Subject: Mathematics Lingyang Middle School Guo
First, multiple-choice questions (3 points for each question, *** 18 points)
1. Three straight lines intersect in pairs, and * * * has an antipodal angle ().
A6 to B5 to C3 to D4
2. It is known that the binary linear equation 3x-y= 1, and when x=2, y is equal to ().
a . 5b-3c-7d
3 If point M( 1+a, 2b- 1) is in the second quadrant, then the quadrant where point N(a- 1, 1-2b) is located is ().
A first quadrant b second quadrant c third quadrant d fourth quadrant
4 Among the following angles of 360,540,1440,600, () may be the sum of the inner angles of a polygon.
A 1 B2 C3 D4
5 The ratio of male to female in a school is 7:5. When making a sector statistical chart, the central angle of the sector corresponding to boys is ().
A70 B50 C2 10 D 150
6 with the following groups of line segments as edges, can form a triangle is ().
A 15cm，30cm，45cm B30cm，30cm，45cm
C30 cm, 45 cm, 75 cm D30 cm, 45 cm, 90 cm
I. Fill in the blanks (3 points for each question, ***27 points)
Seven students 100 in this school were selected to investigate the time for seventh-grade students to do math homework on weekends. The overall survey is (), the individual is (), and the sample size is ().
8 It is known that there is a point A on the Y -axis, and its coordinate is (2a+ 1,-a), so the coordinate of point B which is symmetrical about the X-axis is ().
The two sides of the two corners are parallel respectively. If one angle is 30 times smaller than the other, the degrees of the two angles are respectively
( )
10 If two regular polygon tiles are embedded in the ground (non-overlapping and seamless), then these two regular polygons may be ().
1 1 Supermarket In order to publicize the declining price of Lenovo computers year by year, do you think it is best for supermarkets to use () statistical charts to represent data?
As shown in figure 12, if the straight lines A || B, ∠ 1 = 28 and ∠ 2 = 50, then ∠A =∞ (figure 12).
13 Xiaoming is going to buy pens and notebooks with 24 yuan money. In view of 4 yuan for each pen and 2 yuan for each notebook, he bought three notebooks, so he can buy at most () pens.
14 as shown in the figure, it is known that AB, CD and EF are parallel to each other, and ∠ Abe = 70, ∠ ECD = 150, then ∠BEC= ().
(DrawingNo. 14) (DrawingNo. 15)
15 as shown in the figure, in △ABC, if AD bisects ∠BAC and intersects with BC at point D, ∠ B = 40 and ∠ Bad = 30, then ∠C's degree is ().
Three solutions (***55 points)
16(8 points) to solve the equation.
① 3x+4y= 1 1 ②
5x-y=3
17 (7 points) solves the inequality group, indicating that the solution set is on the number axis.
18 (7 o'clock) In the plane rectangular coordinate system, the vertex coordinates of quadrilateral ABCD are A( 1, 1), B (5,0), C (3,3), D (2,4). Find the area of quadrilateral ABCD.
19 (7 points) As shown in the figure, it is known that ∠ABG and ∠BGC are complementary, and ∠ 1=∠2, then ∠E=∠F? Please provide a justification for the answer.
20 (7 points) A supermarket held a celebration for the "fourth anniversary of its opening" and sold two kinds of goods, A and B, at a discount. Before the discount, you need 84 yuan to buy five items A and B; It costs 108 yuan to buy six A's and B's, while it only costs 960 yuan to buy 50 A's and 50 B's during the celebration. How much less is this than no discount?
2 1 (9 points) The school carries out sunshine sports activities, and the students are more active in participating in physical exercise. In order to know their average weekly exercise time, Wang randomly surveyed 50 students at school and made the following frequency distribution table and fan chart.
Frequency of group exercise time (hours/week)
a 1.5≤t < 3 1
B3≤t < 4.5 2
C4，5≤t < 6m
D6≤t < 7.5 20
e 7.5≤t < 9 15
Feet ≥9n
Answer the following questions based on the above information:
( 1)m=()，n =()；
(2) In the fan-shaped statistical chart, the degree of the central angle occupied by Group D is ();
(3) There are 3,000 students in the school. How many students are estimated to have an average physical exercise time of not less than 6 hours per week?
22 (10) A factory uses rectangular and square cardboard as shown in Figure A to make vertical and horizontal rectangular shapes without covers as shown in Figure B.
Vertical carton horizontal carton
Figure a figure b
(1) At present, there are 162 pieces of square cardboard and 340 pieces of rectangular cardboard. If you want to make two kinds of cartons *** 100, make X vertical boxes.
① According to the meaning of the question, complete the following table:
Vertical carton (piece) Horizontal carton (piece)
x
Square cardboard (sheet) 2 (100-x)
4x rectangular cardboard (sheet)
② According to the production quantity of two kinds of cartons, what kinds of production schemes are there?
(2) If there are 162 square cardboard and one rectangular cardboard, and the cardboard is just used up, it is known that 290 < a < 306, then the value of a is (). (Just write one)
The answer to the seventh grade mathematics final examination paper.
1——6 aaccb
All the seventh-grade students in a school are doing their math homework on weekends. The cost that every seventh-grade student in a school spends on math homework on weekends is 100.
8 (0,-0.5)
9 70, 1 10 or 30,30.
10 Regular triangles and squares have different answers.
1 1 polyline
12 22
13 4
14 40
15 80
16 (1) solution: ②×4, and 20 ⅹ-4Y = 12 ③ solution: ③-①, and Y=3.
①+③, you get 23 ⅹ = 23. Substitute Y=3 into ② and you get Z=5.
Solve this equation and get X= 1. Substitute Z=5 into ① to get X = 1.
Substituting ⅹ = 1 into ② to get Y=2, then the solution of this equation group is X= 1.
So the solution of this system of equations is ⅹ = 1Y = 3.
Y=2 Z=5
17 solution: solve inequality ① and get X≤3.
Solve inequality ② and get x < 0.5-4.
-Six points
So the solution set of inequality group is x < 0.5-7 points.
18 After solving point D, DE⊥X axis is at point E, CF⊥X axis is at point E, AG⊥X axis is at point G .. -2 points.
S quadrilateral ABCD=S trapezoid aging +S trapezoid DEFC+S △ CFB-S △ AGB-5 points.
=( 1+4)× 1÷2+(3+4)× 1÷2+3×2÷2- 1×4÷2
= 7-7 points
19 solution: ∠E=∠F for the following reasons:-1.
∫∠ABG+∠BGC = 180
∴ab∨CD-3 points
∴∠ABG=∠BGD
∠∠ABG =∠ 1+∠3，∠BGD=∠2+∠4
∴ ∠ 1+∠3 =∠2+∠4
∵∠ 1=∠2
∴∠ 3 = ∠ 4-5 points
∴BE∥FG
∴∠ E = ∠ F-7 o'clock
Solution 20: Let's assume that before the discount, each commodity of commodity A is X yuan, and each commodity of commodity B is Y yuan. -1 min
5X+Y=84 gives X= 16.
6x+3y = 108y = 4-4 points.
∴ 50x+50y = 50x16+4 =1000 yuan.
∴ 1000-960 = 40 yuan -6 points.
There is no discount until it arrives, 40 yuan.
2 1 (1) 8 4-2 points
2 144-5
(3) Solution: (20+ 15+4)÷50×3000=2340 (name) -8 points.
A: It is estimated that about 2,340 students in this school have an average physical exercise time of no less than 6 hours per week. -9 points
22 solution: ① 100-x
X
3 (100-x)-3 points
② The solution of x+2 (100-x) ≤162 is 38≤X≤40.
4x+3 (100-x) ≤ 340-6.
X is an integer, ∴X is 38, 39, 40.
∴ There are three production schemes ① 38 vertical schemes and 62 horizontal schemes.
② 39 in the vertical direction and 6/kloc-0 in the horizontal direction.
③ Vertical mode 40, horizontal mode 60-8 points.
2 293 or 298 or 303- 10.
Analysis of the final examination paper of seventh grade mathematics
I. Guiding ideology
At the end of this semester, the mathematics test paper proposition adheres to the spirit of curriculum reform, strengthens the examination of students' thinking quality, and provides a larger space for all candidates to play. Based on the curriculum standards and teaching materials, students' basic knowledge, basic skills, basic methods, calculation ability, logical thinking ability, and their ability to analyze and solve practical problems by using the learned mathematical knowledge and methods are examined.
Second, the examination paper structure
Question type ratio: 22 questions in the test paper * * *, full score 100, time 100 minutes. From chapter 5 to chapter 10, the score ratio of knowledge field is about19:13:12: 21:17:18, which is easy to ask.
Third, the characteristics of the test paper
(1) pays attention to the examination of basic knowledge and skills. Generally, only the direct application of basic knowledge is tested, and knowledge accumulation is not engaged; For basic skills, don't test complicated contents, which is of guiding significance to the current mathematics teaching, can reduce the burden on students and avoid simple and mechanical repeated training.
(2) It reflects the examination of students' practical ability. For example, 10, 1 1, 20, 2 1, 22 are all practical problems, which provide students with a space to reflect their practical ability, let them solve practical problems around them, realize the value of knowledge, and thus stimulate their enthusiasm for learning.
(3) Pay attention to the examination of mathematical thinking methods.
The examination paper focuses on the important thinking methods embodied in junior high school textbooks, such as the combination of numbers and shapes and the transformation of ideas.