What are exercises on first-degree equations in one variable for grade 8 students in Vietnam? How many periods does the grade 8 Mathematics subject in Vietnam have?

What are exercises on first-degree equations in one variable for grade 8 students in Vietnam?

A first-degree equation in one variable is a linear equation of the form ax + b = 0, where a and b are constants, and x is the variable. Here, a is not equal to 0. This is a simple and important equation in basic mathematics.

The steps to solve a first-degree equation in one variable are as follows:

Step 1: Identify the equation: A first-degree equation in one variable is of the form ax + b = 0, where a and b are constants, and x is the variable.

Step 2: Transfer the constant term: Move the term b to the right-hand side of the equation by subtracting b from both sides. The equation becomes ax = -b.

Step 3: Divide both sides by the coefficient a: To find the value of x, divide both sides of the equation by a. The equation becomes x = -b/a.

For example, with the equation 3x + 6 = 0:

Step 1: Rewrite the equation: 3x + 6 = 0

Step 2: Move 6 to the right side: 3x = -6

Step 3: Divide both sides by 3: x = -6/3

Result: x = -2

EXERCISES ON FIRST-DEGREE EQUATIONS IN ONE VARIABLE

Exercise 1. Among the following pairs of equations, which pair is equivalent?

a) 3x - 5 = 0 and (3x - 5)(x + 2) = 0

b) x^2 + 1 = 0 and 3(x + 1) = 3x - 9

c) 2x - 3 = 0 and + 1 =

Exercise 2. Determine whether the following equations are equivalent or not?

a) x - 2 = 0 and (x - 2)(x + 3) = 0

b) 2x - 6 = 0 and x(x - 3) = 0

c) x + 5 = 0 and (x + 5)(x^2 + 1) = 0

d) x + 2 = 0 and = 0

Exercise 3. Solve the equation

a) 13 - 6x = 5

b) 10 + 4x = 2x - 3

c) 7 - (2x + 4) = - (x + 4)

d) (x - 1) - (2x - 1) = 9 - x

Exercise 4. Solve and discuss the equation containing the parameter m.

(m^2 - 9)x – m^2 – 3m = 0.

Exercise 5. Solve and discuss the equation with the parameter m.

a) m(x – 1) = 5 – (m – 1)x. b) m(x + m) = x + 1.

c) m(m – 1)x = 2m + 1. d) m(mx – 1) = x + 1.

Exercise 6. Solve the equation

a) 3x - 15 = 2x(x - 5)

b) (x^2 - 2x + 1) - 4 = 0

HINTS FOR ANSWERS

Exercise 1.

a) The two equations are not equivalent because the solution set of the first equation is S =, and the solution set of the second equation is S =

b) Because the solution set of the first equation is S =, and the solution set of the second equation is S =. Therefore, these two equations are equivalent.

c) These two equations are equivalent because they have the same solution set S =

Exercise 2.

a) The two equations are not equivalent because S1 = {2}; S2 = {2; -3}

b) The two equations are not equivalent because S1 = {3}; S2 = {0; 3}

c) The two equations are equivalent because they have the same solution set S = {-5}

d) The two equations are not equivalent because S1 = {-2}; S2 = {0}

Exercise 3.

a) 13 - 6x = 5 => -6x = 5 - 13 => -6x = -8 => x =

Thus, the solution set of the equation is

b) 10 + 4x = 2x - 3 => 4x - 2x = -3 - 10 => 2x = -13 => x =

Thus, the solution set of the equation S = {}

c) 7 - (2x + 4) = - (x + 4) => 7 - 2x - 4 = -x - 4 => -2x + x = -7

=> -x = -7 => x = 7

Thus, the solution set of the equation S = {7}

d) (x - 1) - (2x - 1) = 9 - x => x - 1 - 2x + 1 = 9 - x => -x + x = 9

=> 0x = 9 (illogical)

Thus, the equation has no solution

Exercise 4.

- If m^2 – 9 ≠ 0, that is, m ≠ 3, the given equation is a first-degree equation (in the variable x) with a unique solution:

- If m = 3, the equation takes the form 0x – 18 = 0, which has no solution.

- If m = -3, the equation takes the form 0x + 0 = 0, all real numbers x ∈ R are solutions of the equation.

Exercise 5.

a) m(x – 1) = 5 – (m – 1)x

=> mx - m = 5 - (m - 1)x => (2m - 1)x = m + 5

- If 2m - 1 ≠ 0, meaning m ≠ then the given equation is a first-degree equation with a unique solution x =

- If m = then the equation takes the form: 0x = => this equation has no solution

b) m(x + m) = x + 1 => mx + m^2 = x + 1 => (m - 1)x = 1 - m^2

- If m - 1 ≠ 0 or m ≠ 1, then the equation is a first-degree equation in one variable having a unique solution x = = = - m - 1

- If m = 1, then the equation takes the form 0x = 0 => this equation has infinitely many solutions.

c) m(m – 1)x = 2m + 1

- If m = 0, then the equation takes the form: 0x = 1 => this equation has no solution

- If m = 1, then the equation takes the form 0x = 3 => this equation has no solution

- If m ≠ 0 and m ≠ 1, then the equation is a first-degree equation in x with a unique solution x =

d) m(mx – 1) = x + 1 => m^2x - m = x + 1 => (m^2 - 1)x = m + 1

- If m^2 - 1 ≠ 0, that is, m ≠ ±1, the given equation is a first-degree equation in x with a unique solution: x = =

- If m = 1, the given equation takes the form: 0x = 2 => the equation has no solution

- If m = -1, the given equation takes the form: 0x = 0 => the equation has infinitely many solutions.

Exercise 6.

a) 3x - 15 = 2x(x - 5)

=> 3(x - 5) - 2x(x - 5) = 0 => (x - 5)(3 - 2x) = 0 => =>

Thus, S = {5; }

b) (x^2 - 2x + 1) - 4 = 0 => (x -1)^2 - 2^2 = 0 => (x - 1 - 2)(x - 1 + 2) = 0

=> (x - 3)(x + 1) = 0 => =>

Thus, S = {3; -1}

Note: The content is for reference only

What are exercises on first-degree equations in one variable for grade 8 students in Vietnam? How many periods does the grade 8 Mathematics subject in Vietnam have?​ (Image from the Internet)

What are practice and experience activities for grade 8 Math in Vietnam?

Based on the general education program for Math subject issued together with Circular 32/2018/TT-BGDDT, the practice and experience activities in grade 8 Math include:

Activity 1: Learn some financial knowledge such as:

- Planning personal spending.

- Familiarizing with personal investment problems (determining the investment capital to achieve the desired interest rate).

- Understanding bank statements (real statements or examples) to identify transactions and track income and expenses; choosing the appropriate payment method.

Activity 2: Apply mathematical knowledge to practice and interdisciplinary topics, for instance:

- Applying Algebra knowledge to explain some rules in Chemistry, Biology. For example: Applying first-degree equations in problems about determining percentage concentration.

Activity 3: Organize extracurricular activities such as practice outside the classroom, study projects, math games, mathematics competitions, for instance:

- Searching for or practicing creating videos about the application of pyramids, similar shapes perspective in the natural world.

- Applying knowledge about similar triangles and the Pythagorean theorem in practice (e.g., measuring the distance between two positions with an obstacle or where only one of the two positions can be reached).

- Practicing calculating the area, volume of some shapes and solids in reality.

Activity 4 (if conditions at the school allow): Organize interactions with students who have skills and interests in Mathematics within the school or with other schools.

How many periods does the grade 8 Mathematics subject in Vietnam have?​

According to the general education program for Math subject issued together with Circular 32/2018/TT-BGDDT, the number of periods for each grade level is as follows:

At the upper secondary level, each grade has an additional 35 periods/year for elective study topics.

Therefore, Grade 8 Math has a total of 140 periods per academic year.