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江苏省南京市白下区2011届高三二模模拟考试(英语).pdf

江苏省南京市白下区2011届高三二模模拟考试(英语).pdf

* * * * * 5.1 认识不等式 下列问题中的数量关系能否用等式表示,若能请用等式表示,若不能,应该用怎样的式子来表示? (1)天平左盘放3个乒乓球,右盘放3g砝码,天平平衡,设每个乒乓球的质量为x(g),怎样表示x与3之间的关系?

(2) 天平左盘放4个乒乓球,右盘放3g砝码,天平倾斜(左低右高),设每个乒乓球的质量为x(g),怎样表示x与3之间的关系?

(3)天平左盘放1个乒乓球,右盘放3g砝码,天平倾斜(左高右低),设每个乒乓球的质量为x(g),怎样表示x与3之间的关系?

(4)天平左盘放1支铅笔,(如果铅笔质量不超过3克)右盘放3g砝码,天平会怎样,设每支铅笔的质量为V(g),怎样表示V与

3之间的关系? (5)如果铅笔质量不低于3克,天平又会怎样?怎样表示V与3之间的关系? (6)如果铅笔质量不等于3克,怎样表示V与3之间的关系? 用符号“”(或“≥”),“≠ ”连接而成的数学式子,叫做不等式。 这些用来连接的符号统称不等号. 像4x>3, X0 (2)a2+1>0 (3)3x2+2x (4)x<2x+1 (5)x=2x-5

(6)a+b≠c < > ≤ ≥ ≠ 2、选择适当的不等号填空 (1) 2____3 (2) - ____-3 (3) -a2 ____ 0 (4) a2+b2 ____ 0 (5) 若x≠y,则 -x____-y (6)实数a,b在数轴上的位置如图, 则 a+b____0, b-a____0

a____b ab 0 a 0 b < > > 0 2y+6c a+c>b b+c>a 小结: 1、确定不等关系两边的代数式(抓住关键词) b ≤ 0 2、根据不等关系,选择适当的不等号(选准不等号) 用不等式表示: (1)a与b的平方和大于3 (2)x与y差的平方不小于2 (3)m与2的差是非负数 关 键 词 语 第一类:明确表明数量的不等关系 第二类:明确表明数量的范围特征 ①大 于 ②比…大 ①小 于 ②比…小 ①不大于 ②不超过 ③至 多 ①不小于

②不低于 ③至 少 正数 负数 非负数 非正数 不等号 > < ≤ ≥ >0 <0 ≤0 ≥0 (1)x1=1,x2=2,请在数轴上表示出x1,x2的位置; (2)x<1表示怎样的数的全体? (3)把x ≥ 2 和 1≤x<2表示在数轴上 1 2 0 3 4 -1 -2 -3 1 2 0 3 4 -1 -2 -3 1 2 0 3 4 -1 -2 -3 X1 x2 x ≥ 2 1≤x<2 2.说出下列各图所表示的不等式 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 ? ? x<-2 x≥0 -3<x≤2 1.在数轴上表示下列不等式 (1) x>-3 (2) x≥3

(3)-2<x≤4(4) X ≤3且X ≠0 x>a表示大于a的全体实数,在数轴上表示a右边的所有点,不包括a在内

x≥a表示小于或等于a的全体实数,在数轴上,表示a左边的所有点,包括a在内 b < x < a (b<a)表示大于b而小于a的全体实数 1、你能在数轴上表示出以下的不等式吗? (2) x ≤ a (3)b < x < a (ba a ? a a b 2、在数轴上表示不等式你认为要注意什么? (1)备好数轴找准点 (2)分清空实定方向 (3) 小于朝左 大于朝右 有等画实 无等画空 例2:水电站的水库水位在12-20m(包括12m,20m)时,发电机能正常工作,设水库水位为x(m) 走进生活 (2)当水位在下列位置时,发电机能正常工作吗?①X1=8, ②X2=10, ③X3=15,

④X4=19请用不等式和数轴给出解释。 (1)用不等式表示发电机的正常工作的水位范围,并把它表示在数轴上; 解:发电机正常工作的水位范围是 12≤ x≤ 20。 在数轴上表示为 16 10 12 14 18 20 0 4 6 8 2 (单位:m) 解:把①X1=8, ②X2=10, ③X3=15, ④X4=19表示在数轴上,如上图 x1 x2 x3 x4 显然,X3、X4 满足不等式12≤ x≤20,即当水位是15m、19m时,发电机能正常工作。 而X1、X2不满足不等式12≤ x≤ 20,即当水位是8m、10m时,发电机不能正常工作。 2、填空 (1)小于4的正整数有(

), (2)不大于3的非负整数( ), (3)绝对值小于3的负整数(

), (4)某食品包装袋上标有“净含量120 5克”的字样,则食品的合格净含量范围是( )。(食品合格净含量设X克) 3、2a>a对吗? 1、2、3 0、1、2、3 -1 、 -2 1、请你找出两个满足下列不等式的未知数的值。 (1) 0

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