20 18 Taizhou senior high school entrance examination mathematics examination paper 1, multiple-choice questions
This big question has ***6 small questions, each with 3 points, *** 18 points. Only one of the four options given in each small question meets the requirements of the topic.
The arithmetic square root of 1.2 is ()
A. The second century BC
Answer B.
Test analysis: the square root of a positive number is called the arithmetic square root of this number. According to the definition of arithmetic square root, you can get the arithmetic square root of 2, so choose B.
Test center: arithmetic square root.
2. The following operation is correct ()
A.a3？ a3 = 2 a6 b . a3+a3 = 2 a6 c .(a3)2 = a6 d . a6？ a2=a3
Answer C.
Test analysis: Option A, a3? A3 = a6 Option B, A3+A3 = 2A3; Option c, (a3)2 = a6；; Option d, a6? A2=a8。 So I chose C.
Test site: the calculation of algebraic expressions.
3. The following with English letters as graphics, both axial symmetry graphics and central symmetry graphics is ()
A.B. C. D。
Answer C.
Test center: central symmetrical figure; Axisymmetric graph.
4. The center of gravity of the triangle is ()
A. the intersection point of the midline of the triangle.
B. Intersections of high lines on three sides of a triangle
C. the intersection of the perpendicular lines of the three sides of a triangle
D. the intersection of three parallel lines and the inner angle of the triangle
Answer a.
Test and analysis: the center of gravity of the triangle is the intersection of three midlines, so choose A.
Test center: the center of gravity of the triangle.
5. There are five members in a popular science group, and their heights are (unit: cm): 160, 165, 170, 163, 167. Add 1 members with a height of 165cm.
A. the average is unchanged and the variance is unchanged. B. the mean value remains unchanged and the variance becomes larger.
C. the average value is unchanged and the variance is small. D. the average value is small and the variance is unchanged.
Answer C.
Test analysis: S2 original =; S2 is new =, the mean value remains unchanged, and the variance becomes smaller, so the branch network C. Learn # is selected.
Test center: general; Variance.
6. As shown in the figure, p is the inverse proportional function y =(k >；; 0) At a point on the first quadrant image, take the intersection point P as the X axis, and the vertical line of the Y axis intersects with 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(0,﹣4),G(﹣4,0)，
? OC=OG，
? OGC=？ OCG=45？
∫PB∨OG，PA∨OC，
∵? AOB= 135？ ,
? OBE+？ OAE=45？ ,
∵? Dao+? OAE=45？ ,
? Tao =? OBE，
At △BOE and △AOD,
? △BOE∽△AOD；
? , that is;
Finishing: nk+2n2=8n+2n2, simplified: k = 8；;
So choose D.
Test center: inverse proportional function synthesis problem.
20 18 Taizhou senior high school entrance examination mathematics examination paper 2. fill (up) a vacancy
(3 points for each question, out of 30 points, fill in the answer sheet)
7.|﹣4|= .
Answer 4.
Test and analysis: the absolute value of a positive number is itself, the absolute value of a negative number is its opposite number, and the absolute value of 0 is 0. From this we can get |-4 | = 4.
Test center: absolute value.
8. Tiangong-2 flew around the earth for about 42,500 kilometers in space, which was expressed as 42,500 by scientific notation.
Answer 4.25? 104.
Test center: scientific notation.
9. Given 2m-3n =-4, the algebraic expression m (n-4)-n (m-6) has the value.
Answer 8.
Test analysis: when 2m﹣3n=﹣4, the original formula = Mn ﹣ 4m ﹣ Mn+6n = ﹣ 4m+6n = ﹣ 2 (2m ﹣ 3n) = ﹣ 2? (﹣4)=8.
Test center: the operation of algebraic expressions; Holistic thinking. Learn # subjects. net
10. An opaque bag * * * contains three balls, and their labels are 1, 2, 3 respectively. Draw 1 ball from it. What's the label? 4? , this event is. (fill in? Inevitable events? 、? The impossible? Or? Random events? )
The answer is impossible.
Test and analysis: It is known that the labels of the three balls in the bag are 1, 2 and 3 respectively. If there is no ball labeled 4, we can know that there are 1 balls drawn from it. What is the label? 4? This event is an impossible event.
Test location: random events.
1 1. Stack a pair of triangles as shown in the figure. What's in the picture? The degree is.
The answer is 15? .
Problem analysis: can we know from the nature of the outer angle of the triangle? =60? ﹣45? = 15? .
Test site: the nature of the outer corner of the triangle.
12. Sector radius 3cm, arc length 2? Centimeters, and the area of the fan is square centimeters.
Answer 3? .
Test and analysis: let the central angle of the sector be n, then: 2? =, the solution is n= 120? So s sector = =3? Square centimeters.
Test center: calculate the sector area.
13. The two roots of the equation 2x2+3x- 1 = 0 are x 1 and x2, so the value is equal to.
Answer 3.
Test and analysis: according to the relationship between root and coefficient, we get X 1+X2 = |, X 1x2 = |, so = =3.
Test center: the relationship between root and coefficient.
14. When Xiao Ming walked on a straight road with a slope I of 1: 50m, Xiao Ming rose by m in the vertical direction.
Answer 25.
Test center: the application of solving right triangle.
15. As shown in the figure, in the plane rectangular coordinate system xOy, the coordinates of a, b and p are (1 0), (2,5) and (4,2) respectively. If point C is in the first quadrant, the abscissa and ordinate are integers, and P is the epicenter of △ABC, then the coordinate of point C is.
Answer (7,4) or (6,5) or (1, 4).
Test center: circumscribed circle of triangle; Coordinate and graphic attributes; Pythagorean theorem
16. As shown in the figure, on 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 the line segment AB vertically, satisfying PC=PA. If point P moves from point A to point B in the AB direction, the path length of point E is.
Answer 6
Test analysis: As shown in the figure, from the meaning of the question, the path of point C is the line segment AC? , the path of point e movement is EE? From the essence of translation, we can know AC? =EE？ ,
At Rt△ABC? , easy to know AB=BC? =6,? ABC？ =90? ,? EE？ =AC？ = =6 .2 1 Century Education Network
Test site: track; Translation and transformation; Pythagorean theorem
20 18 Taizhou senior high school entrance examination mathematics examination paper 3. solve problems
(The big question is *** 10, and the score is *** 102. The solution should be written in words, proof process or calculation steps. )
17.( 1) Calculation: (-1) 0-(-)-2+tan 30? ;
(2) Solve the equation:
Answer (1)-2; (2) The fractional equation has no solution.
Test center: the operation of real numbers; Solve fractional equations.
18.？ Taiwei class? It is a platform for students to learn independently. There are 1200 students in a junior high school, and each student has 6 to 30 math Taiwei classes (including 6 and 30) every week. In order to further understand the weekly learning situation of students in this school, the relevant learning data of some students are randomly selected from three grades, and the statistics are compiled and drawn as follows:
Complete the following questions according to the above information:
(1) to complete the bar chart;
(2) It is estimated that the number of students studying the mathematics Taiwei course in this school every week is between 16 and 30 (including 16 and 30).
The answer (1) can be found in the analysis; (2)960.
(2) Among all the students in our school, there are 16 to 30 students who study mathematics every week. =960 people.
Test center: bar chart; Estimating population with samples. 2 1 Century Education Network
19. In the recitation competition organized by the school, two students, A and B, drew lots from three different articles to participate in the competition. The rules of drawing lots are: mark the letters A, B and C on three identical labels, each label stands for 1, one student randomly selects a label and puts it back, and the other student randomly selects it. By drawing a tree diagram or list,
The answer.
Test center: use list method or tree drawing method to find the probability.
20.(8 points) As shown in the figure, in △ABC,? ACB & gt； ? ABC。
(1) Use a ruler and compasses? The inside of ACB is made of rays centimeters, which makes? ACM=？ ABC (writing method is not required, but drawing traces are kept);
(2) If the ray CM in (1) intersects with AB at point D, AB=9 and AC=6, find the length of AD.
The answer (1) can be found in the analysis; (2)4.
Test and analysis: (1) According to the method of ruler drawing, taking communication as one side, in? Internal strength of ACB? ACM=？ ABC is enough; (2) According to the similarity between △ACD and △ABC, the corresponding edges of similar triangles can be calculated in proportion.
Test analysis:
(1) As shown in the figure, ray CM is the demand;
(2)∵? ACD=？ ABC，？ CAD=？ BAC，
? △ACD∽△ABC，
? , that is,
? AD=4。 Learning @ Kewang
Test center: basic drawing; Similar triangles's judgment and nature.
2 1. In the plane rectangular coordinate system xOy, the coordinates of point P are (m+ 1, m- 1).
(1) Try to judge whether point P is on the image of linear function y = x-2, and explain the reason;
(2) As shown in the figure, the image of the linear function y =-x+3 intersects the X axis and the Y axis at points A and B respectively. If point P is within △AOB, find the range of m. 。
The answer (1) point p is on the image of linear function y = x-2, and explain the reason. (2) 1
Test site: the coordinate characteristics of points on the linear function image; Properties of linear functions.
22. As shown in the figure, in a square ABCD, G is a point on the side of BC, BE? AG, DF in e AG in f, connected to DE.
(1) verification: △ Abe △ daf;
(2) If AF= 1 and the area of quadrilateral ABED is 6, find the length of EF.
The answer (1) can be found in the analysis; (2)2.
Meaning 2 (x+ 1)? 1+ ? x？ (x+ 1)=6，
X=2 or ~ 5 (discarded),
? EF=2。
Test center: the nature of the square; Congruent triangles's judgment and nature; Pythagorean theorem
23. The prices of dishes A and B in Yiran food store are 14 yuan, 20 yuan and 18 yuan respectively. The daily turnover of these two dishes is 1 120 yuan, and the total profit is 280 yuan.
(1) How many copies of these two dishes does this store sell every day?
(2) In order to increase profits, the store intends to reduce the price of A-type dishes and increase the price of B-type dishes. When selling, I found that the price of Type A dishes can be increased by 1 serving for every drop in 0.5 yuan; Every time the price of B-type food increases in 0.5 yuan, it will be sold less 1 serving. 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) These two dishes sell 60 servings a day. (2) The maximum daily profit of these two dishes is 3 16 yuan.
Test analysis: (1) Just establish an equation based on the daily turnover and total profit of vegetables A and B of 280; (2) Assuming that Party A sells more than Party A, Party B sells less than Party A. Finally, we can establish a functional relationship between the profit and the number of Party A's less sold shares and draw a conclusion.
Test analysis:
=(6﹣0.5a)(20+a)+(4+0.5a)(40﹣a)
=(﹣0.5a2﹣4a+ 120)+(﹣0.5a2+ 16a+ 160)
=﹣a2+ 12a+280
=﹣(a﹣6)2+3 16
When a=6, w is the largest, w=3 16.
A: The highest daily profit of these two dishes is 3 16 yuan.
Test center: the application of binary linear equation and quadratic function.
24. As shown in the figure, the diameter ⊙O is AB= 12cm, C is a point on the extension line of AB, CP is tangent to ⊙O at point P, and the chord BD∨CP passing through point B is connected to PD.
(1) Verification: Point P is the midpoint;
(2) What if? C=？ Find the area of quadrilateral BCPD.
The answer (1) can be found in the analysis; (2) 18 .
Test and analysis: (1) Connect OP, and get PC according to the property 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=90？ ,
? C=30？ ,
∫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 center: the nature of tangent; Vertical diameter theorem; Determination and properties of parallelogram.
25. Reading comprehension:
As shown in Figure ①, among all the line segments connecting the point P outside the figure L and the point on the figure L, if the line segment PA 1 is the shortest, the length of the line segment PA 1 is called the distance from the point P to the figure L. 。
For example, in Figure ②, the length of line segment P 1A is the distance from point P 1 to 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, in the plane rectangular coordinate system xOy, the coordinates of point A and point B are (8,4) and (1 2,7) respectively, and point P starts from the origin O and moves in the positive direction of the X axis at the speed of1unit length per second for t seconds.
(1) When t=4, find the distance from point P to line AB;
(2) What is the value of t, and the distance from point P to line AB is 5?
(3) When T meets what conditions, the distance from point P to line AB shall not exceed 6? (Write the result of this little question directly)
Answer (1) 4; (2) t=5 or t =11; (3)8-2? t？ The distance from point P to line AB is no more than 6.
Test analysis: (1) For AC? X axis, from PC=4, AC=4, can be obtained by solving according to Pythagorean theorem; (2) Make BD∨x axis and point P in AC.
AC=4，OC=8，
When t=4 and OP=4,
? PC=4，
? The distance from P to AB line PA = = = 4；;
(2) As shown in Figure 2, the intersection point B is BD∨x axis, and the intersection point Y axis is at point E,
(1) when point p is located on the left side of AC, AC = 4, P 1A=5,
? P 1C= =3，
? OP 1=5, that is, t = 5；;
② When point P is located on the right side of AC, the intersection point A is AP2? AB intersects the x axis at P2,
? CAP2+？ EAB=90？ ,
∫BD∨x axis, AC? X axis,
? CE？ BD，
(3) As shown in Figure 3,
① When point P is located on the left side of AC and AP3=6,
P3C= =2，
? op3=oc﹣p3c=8﹣2；
② When point P is located on the right side of AC and P3M=6,
P2N over P2? P3M is at point n,
Test center: the synthesis of a function.
26. In the plane rectangular coordinate system xOy, the abscissas of points A and B are A and a+2 respectively, and the image of quadratic function y=﹣x2+(m﹣2)x+2m passes through points A and B, and A and M satisfy 2a﹣m=d(d is a constant).
(1) If the image of linear function y 1=kx+b passes through point A and point B. 。
(1) when a= 1 and d =- 1, find the value of k;
② If y 1 decreases with the increase of x, find the range of d;
(2) when d =-4 and a? ﹣2、a？ 4. Judge the positional relationship between straight line AB and X axis, and explain the reasons;
(3) The positions of point A and point B change with the change of A. If the moving routes of point A and point B intersect the Y axis at point C and point D respectively, will the length of line segment CD change? If not, find the length of CD; If yes, please explain why.
Answer (1) ①-3; ②d & gt； ﹣4; (2) axis AB ∨ X, for reasons as shown in the analysis; (3) The length of line segment CD varies with the value of m 。
When 8-2m = 0 and m=4, CD = | 8-2m | = 0, that is, point C coincides with point D; When m>4 o'clock, CD = 2m-8; When m<4 o'clock, CD = 8 ~ 2m.
Test and analysis: (1)① When a= 1, d =- 1, and m = 2a-d = 3, we can get the analytical formula of parabola, then get the coordinates of point A and point B, and finally substitute the coordinates of point A and point B into the analytical formula of straight line AB to get the value of k ② Put X =. (2) m=2a+4 can be obtained from d=﹣4, then the analytical formula of parabola is y=﹣x2+(2a+2)x+4a+8, then the vertical coordinates of point A and point B can be obtained by substituting x=a and x=a+2 into the analytical formula of parabola, and finally the vertical coordinates of point A and point B can be judged. (3) Find out the coordinates of point A and point B first, then find out the functional relationship between the movement routes of point A and point B and the letter A, then find out point C (0,2m) and point D (0,4m ~ 8), and then find out the relationship between CD and m. 。
Test analysis:
(1)① when a= 1, d =- 1, m = 2a-d = 3,
So the expression of quadratic function is y =-x2+x+6.
∫a = 1，
? The abscissa of point A is 1, and the abscissa of point B is 3.
Substituting x= 1 into parabolic analytical formula gives y=6, and substituting x=3 into parabolic analytical formula gives y=0.
? A( 1，6)，B(3，0)。
Substitute the coordinates of point A and point B into the analytical formula of the straight line to get:, and get the solution:,
So the value of k is -3.
Substitute x=a+2 into the analytical formula of parabola and get y=a2+6a+8.
? A(a，a2+6a+8)、B(a+2，a2+6a+8)。
∫ The vertical coordinates of point A and point B are the same,
? AB∨x axis.
(3) The length of line segment CD varies with the value of m 。
∵ y =-x2+(m-2) x+2m passes through point A and point B,
? When x=a, y=﹣a2+(m﹣2)a+2m, when x=a+2, y=﹣(a+2)2+(m﹣2)(a+2)+2m,
? A(a,﹣a2+(m﹣2)a+2m)、B(a+2,﹣(a+2)2+(m﹣2)(a+2)+2m).
? The functional relationship of the movement route of point A is y 1=﹣a2+(m﹣2)a+2m, and that of point B is y2=﹣(a+2).
Test center: Quadratic function synthesis problem.
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