Learning mathematics does not mean picking a topic at random, nor does it mean that the more topics you do, the better your grades will naturally be. Therefore, learning mathematics must first have a study plan, especially for students with poor foundation, which requires a study plan and a study list. Bian Xiao has compiled relevant information here, hoping to help you.

Statistics of mathematics knowledge points in the first volume of the third grade

1. Solutions of one-dimensional linear equations

Definition: The value of the unknown quantity that makes the left and right sides of the linear equation equal is called the solution of the linear equation.

Substituting the solution of the equation into the original equation, the left and right sides of the equation are equal.

2. Solving quadratic equation with unary collocation method.

(1) Match the unary quadratic equation to the form of (x+m)2=n, and then solve it by direct Kaiping method. This method of solving a quadratic equation with one variable is called collocation method.

(2) The step of solving a quadratic equation with one variable by collocation method:

① Transform the original equation into the form of ax2+bx+c=0(a≠0);

② Divide both sides of the equation by the quadratic term coefficient, so that the quadratic term coefficient is 1, and move the constant term to the right of the equation;

③ Add half the square of the coefficient of the first term on both sides of the equation;

④ The left side is matched into a completely flat mode, and the right side is matched into a constant;

⑤ If the right side is non-negative, the solution can be obtained by direct Kaiping method. If the right side is negative, it is determined that the equation has no real solution.

3. Solve quadratic equation with unary formula method.

(1) Let x = √ b √ b2 √ 4ac/2a (b2 √ 4ac ≥ 0) be called the root formula of the unary quadratic equation ax2+bx+c=0(a≠0).

(2) Solving the quadratic equation with one variable by formula method.

(3) The general steps of solving a quadratic equation with one variable by formula method are as follows:

① Turn the equation into a general form, and then determine the values of A, B and C (pay attention to the symbols);

② Find the value of B2-4ac (if B2-4ac

③ On the premise that B2 ~ 4ac ≥ 0, substitute the values of A, B and C into the formula to calculate the root of the equation.

Note: there are two prerequisites for solving a quadratic equation with one variable by formula method: ① a ≠ 0; ②b2﹣4ac≥0.

4. Solving quadratic equation by unary decomposition method

Significance of (1) factorization method in solving quadratic equation with one variable

Factorization is a method of solving equations by factorization. This method is simple and easy to use, and it is the most commonly used method to solve the quadratic equation of one variable.

Factorization is to change the right side of the equation into 0 first, and then change the left side into the product of two linear factors through factorization, so that the values of these two factors may be 0, and then we can get the solutions of two linear equations, thus simplifying the original equation and transforming the solution of a quadratic equation into the solution of a linear equation (mathematical transformation idea).

(2) The general steps of factorization to solve a quadratic equation with one variable:

① Move the term so that the right side of the equation is zero; ② decompose the left side of the equation into the product of two linear factors; (3) respectively making each factor zero to obtain two unary linear equations; Solving these two linear equations, their solutions are all the solutions of the original equation.

5. Discrimination formula of roots

Judging the roots of a quadratic equation by the discriminant (△ = B2-4ac).

The root of the unary quadratic equation ax2+bx+c=0(a≠0) and △=b2﹣4ac: have the following relationship.

(1) when delta >; 0, the equation has two unequal real roots;

② When △=0, the equation has two equal real roots;

③ When △

The above conclusion is also true in turn.

6. The application of quadratic equation in one variable

1), the general steps to solve practical problems are: examining questions, setting unknowns, solving equations, finding solutions to equations, testing and answering.

2), a quadratic equation to solve common problems in application problems:

(1) number problem: if the single digit is a and the ten digit is b, then these two digits are expressed as10b+a.

(2) Growth rate: growth rate = growth quantity/original quantity × 100%.

For example, if the original number is a and the percentage of each increase is x, it will be a (1+x) after the first increase;

After the second growth, it is a( 1+x)2, that is, the original number ×( 1+ growth percentage) 2= the later number.

(3) Product problems:

① Use Pythagorean theorem to make a quadratic equation of one variable and find the side length of triangle and rectangle.

② Using the area of triangle, rectangle, diamond, trapezoid and circle, and the volume formula of cylinder, a quadratic equation of equality relationship is established.

(3) Using similar triangles's corresponding proportional relation and column proportional formula, the product of two internal terms equals the product of two external terms to obtain a quadratic equation.

(4) Motion point problem: the object will move along a route or form a trajectory, and the running route and other conditions will form a right triangle, which can be solved by using the property equation of the right triangle.