Basic knowledge of mathematics: understanding and calculation of plane graphics
■ triangle
1. Triangle is a figure surrounded by three line segments. It has stability. Draw a vertical line from a vertex of a triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle. A triangle has three heights.
2. The sum of the internal angles of a triangle is 180 degrees.
3. Triangle can be divided into acute triangle, right triangle and obtuse triangle according to angle.
4. Triangle can be divided into isosceles triangle, equilateral triangle and equilateral triangle according to its sides.
■ quadrilateral
1, quadrilateral is a figure surrounded by four line segments.
2. The sum of the internal angles of any quadrilateral is 360 degrees.
3. Only one set of quadrilaterals with parallel opposite sides is called trapezoid.
4. Two groups of parallelograms with parallel opposite sides are called parallelograms, which are easy to deform. Rectangular and square are special parallelograms. A square is a special rectangle.
■ circle
A circle is a curved figure on a plane. The same circle or the same circle has the same diameter, and the diameter is equal to twice the radius. A circle has countless axes of symmetry. The center of the circle determines the position of the circle, and the radius determines the size of the circle.
■ fan-shaped
A figure enclosed by two radii of a central angle and the arc it subtends. The sector is an axisymmetric figure.
■ Axisymmetric figure
1. If a graph is folded in half along a straight line, the graphs on both sides can completely overlap. This graph is called an axisymmetric graph. This suffocation is called symmetry axis.
2. Line segments, angles, isosceles triangles, rectangles, squares, etc. They are all axisymmetric figures, and the number of their symmetry axes is different.
■ perimeter and area
1, the length of a plane figure is called perimeter.
2. The size of a plane figure or the surface of an object is called the area.
3. Calculation formula of perimeter and area of common graphics
Proportion and proportion of basic knowledge of mathematics
■ ratio and proportional application problems
In industrial production and daily life, it is often necessary to allocate a quantity according to a certain proportion. This distribution method is often called. Proportional distribution? .
■ Problem solving strategy
When doing exercises related to solution ratio distribution, we should be good at finding out the ratio of total and distribution, and then convert the ratio of distribution into components or copies to answer.
■ Strategies to solve the problem of positive-negative ratio application
1, examine the question and find out two related quantities in the question.
2. Analyze and judge whether the two related quantities in the problem are directly proportional or inversely proportional.
3, unknown, column ratio formula
4. Solution ratio style
5. Test and write the answers
Simple equation of basic knowledge of mathematics
■ Use letters to represent numbers.
Representing numbers by letters is the basic feature of algebra, which is simple and clear, and can also express the general law of quantitative relations.
■ Precautions for using letters to represent numbers
1. When a number is multiplied by letters, letters and letters, the multiplication sign can be abbreviated as? Or omit it. Numbers are multiplied by numbers, and the multiplication sign cannot be omitted.
2. When1is multiplied by any letter,? 1? Omit and not write
When a number is multiplied by a letter, write the number before the letter.
■ Formulas containing letters and their evaluation
Pay attention to the writing format when finding the value of a formula containing letters or evaluating it with a formula.
■ Equality and equality
The formula of equality is called equality.
Equations with unknowns are called equations.
There are two conditions to judge whether a formula is an equation: first, it contains unknowns; The second is equality. Therefore, the equation must be an equation, but the equation is not necessarily an equation.
■ Solutions of equations and solutions of equations
The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.
The process of solving an equation is called solving an equation.
■ When solving text problems with column equations,
If the unknown number needed in the problem has been expressed in letters, you don't need to write it when solving it, otherwise the unknown number needed will be set to X first.
■ Method of solving equations
1, directly using the relationship between parts in the four operations to solve. Such as x-8= 12.
Appendix+Appendix = sum, one addend = sum-another addend.
Minus-Minus = Difference, Minus = Minus-Difference, Minus = Difference+Minus.
Multiplier? Multiplier = product, a factor = product? Another factor.
Dividend? Divider = quotient, divisor = dividend? Quotient, dividend = divisor? Business.
2. First consider the term containing the unknown x as a number, and then solve it. Such as 3x+20=4 1. Think of 3x as a number before solving it.
3, according to the order of the four operations, first calculate and deform the equation, and then solve it. Like 2.5? 4-x=4.2, you have to find 2.5 first? 4, the equation is transformed into 10-x=4.2, and then solved.
4. Transform the equation by algorithm or property, and then solve it. For example, 2.2x+7.8x=20. Firstly, the equation is transformed into (2.2+7.8)x=20 by using the algorithm or properties, then the equation is transformed into 10x=20 by calculating the brackets, and finally it is solved.