20 18 Mathematics Examination Paper for Senior High School Entrance Examination in Guizhou Province I. Multiple choice questions
There are *** 12 small questions in this big question, each with 4 points and ***48 points. Only one of the four options given in each small question meets the requirements of the topic.
1. The logo on the rice packaging bag indicates that this bag of rice is very heavy ()
A.B. C. D。
There are positive and negative test sites.
Analysis can get the result by defining and calculating the opposite meaning quantity.
Solution: +0. 1 means exceeding the standard10kg0.1kg; ? 0. 1 means that it is 0. 1 kg less than the standard1kg. So bagged rice is very heavy.
So choose a.
2. Domestic off-road vehicles? BJ40？ Which number or letter is both a centrosymmetric figure and an axisymmetric figure ()
A. 4th century BC
The symmetrical figure is in the center of the test center; Axisymmetric graph.
According to the concepts of axisymmetric figure and central symmetric figure, the analysis problem is solved.
Solution: A, it is an axisymmetric figure, not a centrally symmetric figure, so the option is wrong;
B, not axisymmetric graphics, not central symmetry graphics, so the option is wrong;
C, not axisymmetric graphics, not central symmetric graphics, so the option is wrong;
D, is an axisymmetric figure, but also a central symmetric figure, so the option is correct.
Therefore, choose: d.
3. The following formula is correct ()
A.B.
C.D.
Addition and subtraction of algebraic expressions.
The analysis is solved according to the addition and subtraction algorithm of algebraic expressions.
Solution:
C, using the law of addition exchange, so the option is correct;
So choose: C.
4. As shown in the figure, in the trapezoid,, ()
A.B. C. D。
The nature of parallel lines in test sites.
Analysis can be obtained by two parallel lines and complementary internal angles on the same side.
Solution: ∫AB∨CD, A=45？ ,
ADC= 180？ -? A= 135？ ;
Therefore, choose: B.
The commentary on this topic examines the nature of parallel lines; Remember that two straight lines are parallel, and the complementary internal angles are the key to solving the problem.
5. It is known that the scores of four people in the group are 90, 60, 90 and 60 respectively, and the scores of four people in the group are 70, 80, 80 and 70 respectively. Which of the following statistical knowledge is more suitable for analyzing and distinguishing two groups ()?
A. Average B. Median C. Mode D. Variance
Test site variance; Average; Median; majority
According to the analysis of group and group scores, find the median, average, mode and variance difference, and then make a judgment.
Solution: Group: average =75, median =75, mode =60 or 90, variance =225.
Group: average =75, median =75, mode =70 or 80, variance =25.
So choose D.
6. The solution set of inequality on the number axis is correct ().
The test site solves the one-dimensional inequality; Represent the solution set of inequality on the number axis.
According to the method of solving inequality, the solution set of inequality can be obtained, so as to know which option is correct.
Solution:
So choose C.
7. The price of domestic large aircraft predicted by mathematical modeling is (unit: USD): 5098,5099,5001,5002,4990,4920,5080,501,490 1, 4902.
A. 5003 BC
Average number of test points
Analysis is based on knowledge points: add or subtract a certain number A in a group of data at the same time, and add or subtract a certain number A in the average value to simplify calculation.
Solution: data 5098, 5099, 500 1, 5002, 4990, 4920, 5080, 50 10, 490 1, 4902, subtract 5000 to get new data: 98, 99, 4902.
Average number of new data: 0.3
? Average value of raw data: 5000.3
So choose a.
8. Make the function meaningful independent variable value range is ()
A.B. C. D。
Test center function, quadratic root
According to the knowledge point: quadratic square root, the analysis is solved by square root.
explain
Solution: 3-x? 0
x？ three
So choose C.
9. Known quadratic function image as shown in the figure, then ()
A.B. C. D。
The image of the quadratic function of the test center.
By analyzing and judging the opening direction, symmetry axis and intersection point with Y axis of quadratic function image, the solution is obtained.
Solution: The parabolic opening knows that a 0, b>0 and option B match.
So choose B.
This question examines the quadratic function image, and mastering the relationship between function image and coefficient is the key to solving the problem.
10. The two sides of the rectangle are respectively, and the following data can form a golden rectangle ().
A.B. C. D。
The test center is in a prime location.
The aspect ratio of the golden rectangle, that is, the golden section ratio, is analyzed.
Solution: a:b= in option D.
So choose D.
1 1. In the geometry placed on the desktop, the difference between the front view and the left view may be ().
A. cylinder B. cube C. sphere D. upright cone
Three views of simple geometry in test sites.
According to the analysis, the front view is the main view, the left view is the left view, and the top view is the top view, so the answer can be obtained.
Solution: b, the front view and left view of the cube may be different;
Therefore, choose: B.
Note This topic studies three views of simple assemblies. The front view is the main view, the left view is the left view, and the top view is the top view.
12. If the included angle between two sides of a triangle is and satisfies the equation, the length of the third side is ().
A.B. C. D。
20 18 Mathematics Examination Paper II of Guizhou Senior High School Entrance Examination. fill (up) a vacancy
(5 points for each question, out of 40 points, fill in the answer sheet)
13 China? Dragon? The diving depth of the submersible is 7062 meters, which is expressed as meters by scientific counting method.
Try some scientific symbols? Represents a bigger number.
The expression of analytical scientific notation is a? 10n, where 1? | a |< 10, n is an integer. When determining the value of n, it depends on how many digits the decimal point moves when the original number becomes a, and the absolute value of n is the same as the number of digits the decimal point moves. 1, n is nonnegative; When the absolute value of the original number
answer
Solution: 7062=7.062? 103,
Comment on this question and investigate the expression of scientific notation. The expression of scientific notation is a? 10n, where 1? | a |< 10, where n is an integer, the key is to correctly determine the value of a and the value of n.
14. Calculation: 20 17? 1983 .
Test the square difference formula.
Analyze the deformation of 20 17 and 1983, and then apply the square difference formula.
answer
Solution: 20 17? 1983=
On the flexible application of the formula of mean variance in simple calculation.
15. Definition:,,, If, then.
Test some new definition operations.
A new definition operation of analysis: a set representing all the numbers of two sets.
answer
Solution:
Calculate the evaluation according to the definition given by the topic.
16. As shown in the figure, in a square, the vertices of an equilateral triangle are on the side and on the top respectively.
Test squares, equilateral triangles and congruent triangles.
Analysis proves that △ Abe △ ADF, get? BAE= 15？ , 75?
answer
Solution: Square
? AD=AB，？ Bad =? B=？ D=90？
equilateral triangle
? AE=AF，？ EAF=60？
? △ABE?△ADF
BAE=？ DAF= 15？
AEB=75？
Comment on memorizing the properties of squares and equilateral triangles, and congruent triangles's judgment theorem and using it flexibly.
17. The solution of the equation is.
Solution of score equation of test center.
The fractional equation analysis is transformed into an integral equation, and the solution of the integral equation is found, and then it is substituted into X2 ~ 1 for testing.
Solution: multiply both sides by x2﹣ 1 to get: 2﹣(x+ 1)=x2﹣ 1.
Finishing and simplifying
x2+x-2=0
Solution: x 1 =-2, x2= 1.
Test: when x =-2, x =-3 =-5? 0, when x= 1, x2- 1 = 0,
Therefore, the solution of the equation is x =-2,
So the answer is: -2.
18. As shown in the figure, in the parallelogram, the diagonal line intersects the point, take a point on the extension line of, and the connecting line intersects the point. If,,, then.
Test center parallelogram, similar triangles.
Analysis and utilization of parallelogram properties and two congruences of AF.
Solution: point o is OG//AB,
In the parallelogram
? AB=CD=5，BC=AD=8，BO=DO
∫OG//AB
? △ODG∽ △BDA and similarity ratio are 1:2, △OFG∽△EFA.
? OG= AB=2.5，AG= AD=4
? AF:FG=AE:OG=4:5
? AF= AG=
19. If white chess is known to fly, the coordinates of black chess spire and black chess are (,).
Test the rectangular coordinate system of the central plane.
Analyze the foundation, establish the plane rectangular coordinate system, and then find the black chess coordinate.
explain
Solution: According to,, establish a plane rectangular coordinate system, as shown in the figure.
? C(- 1， 1)
20. The sum of the first item calculated is.
Test center series.
The original formula is analyzed and deformed, and calculated by sequence formula.
explain
Solution:
20 18 Mathematics Examination Paper III of Guizhou Senior High School Entrance Examination. solve problems
(This big question is ***6 small questions, with a score of ***62. The solution should be written in words, proof process or calculation steps. )
2 1. Calculation: (1);
(2) .
Calculate the actual number of test sites; Zero exponential power; Negative integer exponential power; Trigonometric function value of special angle.
The analysis of this topic involves five test sites: absolute value, quadratic root simplification, trigonometric function value of special angle, negative exponential power and zero exponential power. When calculating, each test center needs to be calculated separately, and then the calculation result is obtained according to the real number algorithm.
explain
Solution:
22. As shown in the figure, in a square grid with a side length of 1, all vertices are on the grid.
(1) Draw the center symmetry about the origin, and write the coordinates of each vertex directly.
(2) Find the path from point rotation to point (the result remains unchanged).
Test center coordinates and graphic change-rotation (center symmetry); Calculation formula of arc length.
Analysis (1) Draw a figure and write the coordinates by using central symmetry; (2) Calculate the path from point to point through the arc length calculation formula.
Solution: (1) The graph is as shown in the figure.
On the Dragon Boat Festival, Xiaoming brought four zongzi (all the same except for their different tastes), two of which are jujube-flavored and the other two are ham-flavored. He intends to divide it equally between Xiaohong and Xiaogang.
(1) Please use a tree diagram or list to show all the possibilities for Xiaohong to get two zongzi.
(2) Please calculate the probability that the two zongzi that Xiaohong got are just the same taste.
Draw a tree diagram or list at the test center and find the probability.
Note when analyzing (1) drawing a tree diagram or list: not all cases; (2) 12 cases, 4 cases had the same taste.
Solution:
24. During the construction of Liu 'an (Liupanshui Anshun) intercity high-speed railway, Team A laid 100m more rails every day than Team B, and the distance laid by Team A for five days was exactly equal to the distance laid by Team B for six days. If Team A is set to spread rice every day, Team B will spread rice every day.
(1) List the binary linear equation according to the meaning of the question;
(2) Know how many meters each construction team of Party A and Party B lays every day.
The test center lists binary linear equations to solve application problems.
With the analysis that Team A lays more rails 100m than Team B every day (1), X-Y =100; The distance of team A laying for 5 days is exactly equal to the distance of team B laying for 6 days. By solving the equations, 5x=6y(2) is obtained.
Solution:
25. As shown in the figure, yes is the diameter, the point is at the top, and yes is the midpoint, which is the fixed point on the diameter.
(1) Draw and determine the position of the minimum hour point with a ruler (there is no writing method, but traces of drawing are reserved).
(2) Find the minimum value.
The test center is round, and the shortest route is the problem.
Analyze (1), draw the symmetry point of point A about MN, and connect point B to get point P.
(2) use it? AON=？ =60? And is the midpoint of the arc AN, BON=30? , so? ON=90？ Then find the minimum value.
Solution:
26. Known functions, k and b are the sum of integers.
(1) Discuss the values of b and k 。
(2) Draw all the images of the two functions respectively. (No list required)
(3) The number of intersections of summation.
Linear function of test center, inverse proportional function, classified discussion idea, graphic combination idea.
Analysis (1)∵, discussed in four cases.
(2) Discuss the values of K and B by classification and draw pictures respectively.
(3) Using images to find four intersections.
Solution:
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