《2025年暑假作业新疆青少年出版社七年级数学人教版》

1.如图,数轴上的点A,B,O,C,D分别表示数-2,-1,0,1,2,则表示数$2-\sqrt {5}$的点P应落在 ()

A.线段AB上
B.线段BO上
C.线段OC上
D.线段CD上

答案： B

2.如图,一只蚂蚁从点A沿数轴向右爬$2\sqrt {2}$个单位后到达点B,点A表示-2,设点B所表示的数为m.
(1)求m的值;
(2)求$|m-3\sqrt {2}|+(m-\sqrt {2})^{2}$的值.

答案：
(1) 根据题意得：$-2 + 2\sqrt{2} = 2\sqrt{2} - 2$，则$m$的值为$2\sqrt{2} - 2$；
(2) 当$m = 2\sqrt{2} - 2$时，原式$=|2\sqrt{2} - 2 - 3\sqrt{2}| + (2\sqrt{2} - 2 - \sqrt{2})^2 = |-2 - \sqrt{2}| + (\sqrt{2} - 2)^2 = 2 + \sqrt{2} + 2 - 4\sqrt{2} + 4 = 8 - 3\sqrt{2}$．

3.已知x,y为实数,且满足$\sqrt {1+x}-(y-1)\sqrt {1-y}= 0$,求$x^{2025}-y^{2025}$的值.

答案： $\because \sqrt{1 + x} - (y - 1) \cdot \sqrt{1 - y} = 0$，$\therefore \sqrt{1 + x} + (1 - y)\sqrt{1 - y} = 0$，$\therefore 1 + x = 0$，$1 - y = 0$，解得$x = -1$，$y = 1$，$\therefore x^{2025} - y^{2025} = (-1)^{2025} - 1^{2025} = -1 - 1 = -2$．

4.若$|x-1|+(y+3)^{2}+\sqrt {x+y+z}= 0$,求$4x-2y+3z$的平方根.

答案： 由题意得，$x - 1 = 0$，$y + 3 = 0$，$x + y + z = 0$，解得$x = 1$，$y = -3$，$z = 2$，所以，$4x - 2y + 3z = 4 \times 1 - 2 \times (-3) + 3 \times 2 = 16$，$\because (\pm 4)^2 = 16$，$\therefore 4x - 2y + 3z$的平方根是$\pm 4$．