(Time:120min, full mark:120min)
Dear students, this paper will once again record your confidence, composure, wisdom and gains. Please carefully examine the questions, read them clearly and ask for serious answers. I believe I can do it.
The title 12345 is divided into six additional questions.
Take the lead
First, fill in carefully: (3 points for each question, 30 points * * *)
1, No.2 in the fifth row of the cinema can be represented by (5,2), and (7,4) represents No.4 in the seventh row.
2. The positive integer solution of inequality -4x ≥- 12 is x≤3.
3. In order to be meaningful, the range of X is x≥4.
In order to prevent the deformation of an old wooden door, the carpenter nailed a batten on the back of the wooden door. The reason is that triangles are stable.
5. As shown in the figure, if ∠ A = 60 and ∠ B = 30, then ∠BCD=90.
6. If one side is equal to 5 and the other side is equal to 8, the circumference of an isosceles triangle is 18 or 2 1.
7. As shown in the figure, please add a condition to make AD BC, ∠EAD=∠EBC.
8. If the cube root of a number is itself, then the number is 1 or 0.
9. The coordinate of point P (-2, 1) after moving up by two units is (-2, 3).
10. Last year, a school had 1000 students, an increase of 4.4% over last year, of which 6% were boarding students and 2% were day students. How many boarding students and day students were there in this school last year? Suppose there were x boarding students and y day students last year, then the equations can be listed as.
Second, choose one item carefully: (3 points for each question, ***30 points)
1 1, the following statement is correct (d)
A, the same angle is equal; B, on the same plane, if a⊥b, b⊥c, then ⊥c.
C, isometric is diagonal; D, in the same plane, if a‖b, b‖c, then a ‖ c.
12. Observe the following patterns. Among the four patterns A, B, C and D, the pattern (1) can be translated into get (C).
13, with the following statement:
(1) irrational number is an inexhaustible number; (2) Irrational numbers are infinitely cyclic decimals;
(3) Irrational numbers include positive irrational numbers, zero irrational numbers and negative irrational numbers; (4) Irrational numbers can be represented by points on the number axis.
The correct statement is ()
A. 1
14, if the number of sides of a polygon increases from 3 to n, the degree of the sum of its outer angles (b)
A. add B. reduce C. change D. to (n-2) 180?
15, someone went to the tile shop and bought a polygonal tile with a seamless floor. The shape of the tile he bought can't be (c).
A, equilateral triangle; B, square; C, regular octagon; Regular hexagon
16, as shown in the figure. In the following reasoning, the correct one is (c).
A.∵∠a+∠d = 180 ,∴ad‖bc； b .∫≈c+∠d = 180 ,∴ab‖cd；
C.∵∠a+∠d = 180 ,∴ab‖cd； d .∫≈a+≈c = 180 ,∴ab‖cd
17, the equation 2x-3y = 5, x+= 6, 3x-y+2z = 0, 2x+4y, 5x-y > 0 is a binary linear equation ().
A. 1
18. In order to protect the ecological environment, a county in Shaanxi Province responded to the national call of "returning farmland to forests" and changed part of cultivated land into forest land. After the change, the forestland area and cultivated land area * * * are 180 square kilometers, and the cultivated land area is 25% of the forestland area. In order to find out how many square kilometers the forestland area and cultivated land area are after the change. Let the changed cultivated land area be x square kilometers and the forestland area be y square kilometers. According to the meaning of the question, list the following four equations, of which the correct one is ().
A B C D
19, the solution set of inequality group is ()
A.x & lt-3 b . x & lt； -2c .-3 & lt； X<-2 D. No solution
20. If the solution set of the inequality group is-1≤x≤3, the figure indicates that it is correct ().
Third, answer questions: (geometry part 2 1 ~ 24 questions. ***20 points)
2 1. Xiaoming's home is in A, and he needs to build a road to get water by the river. Please help him design a shortest route and find out the distance from Xiaoming's home to the river. (The ratio is 1: 20000) (3 points)
22. This is a schematic diagram of a zoo tour. Try to design a method to describe the location of each scenic spot in this zoo map and draw a picture to illustrate it. (6 points)
23. Fill in the blanks by reasoning: (6 points)
As shown in the figure, ef ‖ ad, ∠ 1 = ∠ 2, ∠ BAC = 70. Complete the process of finding ∠AGD.
Because EF‖AD,
So ∠ 2 = _ _ _ _ _ (_ _ _ _ _ _ _ _).
Because ∠ 1=∠2
So ∠1= ∠ 3 (_ _ _ _ _)
So AB \\_ _ _ _ _ _(_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
So ∠ BAC+_ _ _ =180.
(___________________________)
Because < BAC = 70.
So ∠ AGD = _ _ _ _ _ _
24. As shown in the figure, in △ ABC, AD and AE are bisectors of the height and angle of △ ABC respectively. If ∠ b = 30,
∠ C = 50。 (6 points)
(1) Find the degree of ∠DAE. (2) What is the relationship between ∠ DAE and ∠C-∠B? (No proof required)
Solution: (1) ∵∠ B = 30 ∠ C = 50.
∴∠A= 100
And AE is the bisector of △ABC.
∴∠BAE=∠CAE=50
∠∠B = 30
And AD is the height of △ABC.
∴∠BAD=60
∴∠DAE=∠BAD-∠BAE
= 10
Fourth, answer questions: (
25. Solving equations and inequalities (group): (10, 3 points for each question)
( 1)
(2) Solving inequality 2x- 1
(3) (4) .
V. Application problems:
26. Calculate the price of each kitten and puppy according to the given information. (4 points)
Buy a * * * to 70 yuan,
Buy a 50 yuan.
27, a math contest ***20 questions. Get 10 for each question correctly, and deduct 5 points for wrong or no answer. Answer a few questions wrong or not at most, and the score can be no less than 82 points. (4 points)
Sixth, additional issues.
28, the shape of a part as shown in the figure, according to the rules ∠A=90? ，∠ C=25？ ，∠B=25？ , check the measured BCD = 150? , judge that the part is unqualified, and explain the reason of the unqualified part with the knowledge of triangle. (3 points)
29. During May Day, the central shopping mall held a preferential promotion. The mall sold 96 sets of 29-inch and 25-inch color TVs at 20% discount and 30% discount respectively, and * * * got 184400 yuan. It is known that the original price of 29-inch color TV is 3000 yuan, and the original price of 25-inch color TV is 2000 yuan. How many 29-inch and 25-inch color TVs do you sell? (6 points)
30. (6 points for this question) Observation
Namely;
Namely;
Guess: what is equal to? Verify your guess through calculation.
3 1, as shown in figure AB‖CD, and discuss the relationship between ∠APC and ∠PAB and ∠PCD in the following four figures respectively. Please select an obtained relationship to explain. (It is not difficult to add auxiliary lines appropriately) (6 points)
( 1) (2) (3) (4)
Reference answer:
1. Fill in the blanks: (3 points for each question, ***30 points)
1, line 7, No.4
2、x≤3
3、x≥4
4. Stability of triangles
5、9
6, 18 or 2 1
7.∠EAD=∠B(∠CAD=∠C or ∠ Bad+∠ B = 180).
8、 1,0,- 1
9、(-2,3)
10.
Second, multiple-choice questions (3 points for each question, ***30 points)
1 1、D 12、C 13、C 14、C 15、C 16、C 17、A 18、B 19、A 20、D
Third, answer questions.
2 1, as shown in the figure, the intersection point A is the point where AB is vertical to the river and L is vertical.
Measuring distance AB=2. 1cm.
Actual distance =2. 1×20000
= 42,000 cm
=420 meters
A: The shortest actual distance from Xiaoming to Xiaohe is 420 meters.
22. Establish a rectangular coordinate system with the south gate as the origin, the horizontal right as the positive direction of the X axis and the vertical as the positive direction of the Y axis, and mark the origin and unit length (1 point).
South gate (0, 0); Amphibians (41); Birds (3, 4); Lions (-4, 5), horses (-3, -3) (positions are expressed in ordered pairs, each pair is 1 min).
23, empty ∠3 in turn (two straight lines are parallel and the same angle is equal).
∠3 (two generations)
DG (internal dislocation angles are equal and two straight lines are parallel)
∠AGD (complementary angle of two parallel lines with internal angles)
∠AGD= 1 10
24 、( 1) ∵∠B=30 ∠C=50
∴∠A= 100
And AE is the bisector of △ABC.
∴∠BAE=∠CAE=50
∠∠B = 30
And AD is the height of △ABC.
∴∠BAD=60
∴∠DAE=∠BAD-∠BAE
= 10
∴∠DAE= 10
(2)∠C - ∠B=2∠DAE
Fourth, answer questions.
25. Solve equations, inequalities and inequality groups and calculate real numbers.
( 1)
(2) x>-7
(3)x