First, multiple-choice questions (30 points)
1, as shown in figure), if AB∑CD, the equivalent internal angle in the figure is ().
A.∠ 1 and ∠5, ∠2 and ∠6 B.∠3 and ∠7, ∠4 and ∠8 C.∠5 and ∠/kloc-0.
2. As shown in the figure, AB∨CD cannot be judged as () in the following situations.
A.∠3 =∠4 b .∠ 1 =∠5 c .∠ 1+∠4 = 180d .∠3 =∠5
3, as shown in figure, AB∨CD, the following correct conclusion is () A.B.C.D
4, the following statement is correct ()
(A)7 is the arithmetic square root of 49, that is, (B)7 is the square root, that is,
(c) is the square root of 49, that is, (d) is the square root of 49, that is
5, the arithmetic square root is equal to its reciprocal is ()
A.0b. 1 c.0 or 1 d. 0 or 1
6. Estimate 3. In the following categories, the correct one is ()
A.= B. =C. = D.=
7. Given that =0, find the value of yx ()
a 、- 1 B 、-2 C、 1 D、2
8. If m is an arbitrary real number, the point P(m-4, m+ 1) must not be in ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
9, if the point on the axis, then the point in ()
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
10, add-1 to the abscissa of the three vertices of △ABC, and the ordinate is unchanged, then the relationship between the obtained graph and the original graph is ().
A. translate the original image to the positive direction of the x axis by 1 unit; B. Translate the original image in the negative direction of X axis by 1 unit.
C, the original image translates 1 unit d in the positive direction of the y axis, and the original image translates 1 unit in the negative direction of the y axis.
I. Fill in the blanks (30 points)
1, as shown in figure,, you need to add a condition:, OK.
2. As shown in the figure, if the right vertex of the triangle is placed on one side of the ruler, ∠ 1 = 300, ∠ 2 = 500, then ∠3 is equal to degrees.
3. If point P (,) is in the second quadrant, then point Q (,) is in the _ _ _ _ quadrant.
4. It is known that point (a, ﹣ 1) and point (2, 2b﹣5) are axisymmetric with respect to X, then a=, b =.
5. If the distance from point P to the axis is 12 and the distance from point P to the axis is 15, then the coordinate of point P is _ _ _ _ _ _ _.
6. In the plane rectangular coordinate system, if the distance between point m (1, 3) and point n (x, 3) is 5, then the value of x is ().
7. Translate point A (2, -3) to point A'(4, -2), and translate point B (3, 1) to point B' by the same translation method, then the coordinate of B' is _ _ _ _ _ _ _.
8. If the positions of real numbers A and B on the number axis are as shown in the figure, the simplified result of is _ _ _ _ _.
9. As we all know, the cube of 35 and 8 is.
10, the number of -8 obtained by the cube root is.
Three. Calculation problems and equations (10)
1. Calculation:
2. Equation
25x2？ 1 = 0 (x+ 1)3= 16
Four. Answer questions (30 points)
1, (6 points) It is known that the square root of 2a- 1 is 3, and the arithmetic square root of 3a+b- 1 is 4. Find the value of a+2b.
2. Known: as shown in figure,, and verified:.
3. The homes of Xiao Qiang, Xiaohua, Xiao Sally, Xiao Ming, Xiao Ying and Xiao Lan in Class 6, Grade 8 are all very close (as shown in the figure, the side length of the small square is 100 meter). With Xiaoming's family as the "center", please indicate the positions of the other five families with angles and distances.
4. As shown in the figure, the position of the known triangle ABC in the plane rectangular coordinate system is shown in the figure.
(1) Please write down the coordinates of points A, B and C;
(2) Can you calculate the area of triangle ABC?
(3) Translate the triangle ABC by 6 units to the right, and then translate it up by 2 units. Please draw a translated triangle on the map and write down the coordinates of each point of the triangle.