A, multiple-choice questions (this topic is entitled *** 10 small questions, 3 points for each small question, 30 points for each small question. Only one of the four options given in each small question is correct)
1. In shape, which is both a central symmetric figure and an axisymmetric figure?
.2. The following operations are correct: (▲) A.A2+A2 = 2a4b. (-A2) 3 =-A8c。 (-AB) 2 = 2ab2d。 (2A) 2？ a=4a
3. What is the range of X that makes 3x- 1 meaningful? (▲)a . x & gt； - 13 b . x & gt； 13 C.x？ 13 D.x？ - 1 3
4. As shown in the figure, points A and B on the number axis correspond to real numbers A and B respectively. What is the correct conclusion? (▲)a . ab & gt； 0b . a-b & gt； 0c . a+b & gt； 0 D.|a|-|b| >0
5. Given that the radius of the bottom of the cone is 4cm, the length of the bus is 3cm, and the lateral area of the cone is (▲) A. 15cm2 B. 15? cm2 C. 12 cm2 D. 12？ Square centimeter
6. As shown in the figure, in the parallelogram ABCD, CE? AB is in e, if? A= 125？ And then what? The degree of BCE is (▲) A. 35? B. 55？ C. 25？ D. 30？
7. As shown in the figure, it is an enlarged view of a rectangular box without a cover (excluding the overlapping part). According to the data in the figure, we can know that the volume of a cuboid without a cover is (▲) A. 4 B.6 C. 8 D. 12.
8. Among the following propositions, the correct proposition is (▲) A. Two quadrangles with equal diagonals are rectangles B. Two quadrangles with vertical diagonals are diamonds C. Two quadrangles with vertical diagonals are squares D. Two parallelograms with equal diagonals are rectangles.
9. As shown in the figure, in the plane rectangular coordinate system, A( 1, 0), B (0,3), with AB as the edge, make a square ABCD in the first quadrant, and point D is in the hyperbola y=k x(k? 0), after the square is translated by m unit lengths in the negative direction of the X axis, the point C just falls on the hyperbola, so what is the value of m? (▲ ) A. 2 B. 3 C. 2 D. 3
10. As shown in the figure, in right-angled triangular paper,? C=90？ ，AC=6，BC=8。 If you want to cut two circles with equal circumscribed on a piece of paper, what is the maximum radius of the circle? (▲)a . 4 3 b . 107 c . 1d . 125
2. Fill in the blanks (this big question is ***8 small questions, 2 points for each small question, *** 16 points. You don't need to write the answer process, just fill in the answer in the corresponding position on the answer sheet)
1 1. Factorization: x3? 4x= ▲。
12. According to media reports, the huge economic loss caused by environmental pollution in China is as high as 680 million yuan every year, which is expressed as ▲ yuan by scientific notation.
13. If x 1, x2 is the equation x2+2x? 3 = 0.2, then x 1+x2= ▲.
14. The sum of the internal angles of the hexagon is equal to ▲? .
15. As shown in the figure, after △ABC is folded along its midline MN, point A falls on point A? What if? A=28？ ,? B= 130？ And then what? Answer? NC= ▲？ .
16. As shown in the figure, in △ABC,? A=90？ ,? C=75？ , AC=6, DE vertical BC, then BE= ▲.
17. As shown in the figure, point C and point D are respectively on the extension lines of radius OA and OB ≥O, with OA=6 and AC=4. CD is parallel to AB and intersects AB at two points MN. If Tan? C =12, then the length of CN is ▲.
18. Known trapezoidal ABCD, AD∨BC, AB? BC，AD= 1，AB=3，BC=4。 If p is any point on the AB line, extend PD to E to make DE=2PD, and then make □PCQE with PE and PC as edges to find the minimum value of diagonal PQ ▲. (no.16) ABD C E ABD C O M N (. (DrawingNo. 15)
Three. Problem solving (this big question is a small question of *** 10, and * * * is 84 points. Write the necessary proof process or calculus steps when answering.
19. (8 points for this question)
(1) calculation: (1 4)- 1-27+(5-? )0(2)(2x- 1)2+(x-2)(x+2)-4x(x- 1
2) 20. (The full mark of this question is 8) (1) Solve the equation:1x-3 = 2+x3-x.
(2) Solving inequality group: x-3(x-2)? 4， 1+2x3 >x- 1
2 1. (8 points in this question) As shown in the figure, in △ABC, D is a point on the side of BC, E is the midpoint of AD, and the parallel line passing through point A is the extension line of CE, AF=BD, connecting BF. (1) verification: BD=CD. (2) If AB=AC, try it.
. 22. (The full mark of this question is 6) In order to know the scores of the ninth-grade students in a school, the sports scores of some students are randomly selected as follows, in which the central angle in the right fan-shaped statistical chart is? For 36? According to the information provided above, answer the following questions: (1) m = ▲; The median sports scores of some students are ▲;
(2) There are 500 ninth-grade students in this school. If the physical education score is above 33 (inclusive), please estimate the total number of students with excellent physical education scores in the ninth grade of this school.