Examination time: 90 minutes.
1. Multiple choice questions: (3 points for each question, ***39 points. Only one of the four options in each question is correct. Please fill in the correct option number in the brackets on the right. )
1. If all the values in the score are expanded by 10 times, the value of the score will be
A. zoom in 20 times. B. keep it the same. C. magnification 10 times. D. it's original.
2. If the fractional equation has an increasing root, the value of is
A. 1 B.- 1 C.3 D.-3
3. Point P is in the fourth quadrant, the distance from P to axis is 4, and the distance from P to axis is 3, so the coordinate of point P is
A.(-4，3)b .(4. 13)c .(3，4) D. (3，4)
A bus departs from Shanghai to Beijing, and the distance from the bus to Beijing is kilometers. The following figure can roughly reflect the functional relationship between and.
5. Given that there are two points A () and B () on the image of the inverse function, the following conclusion is correct.
A.& ltb . >；
The size relationship between C. = D. and cannot be determined.
6. Use a ruler and compasses to make a drawing trajectory with an angle equal to the known angle, as shown in the figure, and the basis of drawing is
A. Social Service Bureau
7. Find the point P, so that the distances from P to the three sides of the triangle are equal.
A. the two sides are the intersections of the vertical lines. B. the two sides are the intersections of the high lines.
C. Make the intersection of the median lines on both sides D. Make the intersection of the bisectors of two internal angles.
8. As shown in the following figure, in Rt△ABC, a point P on the right-angled side AC intersects, the straight line de intersects with AB at D, and the extension line of BC intersects with E. If ∠DPA=∠A, then the point D exists.
The median vertical line in A.BC leads to the median vertical line in B.BE
The middle vertical line of C.AC to D. None of the above answers are correct.
9. In quadrilateral ABCD, ∠ A: ∠ B: ∠ C: ∠ D = 2:1:2, then the shape of quadrilateral ABCD is
A. diamond B. rectangle C. isosceles trapezoid D. parallelogram
10. The following statement is correct.
A. A set of quadrangles with parallel opposite sides and another set of quadrangles with equal opposite sides are parallelograms;
B. Quadrilaterals whose diagonals are perpendicular to each other are diamonds;
C. A quadrilateral with equal diagonals is a rectangle;
D a set of rectangles with equal adjacent sides is a square.
1 1. In a certain sports activity, the scores of skipping rope per minute of students in Group A and Group B (unit: times) are as follows:
Median variance of the average number of class participants
Grade a 55135149190
Class b 5513515110.
There are three propositions: ① the average score of class A students is higher than that of class B students; ② The fluctuation of students' grades in Class A is greater than that in Class B; ③ Excellent students in Class A will not be more than those in Class B (skipping classes ≥ 150 is excellent). Which one is correct?
A.① B.② C.③ D.②③
12. The math teacher made a statistical analysis of Xiaoming's five simulated math exams before the college entrance examination to judge whether Xiaoming's math scores were stable, so the teacher needed to know Xiaoming's five math scores.
A. mean or median B. variance or extreme range C. mode or frequency D. frequency or mode
13. A set of data 5, 5, 6, 7, 7, 8. Assuming that the average value of this set of data is 6, the median value of this set of data is
a7 b . 6 c . 5.5d . 5
Fill in the blanks (only the final result is needed, 3 points for each small question, 24 points for * * *)
1. The form of the score is _ _ _ _ _ _, which is meaningful when _ _ _ _ _.
2. If, then = _ _ _ _ _.
3. The triangle area surrounded by a straight line and two coordinate axes is _ _ _ _ _ _ _ _.
4. The inverse proposition of the proposition "congruent triangles's corresponding angles are equal" is _ _ _ _ _.
5. It is known that the bisector of □ABCD, AB=5, AD=8, ∠ABC intersects with AD at point E, and the extension line of intersection CD is at point F, then DF = _ _ _ _ _ _ _
6. If the base angle of the isosceles trapezoid is equal to 60. Its two bases are 12 and 19 respectively, so its waist length is _ _ _ _ _.
7. There are 50 students in a class, 15, and there are three excellent students. On the pie chart, the degree of the fan-shaped central angle representing the number of students with three good qualities is _ _ _ _ _ _.
8. A shooter shoots five times in a row, and the number of rings obtained is 8, 6, 10, 7, 9, so the standard deviation of the number of rings obtained by this shooter is _ _ _ _ _ _ _ _.
Three, solve the problem (the answer should write the necessary calculation process, deduction steps or text description, out of 57 points)
1. (quarter) calculation:
2. (Full mark is 6) As shown in the figure, point D and point B are on both sides of ∠A, point C is inside ∠A, AB=AD, BC=DC, CE⊥AD, CF⊥AB, and the steps are E and F respectively.
Verification: CE=CF
3. (Full score: 7) As shown in the figure, AB=AC, AD=AE, DE=BC, ∠ Bad = ∠ CAE.
Verification: quadrilateral BCED is a rectangle.
4. (Full score 10) As shown in the figure, in □ABCD, e and f are the midpoint of AB and CD edges, BD is diagonal, and the extension lines of AG∨DB and CB are at G. 。
(1) Verification: △ ade △ CBF;
(2) If the quadrangle BEDF is a diamond, what special quadrangle is the quadrangle AGBD? And prove your conclusion.
5. (Full score: 10) A company wants to recruit a manager from within, and has conducted two tests on three candidates, A, B and C. The test scores of the three candidates are shown in the following table:
Test scores/scores of test items
Methyl ethylene propylene
Written test 75 80 90
Interview 93 70 68
According to the recruitment procedure, 200 employees were organized, and three people were democratically evaluated by voting recommendation, and three people won the votes (each employee can only recommend 1 person, and cannot abstain), as shown in figure 1, and each vote was recorded as 1 point.
(1) Please calculate the democratic appraisal scores of three people;
(2) According to the actual needs, the unit determines the individual performance according to the ratio of written test, interview and democratic appraisal of 4:3:3, so who will be hired?
6. (Full score: 10) A medical research institute developed a new drug. It was found in the efficacy test that if adults took the prescribed dose, the drug content in blood was the highest 2 hours after taking the drug, reaching 6 micrograms per milliliter, and then gradually decreased. After 10 hour, the drug content in blood is 3 micrograms per milliliter, and the change of drug content per milliliter (micrograms) with time (hours) is shown in the figure.
The functional relationship between (1) and.
(2) If the drug content per milliliter of blood is more than 4 micrograms, it is effective for treating diseases, so how long is this effective time?
7. (Full score is 10) As shown in the following figure, in the right-angled trapezoidal PQCD, AD∑BC, AD=24, BC=26, and ∠ B = 90, the moving point P starts from A and moves along the edge of AD at the speed of 1, and the moving point Q starts from point C and is 3.