9.(3 points) The World Garden Expo will be held in Jinzhou, China from May to June, 20 13. This is the world's first maritime world garden Expo, and its theme is: city and ocean, harmonious future. In this English sentence, the frequency of the letter A is 3.
Test sites: frequency and frequency.
Analysis: According to the definition of frequency: the number of times each object appears, just solve it.
Answer: Solution: In? Will the city and the sea be harmonious in the future? Of all the letters in this sentence, the letter? Answer? Appeared three times, so what about the letter? Answer? The frequency of occurrence is 3.
So the answer is: 3.
Comments: This question examines the definition of frequency. The key to solving this question is to grasp that frequency refers to the number of times each object appears.
10.(3 points) Real number 3. 14,?? There are three irrational numbers.
Test center: irrational number.
Analysis: irrational numbers include three aspects: ① Including? Yes, the roots that can't be opened can be judged according to the above contents.
Answer: Solution: The irrational number is,,? ***3,
So the answer is: 3.
Comments: This topic examines the application of the definition of irrational numbers. Note: Irrational numbers refer to infinite cyclic decimals.
1 1.(3 points) In the same plane, if lines B and C are perpendicular to line A, the positional relationship between lines B and C is parallel.
Test center: vertical line.
Analysis: Answer according to the fact that two straight lines are perpendicular to the same straight line in the same plane and two straight lines are parallel.
Answer: Solution: ∵ In the same plane, B? a，c？ One,
? b∑c，
That is, the positional relationship between straight lines b and c is parallel.
So the answer is: parallel imports.
Comments: This question examines the knowledge points of judging parallel lines. Topic: In the same plane, two straight lines are perpendicular to the same straight line, so the two straight lines are parallel.
12.(3 points) (20 1 1? In the plane rectangular coordinate system, if the distance between point m (1, 3) and point n (x, 3) is 5, then the value of x is ﹣4 or 6.
Test Center: Coordinate and Graphic Properties.
Special topic: calculation problems.
Analysis: If the vertical coordinates of point M and point N are equal, then the straight line MN is on a straight line parallel to the X axis. According to the distance between two points, the equation | x- 1 | = 5 can be listed, and the value of x can be obtained.
Solution: Solution: The distance between point M (1, 3) and point N (x, 3) is 5.
? |x﹣ 1|=5，
X =-4 or 6 years old.
So the answer is: -4 or 6.
Comments: This topic is entitled Basic Question, which examines the nature of coordinates and graphics. When the vertical coordinates of two points are equal, the two points are on a straight line parallel to the X axis.
13.(3 points) The integer solution of the inequality group is 0, 1, 2, 3.
Test site: integer solutions of unary linear inequalities.
Special topic: calculation problems.
Analysis: first find the solution set of each inequality in the inequality group, then find its common solution set, and finally find its integer solution.
Answer: Solution:,
From ①, x >1,
From 2, x? 3,
So the solution set of inequality group is-1.
The integer solution of the inequality group is 0, 1, 2, 3.
So the answer is: 0, 1, 2,3.
Comments: This question examines the solution of inequality groups and the determination of integer solutions. To find the solution set of inequality groups, we should follow the following principles: take the big with the big, take the small with the small, find the small in the middle, and the big and small can't be solved.
14.(3 points) The sum of squares of two numbers A and B is not less than twice the product of these two numbers, and it is expressed as ι 2+B2? 2b。
Test center: abstract a linear inequality from practical problems.
Analysis: According to the sum of squares of two known numbers A and B, and then get twice the product of these two numbers, you can get the answer.
Solution: Solution: According to the meaning of the problem:
ɑ2+b2？ 2b。
So the answer is: ι 2+B2? 2b。
Comments: This question mainly examines the unary linear inequality abstracted from practical problems, and finding the square of two numbers and the product of two numbers according to the known results is the key to solving the problem.
15.(3 points) When the straw sucks the beverage in the can, as shown in the figure,? 1= 1 10? And then what? 2= 70 degrees. (The top and bottom surfaces of the tank are parallel to each other)
Test site: the nature of parallel lines; Opposite vertex angle and adjacent complementary angle.
Special topic: application problem.
Analysis: This problem is mainly solved by using two parallel lines, complementary internal angles on the same side and equal vertex angles.
Solution: Solution: Because the top and bottom surfaces of cans are parallel to each other, so? 2 and? The sum of antipodes of 1 is 180? .
Because again? 1 equals its diagonal, so? 2+? 1= 180? , so? 2= 180? ﹣? 1= 180? ﹣ 1 10? =70? .
Remarks: Study the properties of parallel lines and equal vertex angles.
16.(3 points) Xiaohong solved the equations because he accidentally dropped the ink and covered the two numbers ● and ☆. Please try to help her find these two numbers ●= 8, ☆ =-2.
Test site: the solution of binary linear equations.
Special topic: calculation problems.
Analysis: Substitute x=5 into the second equation of the equations to find the value of y, and get the number represented by ☆; Substitute the values of x and y into the first equation to find the result, which is the number represented by ●.
Solution: Solution: Substitute x=5 into 2x﹣y= 12 to get:/kloc-0 ﹣ y =12, which means y=﹣2.
Substitute x=5 and y=﹣2: 2x+y= 10﹣2=8.
Then ●=8, ☆ =-2.
So the answer is: 8; ﹣2
Comments: This question examines the solution of a binary linear equation. The solution of the equation is an unknown number that can make two equations in the equation hold.
Third, answer questions (***3 small questions, full score 12)
17.(4 points) Calculation: +3? ﹣ .
Test center: the operation of real numbers.
Analysis: first calculate the number according to the root of the number, and then calculate it according to the law of mixed operation of real numbers.
Solution: Solution: Original formula =-+6+2.
= .
Comments: This question examines the operation of real numbers, and knowing the roots of numbers is the key to solving this question.
18.(4 points) The known sum is the solution of the equation Y = AX+B, and the values of a and b are found.
Test site: the solution of binary linear equation.
Analysis: Substitute two groups of solutions into the equation respectively to get the equations about A and B, and then solve them.
Solution: substitute sum into equation y=ax+b,
,
The solutions are a= 1 and b= 1.
Comments: This question mainly examines the definition of the solution of binary linear equations and the basic method of solving binary linear equations.
19.(4 points) Solve the inequality group and express the solution set on the number axis.
Test site: solving a set of linear inequalities; Represent the solution set of inequality on the number axis.
Analysis: Find the solution set of each inequality and the solution set of inequality group.
Answer: Solution:,
∵ Solving inequality ①: x > ﹣2,
Solve inequality ②: x? ﹣
? The solution set of the inequality group is:-2.
On the number axis, the solution set of the inequality group is:
Comments: This topic examines the application of understanding one-dimensional linear inequalities (groups) and expressing the solution set of inequality groups on the number axis. The key is to find the solution set of inequality group according to the solution set of inequality.
4. Answer questions (***3 small questions with 20 questions and 5 points, 2 1 question with 5 points, 22 questions with 7 points, *** 17 points)
20.(5 points) ① Draw △ABC with vertices A(﹣3, ﹣ 1, B (1, 3) and C (﹣2) in the plane rectangular coordinate system.
(2) if the triangle translation, the corresponding point of b is b? Coordinate is (-1, 0), try to draw the △A of translation? b？ c？ .
3 looking for △A? b？ c？ The area of.
Test center: drawing-translation conversion.
Special topic: drawing problems.
Analysis: (1) Find out the positions of points A, B and C according to the plane rectangular coordinate system, and then connect them in turn;
(2) According to the grid structure, the corresponding points A and C are found after translation. 、C？ Position, and then connect in order;
(3) using △A? b？ c？ Subtract the area of three small right-angled triangles from the area of a rectangle, and get the solution through column calculation.
Solution: solution: (1)△ABC as shown in the figure; (2)△A？ b？ c？ As shown in the figure; (3)△A？ b？ c？ Area =5? 5﹣ ? 4? 4﹣ ? 1? 5﹣ ? 1? five
=25﹣8﹣ ﹣
= 17﹣5
= 12.
Comments: This question examines the key to solving the problem by using translation transformation to draw, mastering the grid structure skillfully and accurately finding out the corresponding point position.
2 1.(5 points) There are 2870 students in a middle school. In order to further enrich students' after-school life, the school plans to adjust interest activity groups and conduct a sample survey for this purpose. The statistical chart drawn according to the collected data is as follows (incomplete):
Please complete the following questions according to the information provided in the picture:
(1) in the figure 1,? Computer? The central angle of the part is 126 degrees;
(2)*** Selected Graduates 80;
(3) in figure 2,? Sports? Some graphics are complete;
(4) hobbies? Painting and calligraphy? 10% of the respondents;
(5) It is estimated that 287 students have hobbies? Painting and calligraphy? .
Test center: bar chart; Estimate the population with samples; Department statistical chart.
Special topic: calculation problems.
Analysis: (1) by? Computer? Multiply the percentage of parts by 360 to get the result;
(2) by? Computer? Divide the number of students by the percentage to get the total number of students surveyed;
(3) Calculate by subtracting other students from the total number of students? Sports? Part of the number of people, complete the statistical chart;
(4) by? Painting and calligraphy? Divide some students by the total number of students to get the result;
(5) By solving? Painting and calligraphy? Multiply the percentage of this part by 2870 to get the result.
Answer: Solution: (1) According to the meaning of the question: 36035%= 126? ;
(2) According to the question: 28? 35%=80 (person);
(3)? Sports? Part of it is 80% (28+24+8) = 20 people, and the statistical chart is completed.
As shown in the figure:
(4) According to the question: 8? 80= 10%;
(5) According to the question: 2870? 10%=287 (person).
So the answer is: (1)126; (2)80; (4) 10%; (5)287.
Comments: This question examines bar charts and fan charts, and estimates the population with samples. Understanding the meaning of the problem is the key to solve this problem.