First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1. Among the following triangles with side lengths, the one that can form a right triangle is ().
A.3、4、6 B. 15、20、25 C.5、 12、 15 D. 10、 16、25
2. Assuming that the distance from point P to X axis is 3 and the distance from point P to Y axis is 2, the coordinates of point P must be
A, (3,2 2) B, (2,3 3) C, (-3, -2) D, none of the above answers are correct.
3. The main view of the geometry in the figure below is
4. It is known that point P(3, -2) and point Q are symmetrical about X axis, so the coordinate of point Q is ().
A.(-3，2) B.(-3，-2) C.(3，2) D.(3，-2)
5. If the image of the proportional function y = (1-2m) x passes through point A (x 1, y 1) and point B (x2, y2), if X 1 < X2, Y 1 > Y2, then
A.m < 0 b . m > 0 c . m < 12d . m > 12
6. As shown in the figure, ∠ 1 and ∠2 are complementary, ∠ 3 = 130, so the degree of ∠4 is ().
A.50 years ago, 60 years ago, 70 years ago and 80 years ago
7. In the figure below, the straight line y=x- 1 is ().
8. In the picture below, what can't be folded into a square is ().
(A) (B) (C) (D)
9. The two sides of an isosceles triangle are 4 and 5 respectively, so its circumference is ().
A.12b.13c. 14d.13 or14.
10. The following judgment is correct ()
A. Two isosceles triangles with equal vertex angles are congruent.
B. Two isosceles triangles with equal waist are congruent.
Two right triangles with one side and an equal acute angle are congruent.
Two isosceles triangles with equal vertices and bases meet.
Fill in the blanks (4 points for each small question, 24 points for * * *)
1 1. Given the sample: 3, 4, 0, -2, 6, 1, then the variance of this sample is _ _ _ _ _ _ _.
12. Inequality 2x- 1
13. Given the image passing point (-1 2) of a function, the value of function y decreases with the increase of independent variable X. Please write the function relation that satisfies the above conditions: _ _ _ _ _ _ _.
14. If the right side of an isosceles right triangle is 1 cm, then the high line on its hypotenuse is _ _ _ _ _ cm.
15. in Rt△ABC, AB = 5 and BC = 3, then AC = _ _ _ _ _ _ _ _
16. move the point P(-3, y) down by 3 units and to the left by 2 units to get the point Q(x,-1), then xy = _ _ _ _ _ _ _ _ _ _ _ _
Third, answer questions.
17. Solve the inequality group and express its solution set on the number axis: (The full mark of this question is 6 points)
18. As shown in the figure, BD and CE are the high lines of △ABC, BD = CE, and △ABC is an isosceles triangle? Please explain your reasons. (The full mark of this question is 6 points)
19. Teacher Wang gives exercise books to the students in Class 2, Grade 2 (1). If four copies are given to each student, there are still 24 copies left.
Ben; If each student is assigned five copies, then only one student is assigned less than five exercise books.
Please count the number of people in this class. (The full mark of this question is 6 points)
20. (The full mark of this question is 8) It is known that the image of a linear function passes through (2,5) and (-1,-1).
(1) Find the analytical expression of this linear function.
(2) Draw the image of this function.
2 1. (The full mark of this question is 8) A middle school held a speech contest of "Eight Honors and Eight Disgraces". Five players from Class 9 (1) and Class 9 (2) will participate in the semi-finals. The results of the semi-finals of the five players selected by the two classes (full marks are 100) are shown in the figure below. (1) Fill in the following table according to the picture on the left.
Average score (score), median score (score) and mode score (score)
Category 9 (1) 85 85
Nine (Class Two 85 80
(2) Combining the average score and median score of the two classes, analyze which class has better score in the rematch.
(3) If each class chooses two players to participate in the semi-finals, which class do you think is stronger, and explain the reasons.
22. (The full mark of this question is 10) Write the coordinates of each vertex as shown in figure △ABC, and work out the area of this triangle.
23. (The full mark of this question is 10)
As shown in the figure, EF‖AD, ∠ 1 =∠2, ∠ BAC = 70, and find the degree of ∠AGD.
24. (The full mark of this question is 12) In order to encourage Xiao Qiang to do housework frequently and cultivate his labor consciousness, Xiao Qiang's monthly expenses are obtained from his parents according to the reward he got for doing housework last month and the basic living expenses. If Xiao Qiang spends x hours doing housework every month, and the total sum he can get this month (that is, next month) is Y yuan, then the function image between Y (yuan) and X (hours) is as shown in the figure.
(1) Please write down the basic monthly living expenses in Xiao Qiang according to the pictures; How do parents reward Xiao Qiang for doing housework?
(2) Write the corresponding functional relationship between Y and X when 0≤x≤20;
(3) If Xiao Qiang needs 250 yuan's expenses in May, how much time does Xiao Qiang need to do housework in April?