八下 数学（Under the eight math）.doc

八下 数学（Under the eight math） A summary of the mathematical theorem of junior high school Eighth grade (book) The first chapter is one dollar inequality and one dollar inequality group One. Inequality 1. Generally, the expression (or greater than) is called an inequality, with the symbol (or less than or equal). To distinguish equations and inequalities: equations represent equal relationships; Inequality represents a relationship that is not equal. 3. Accurately translate inequality, correctly understand non-negative, no less than and other mathematical terms. The non-negative value is greater than or equal to 0 and a positive number The non-positive number is equal to 0, which is less than or equal to 0 (or less than 0) The basic property of inequality 1. Grasp the basic nature of the inequality and apply it flexibly: (1) add (or subtract) the same integral to both sides of the inequality, and the inequality is the same. If a b, then a plus c b plus c, a minus c , b minus c. (2) both sides of the inequality are multiplied by (or divided by) the same positive number, and the inequality is the same If a b, and c 0, then ac BC. (3) both sides of the inequality are multiplied by (or divided by) the same negative, the direction of inequality is changed, namely: If a BBB 0, b, and c 0, then ac BC, 2. Comparison size: (a and b respectively represent two real or integral) In general: If a b, then a minus b is positive; If a minus b is positive, then a, b; If a is equal to b, then a minus b is equal to 0; If a minus b is equal to 0, then a is equal to b; If a is less than b, then a minus b is negative; If a minus b is positive, then a is less than b; That is: = = = a b a - b 0 A = b = = = a - b = 0 A b = = = a - b 0 (thus, to compare the size of two real Numbers, just look at the difference between them. Iii. Solution set of inequalities: 1. The value of the unknown quantity which can make the inequality, is called the solution of the inequality; All th