 9+ book with:

This book is a complete system of key knowledge by subject, covering every corner of knowledge from theory to practice, from basic to advanced.

Each knowledge unit comes with all kinds of articles.

Focus on solving methods of each type of problem: Solution direction, identification characteristics, quick solution formula…

The whole series of books has 4 subjects Mathematics, Physics, Chemistry and English to help students consolidate their knowledge and improve their application skills, mastering methods to help students achieve high grades in class.

Just like Breaking Math 2 (grade 11), Breaking Math 3 (grade 12), this Breaking Math 1 book will also help you solve the following problems:

Firstly, this book helps them to systematize all the methods and ideas to solve the mathematics required in the grade 10 program. In addition, we pay great attention to the ranking of grade 10 knowledge with other classes at the junior secondary level, related to the high school curriculum. We are also actively proposing a rich and varied practice system with many new types of grade 10 multiple choice mathematics.

Second, this book helps students master the skills needed to use a hand-held calculator to solve 10th grade math. However, the skills introduced are related to mathematical problem-solving thinking, not just simple math, but just normal shooting operations.

** Tuesday **, this book has integrated a document delivery system via e-mail, so that students have the opportunity to practice and apply the knowledge gained while reading. In addition to emailing questions and detailed answers to self-practice questions in chronological order, we also send out some great documents regarding book content as they are collected to students once again. It’s also a way to ensure children’s and readers’ rights to use authentic books.

Stick to the curriculum content of the current textbook. This book collects types of questions, general questions in exams and semester exams. The content is classified and arranged from easy to difficult, appropriate for each lesson so that students can immediately apply the knowledge they have learned for 15-minute, 45-minute tests and take semester exams. Good problems, quick solutions, how to use Casio calculators are integrated into the system of problems selected by the author. Thus, helping students gain a deeper understanding of the nature of mathematics, training their thinking and skills to take tests quickly and effectively, helping students master easily and most effectively, thus improvising with Assorted Mathematics multiple choice questions.

It can be said that this book is the heart of writer Nguyen Phu Khanh and other writers and will definitely become a reliable source document to help students practice and confidently master all tests and examinations. . When using books, you should first try to find the solution yourself; When the solution is complete or no solution is found, then read the solution to understand how to do it.

Summary of multiple choice exercises with answers for grade 10 students. The book is divided into 2 parts Algebra and Geometry according to different topics and subject types. The book covers the following:

** Algebra: **

Chapter 1: Propositions – sets

Chapter 2: First Functions and Quadratic Functions

Chapter 3: Equations and systems of equations

Chapter 4: Inequality and inequality

Chapter 5: Statistics

Chapter 6: Trigonometry Angles – Trigonometry Formulas

** Geometry: **

Chapter 1: Vectors

Chapter 2: Scalar Products of Two Vectors and Their Applications

Chapter 3: In-plane coordinate methods

Thus, students can safely absorb new knowledge and easily review and systematize old knowledge.

** **

With concise content, the author tries to compile and select specific problems for each different genre according to the contents of the textbook. Some exercises may be difficult, but the solutions are based on basic knowledge and skills. Students need to improve their skills and develop their thinking by completing practice questions in the book before comparing them with the solutions in this book, maybe some of the solutions in the book are still condensed. and discover new ways of reasoning.

The book covers the following:

Bab I: Vektor

Chapter II: Scalar Product of 2 Vectors and Its Applications

Chapter III: Coordinating methods within the field

** Hopefully the key knowledge, the 10th math formula and the 10th math reference book above will be a valuable resource for students. We wish you success on your path to conquering the heights of knowledge. **

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## Chemistry

- Chemistry Textbook 10 – Linking knowledge
- Chemistry Textbook 10 – Creative horizons
- Chemistry Textbook 10 – Kites
- SBT Chemistry 10 – Linking knowledge
- Chemistry SBT 10 – Creative horizons
- Chemistry SBT 10 – Kites
- Chemistry 10 learning topics – Linking knowledge
- Chemistry 10 learning topics – Creative horizons
- Chemistry learning topic 10 – Kites
- Chemistry Quiz 10 – Linking knowledge
- Chemistry 10 multiple choice exercises – Connecting knowledge
- Chemistry 10 Quiz – Creative Horizons
- Chemistry 10 multiple choice exercises – Creative horizon
- Class 10 Chemistry exam questions and test questions
- Chemistry Quiz 10 – Kites
- Chemistry 10 – Kite multiple choice exercise
- Class 10 Chemistry exam questions and tests – Connection of knowledge
- Grade 10 Chemistry exam questions and test questions – True creativity
- Class 10 chemistry questions and tests – Kites

## Some reference books for Algebraic Mathematics 10

From the knowledge content that is built will help students master the knowledge to properly practice basic skills (such as solving equations, solving systems of equations and solving inequalities). At the same time, the two most difficult questions in the national exam are also included in this section, so starting in grade 10, we need to practice math problems to be able to solve the questions that classify candidates in the exam questions. high school national exam Carefully study the examples and apply them to complete each exercise. Then review the solutions, to adapt your own thinking. It is important to know how to infer for yourself how to solve and how to present the solution in each mathematical form.

The current integration process demands high self-learning from each individual. In my opinion, besides the guidance of teachers and teachers in class, this book will be a good companion for students in facing upcoming exams.

By presenting a method of solving grade 10 geometry problems, students will be more confident in solving grade 10 geometry problems.** This book consists of 3 chapters: **

Chapter 1: Vectors

Chapter 2: The dot product of two vectors

Students need to pay special attention to chapters 2 and 3 which need to be mastered to practice good basic skills (such as solving triangles, calculating line lengths). Questions that are difficult to classify in the national exam are also in chapter 3, so starting in grade 10 we need to practice math questions to be able to solve questions that classify candidates in the exam questions for the high school national exam. .

With 9 topics and exam questions spread across 38 main knowledge topics. This book will provide a wide range of math for eliminating knowledge in grade 10.

Every grade 10 student must have a Class 10 BREAKOUT 9+ book with:

This book is a complete system of key knowledge by subject, covering every corner of knowledge from theory to practice, from basic to advanced.

Each knowledge unit comes with all kinds of articles.

Focus on solving methods of each type of problem: Solution direction, identification characteristics, quick solution formula…

The whole series of books has 4 subjects Mathematics, Physics, Chemistry and English to help students consolidate their knowledge and improve their application skills, mastering methods to help students achieve high grades in class.

Just like Breaking Math 2 (grade 11), Breaking Math 3 (grade 12), this Breaking Math 1 book will also help you solve the following problems:

Firstly, this book helps them to systematize all the methods and ideas to solve the mathematics required in the grade 10 program. In addition, we pay great attention to the ranking of grade 10 knowledge with other classes at the junior secondary level, related to the high school curriculum. We are also actively proposing a rich and varied practice system with many new types of grade 10 multiple choice mathematics.

Second, this book helps students master the skills needed to use a hand-held calculator to solve 10th grade math. However, the skills introduced are related to mathematical problem-solving thinking, not just simple math, but just normal shooting operations.

** Tuesday **, this book has integrated a document delivery system via e-mail, so that students have the opportunity to practice and apply the knowledge gained while reading. In addition to emailing questions and detailed answers to self-practice questions in chronological order, we also send out some great documents regarding book content as they are collected to students once again. It’s also a way to ensure children’s and readers’ rights to use authentic books.

Stick to the curriculum content of the current textbook. This book collects types of questions, general questions in exams and semester exams. The content is classified and arranged from easy to difficult, appropriate for each lesson so that students can immediately apply the knowledge they have learned for 15-minute, 45-minute tests and take semester exams. Good problems, quick solutions, how to use Casio calculators are integrated into the system of problems selected by the author. Thus, helping students gain a deeper understanding of the nature of mathematics, training their thinking and skills to take tests quickly and effectively, helping students master easily and most effectively, thus improvising with Assorted Mathematics multiple choice questions.

It can be said that this book is the heart of writer Nguyen Phu Khanh and other writers and will definitely become a reliable source document to help students practice and confidently master all tests and examinations. . When using books, you should first try to find the solution yourself; When the solution is complete or no solution is found, then read the solution to understand how to do it.

Summary of multiple choice exercises with answers for grade 10 students. The book is divided into 2 parts Algebra and Geometry according to different topics and subject types. The book covers the following:

** Algebra: **

Chapter 1: Propositions – sets

Chapter 2: First Functions and Quadratic Functions

Chapter 3: Equations and systems of equations

Chapter 4: Inequality and inequality

Chapter 5: Statistics

Chapter 6: Trigonometry Angles – Trigonometry Formulas

** Geometry: **

Chapter 1: Vectors

Chapter 2: Scalar Products of Two Vectors and Their Applications

Thus, students can safely absorb new knowledge and easily review and systematize old knowledge.

** **

Bab I: Vektor

Chapter II: Scalar Product of 2 Vectors and Its Applications

Chapter III: Coordinating methods within the field

** Hopefully the key knowledge, the 10th math formula and the 10th math reference book above will be a valuable resource for students. We wish you success on your path to conquering the heights of knowledge. **

** **

## A comprehensive solution to help your child reach 9-10 in Maths easily with Toppy

*With a student-centered goal, Toppy focuses on building personalized learning paths for students, helping students master the basics and access advanced knowledge thanks to reminder systems, lesson libraries, and more. from 9 to 10.*

** Huge repository of materials **

*Video lectures, illustrated content clearly, easy to understand, involve students in independent learning activities. Practice library, rich exam questions, hierarchical level self-practice exercises Self-practice – self-correction helps increase efficiency and shorten study time. Combine a virtual exam room (Mock Test) with a real tutor to get ready and take the anxiety out of the IELTS test.*

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** Reference source: **

- Summary of Important Grade 10 Math Formulas, https://truongxaydunghcm.edu.vn/file-cong-thuc-toan-10/
- Grade 10 math: Basic knowledge systems & synthesis – Practice, https://toppy.vn/blog/toan-lop-10/
- 10th grade math, 10th grade math solutions connecting knowledge with life, https://loigiaihay.com/sgk-toan-10-ket-noi-tri-thuc-c811.html
- Math formula for class 10 semester 1, https://bloghong.com/cac-cong-thuc-toan-lop-10-hoc-ki-1-1659723918
- Synthesis of All Knowledge of Algebra 10 per Chapter, https://newshop.vn/tin-tuc/tong-hop-toan-bo-kien-thuc-toan-dai-so-10-theo-tung-ring-id821.html

Any reproduction of quotations must be approved in writing or by acknowledging the source**trungcapluatbmt.edu.vn**