218 Taizhou Senior High School Entrance Examination Paper 1. Multiple-choice questions
There are * * 6 small questions in this big question, with 3 points for each small question and 18 points for * *. Of the four options given in each small question, only one meets the requirements of the question.
The arithmetic square root of 1.2 is ()
A.B.C.D.2. According to the definition of arithmetic square root, we can get that the arithmetic square root of 2 is, so choose B.
Test center: arithmetic square root.
2. The following operation is correct ()
A.a3? a3=2a6 B.a3+a3=2a6 C.(a3)2=a6 D.a6? A2=a3
Answer C.
Question analysis: Option A, a3? a3=a6; Option b, a3+a3=2a3; Option c, (a3)2=a6; Option d, a6? A2=a8. Therefore, C.
Test site: algebraic expression's operation.
3. Consider the following English letters as graphs, which are both axisymmetric and centrosymmetric ()
A. B. C. D.
Answer C.
Test site: centrosymmetric graphs; Axisymmetric figure.
4. The center of gravity of the triangle is ()
A. The intersection of the midline on three sides of the triangle
B. The intersection of the high lines on three sides of the triangle
C. The intersection of the perpendicular bisector on three sides of the triangle
D. The intersection of the parallel lines on three internal angles of the triangle
Answer A.
Question analysis: The center of gravity of the triangle is Therefore, A.
test site is the center of gravity of the triangle.
5. There are five members in a popular science group, and their heights are (unit: cm): 16, 165, 17, 163 and 167. After adding a member with a height of 165cm, the following statement is correct: () < S2 is new =, the average is unchanged, and the variance becomes smaller, so C. Learning # Science Network < P > test site: average; Variance.
6. As shown in the figure, p is the inverse proportional function y= (k> ) At a point on the image in the first quadrant, the crossing point P is taken as the X axis, and the vertical line of the Y axis intersects the image of the linear function Y =-x-4 at points A and B. What if? AOB=135? , then the value of k is ()
A.2 B.4 C.6 D.8
Answer D.
? C(，﹣4)，G(﹣4，)，
? OC=OG，
? OGC=? OCG=45?
∵PB∥OG，PA∥OC，
∵? AOB=135? ，
? OBE+? OAE=45? ，
∵? DAO+? OAE=45? ，
? DAO=? OBE,
∵ In △BOE and △AOD,,
? △BOE∽△AOD;
? , that is;
sorted: nk+2n2=8n+2n2, simplified: k=8;
So choose D.
Test center: inverse proportional function comprehensive question.
218 Taizhou senior high school entrance examination mathematics test paper II. Fill in the blanks
(3 points for each question, out of 3 points, fill in the answers on the answer sheet)
7. | | | =.
Answer 4.
Test center: Absolute value.
8. Tiangong-2 flew about 42,5 kilometers around the earth in space, and expressed 42,5 as. < P > Answer 4.25? 14.
Test center: scientific notation.
9. Given that 2m﹣3n=﹣4, the value of the algebraic formula m(n﹣4)﹣n(m﹣6) is.
Answer 8. < (-4) = 8.
Test center: algebraic expression's operation; Overall idea. learning # subject. net
1. An opaque bag * * * contains three balls, and their labels are 1, 2 and 3 respectively. One ball is pulled out of it, and the label is? 4? , this event is. (Fill in? An inevitable event? 、? Impossible event? Or? Random events? )
The answer is impossible.
Question analysis: It is known that the labels of the three balls in the bag are 1, 2 and 3 respectively, and there is no ball with the label of 4, so you can know that you have pulled out a ball with the label of? 4? , this event is an impossible event.
Test site: random event.
11. Stack a set of triangles as shown in the figure, and what is in the picture? The degree of is.
Answer 15? .
test analysis: according to the nature of the external angle of the triangle, =6? ﹣45? =15? .
test center: the nature of the outer corner of the triangle.
12. The radius of the sector is 3cm and the arc length is 2? Cm, the area of the sector is cm2.
Answer 3?
test analysis: let the central angle of the sector be n, then: 2? =, the solution is: n=12? So s-sector = =3? Cm2.
Test center: calculation of sector area.
13. Equation 2x2+3x﹣1= has two roots of x1 and x2, so the value is equal.
Answer 3.
Test analysis: According to the relationship between roots and coefficients, x1+x2=﹣, x1x2 =. So = =3.
Test center: the relationship between root and coefficient.
14. When Xiao Ming walked up a straight road with a slope I of 1: 5m, Xiao Ming rose m in the vertical direction.
Answer 25.
Test center: the application of right triangle.
15. As shown in the figure, in the plane rectangular coordinate system xOy, point A. 2). If point C is in the first quadrant, and the abscissa and ordinate are integers, and P is the epicentre of △ABC, the coordinates of point C are.
Answer (7,4) or (6,5) or (1,4).
Test center: the circumscribed circle of the triangle; Coordinate and graphic properties; Pythagorean theorem.
16. As shown in the figure, in the plane, the line segment AB=6, P is the moving point on the line segment AB, and the straight line where the edge CD of the triangle paper CDE is located intersects with the line segment AB vertically, and satisfies PC=PA. If the point P moves from point A to point B along the AB direction, the path length of the point E is.
Answer 6
Test analysis: As shown in the figure. , the path of point e movement is EE? From the nature of translation, we can know AC? =EE? ,
in Rt△ABC? , easy to know AB=BC? =6，? ABC? =9? ，? EE? =AC? = = 6. 21st Century Education Network
Test site: track; Translation transformation; Pythagorean Theorem.
218 Taizhou Senior High School Entrance Examination Paper III. Solution
(This big question * * 1 small questions, ***12 points. The solution should be written in words, proof process or calculus steps.)
17.(1) Calculation: (1) . ;
(2) Solve the equation:.
Answer (1)-2; (2) The fractional equation has no solution.
Test center: the operation of real numbers; Solve the fractional equation.
18. Taiwei class? It is a platform for students' autonomous learning. There are 12 students in a junior middle school, and each student takes 6 to 3 math Taiwei classes every week (including 6 and 3). In order to further understand the situation of students' weekly learning of math Taiwei classes in this school, some students' relevant learning data are randomly selected from three grades, and the statistics are sorted out and drawn as follows:
According to the above information, the following questions are completed:
(2) It is estimated that the number of all students in this school who study mathematics Taiwei courses every week is between 16 and 3 (including 16 and 3).
For the answer (1), see the analysis. (2)96.
(2) Among all the students in this school, there are 1,2 students who take 16 to 3 courses in mathematics every week. =96 people.
Test center: bar chart; Estimate the population with samples. 21st Century Education Network
19. In the recitation competition organized by the school, two students, A and B, take part in the competition by drawing lots from three different articles. The rules of drawing lots are as follows: mark the letters A, B and C on three identical labels, each representing an article, one student randomly draws a label and puts it back, and the other student randomly draws it. Draw a tree diagram or. And find the probability that A and B win the same article.
Answer.
Test center: find the probability by list method or tree drawing method.
2.(8 points) As shown in the figure, △ABC,? ACB> ? ABC.
(1) Use a ruler and compasses in? The inside of ACB is made of ray CM, which makes? ACM=? ABC (no writing method is required, but drawing traces are reserved);
(2) If the ray CM in (1) crosses AB at point D, AB=9 and AC=6, find the length of AD.
See the analysis for the answer (1); (2)4.
Analysis of test questions: (1) Drawing according to ruler, with AC as one side, in? ACB's internal work? ACM=? ABC is enough; (2) According to the similarity between △ACD and △ABC, the corresponding sides of similar triangles can be used for calculation in proportion.
Analysis of the test questions:
(1) As shown in the figure, the ray CM is the demand;
(2)∵? ACD=? ABC，? CAD=? BAC，
? △ACD∽△ABC，
? That is,
? AD=4. learning @ kewang
test site: basic drawing; Judgment and properties of similar triangles.
21. In the plane rectangular coordinate system xOy, the coordinate of point P is (m+1, m﹣1).
(1) Try to judge whether point P is on the image of linear function y=x﹣2 and explain the reasons;
(2) As shown in the figure, the image of the linear function y=﹣ x+3 intersects with the X axis and the Y axis at points A and B respectively. If the point P is inside the △AOB, find the value range of m.
The answer (1) is that the point P is on the image of the linear function y = ﹣ x+2. See the analysis for the reason. (2)1
test site: the coordinate characteristics of points on the linear function image; Properties of linear function.
22. As shown in the figure, in the square ABCD, G is a point on the side of BC, BE? AG in e, DF? AG in F, connecting DE.
(1) Verification: △ABE≌△DAF;
(2) If AF=1 and the area of quadrilateral ABED is 6, find the length of EF.
See the analysis for the answer (1). (2)2.
What is the meaning of the question 2 (x+1)? 1+ ? x? (x+1)=6,
x=2 or ~ 5 (discard),
? EF=2.
Test center: the nature of a square; Congruent triangles's judgment and nature; Pythagorean Theorem.
23. The cost of each dish A and B in Yiran Food Store is 14 yuan, and the price is 2 yuan and 18 yuan respectively. The daily turnover of these two dishes is 112 yuan, and the total profit is 28 yuan.
(1) How many copies of these two dishes does this store sell every day?
(2) In order to increase profits, the store is going to lower the price of A-type dishes and increase the price of B-type dishes. When selling, it is found that every time the price of A-type dishes drops in .5 yuan, it can sell one more copy; For every increase in the price of .5 yuan, the price of B dishes will be reduced by 1. If the total number of copies of these two dishes sold every day remains the same, what is the maximum profit of these two dishes every day?
Answer (1) The store sells 6 copies of these two dishes every day; (2) The maximum daily total profit of these two dishes is 316 yuan. < P > Analysis of test questions: (1) Set up equations based on the daily turnover of vegetables A and B of 112 and the total profit of 28; (2) If a vegetable is set to sell more copies of A, then B vegetable will sell less copies of A, Finally, we can draw a conclusion by establishing the functional relationship between the profit and the number of copies of A vegetables sold less.
Analysis of test questions:
= (6-.5A) (2+A)+(4+.5A) (4-A)
= (-.5A2). W is the largest, w=316
A: The daily total profit of these two dishes is 316 yuan at most.
Test center: the application of binary linear equations and quadratic functions.
24. As shown in the figure, the diameter of ⊙O is AB=12cm, C is a point on the AB extension line, and CP and ⊙O are tangent to point P.
(2) if? C=? D, find the area of quadrilateral BCPD.
See the analysis for the answer (1); (2)18 .
Analysis of test questions: (1) Connect OP and get PC according to the nature of tangent? OP, get BD according to the properties of parallel lines? OP, according to the vertical diameter theorem
∵? POB=2? D，
? POB=2? C，
∵? CPO=9? ，
? C=3? ，
∵BD∥CP，
? C=? DBA，
? D=? DBA，
? BC∥PD，
? The quadrilateral BCPD is a parallelogram,
? Area of quadrilateral BCPD =PC? PE=6 ? 3=18. subject% net
test site: the nature of tangent; Vertical diameter theorem; The determination and properties of parallelogram.
25. Reading comprehension:
As shown in Figure ①, among all the line segments connecting a point P outside the figure L with points on the figure L, if the line segment PA1 is the shortest, the length of the line segment PA1 is called the distance from the point P to the figure L.
For example, in Figure ②, the length of the line segment P1A is the distance from the point P1 to the line segment AB; The length of line P2H is the distance from point P2 to line AB.
Solve the problem:
As shown in Figure ③, the coordinates of points A and B in the plane rectangular coordinate system xOy.