Selected final questions and answers of the second volume of junior one mathematics

The following questions are accompanied by four alternative answers, one and only one of which is correct. Please fill in the code of the correct answer in the corresponding question number on the answer sheet above.

1. In an international table tennis singles competition, two players from China, A and B, entered the finals, so the following events are inevitable ().

A. The champion belongs to China. B.the champion belongs to foreign players.

C. The champion belongs to player A of China. D. The champion belongs to player B of China.

2, the following factorization is correct ()

A.B.

C.D.

3. By using the equivalence relation of areas in the graph, some mathematical formulas can be obtained. For example, according to Figure A, we can get the square formula of the sum of two numbers. According to Figure B, the mathematical formula is ().

A.B.

4. As shown in the figure, the following conditions cannot determine that AB∨CD is

(A)3 =∠4(B) 1 =∠5

5. Assuming that the lengths of two sides of a triangle are 4cm and 9cm respectively, which of the following four line segments can be used as the third side?

(a)13cm (b) 6cm (c) 5cm (d) 4cm

6, to reflect the daily temperature changes in Wuhan within a week, appropriate use.

(a) Bar chart (b) Fan chart

7. If a>b, then the following conclusion must be correct.

(A)A-3

(C)ac2 >bc2(D)a2 & gt； b2

8. As shown in the figure, in the right angle △ADB, ∠ d = 90, and c is a point above AD, ∠ degree ∠ACB.

Is (5x- 10), then the value of x can be

10 (B)20

9. Place a pair of triangular wrenches as shown in the figure, and the degree of ∠ 1 is 50 greater than that of ∠2. If ∠ 1 = x ∠ 2 = y,

Then the following equation can be obtained

10. The toy workshop can produce 24 class A toy parts or 12 class B toy parts every day. If one toy part of Class A and two toy parts of Class B can form a complete toy, how to arrange production to assemble the most toys in 60 days? Suppose it takes x days to produce a toy part and y days to produce a toy part, then there are

(A) (B)

1 1. In recent years, the municipal government has invested in building a number of low-rent houses every year, which has improved the housing situation of urban residents with housing difficulties. The following is a line chart of a certain district's annual population and per capita housing area statistics from 2006 to 2008 (per capita housing area = total housing area/total population of this district, unit: ㎡/person).

According to the above information, the following explanations are made: ① the total housing area of the community in 2008 during the three years from 2006 to 2008; ② In 2007, the total residential area in this residential area reached1.728×106m; ③ The growth rate of per capita housing area in this community in 2008 was 4%. Among them, the correct ones are

(A)①②③ (B)①② (C)① (D)③

12 As shown in the figure, the bisectors of AB∨CD, ∠BAC and ∠DCA intersect at the G point.

GE⊥AC is at point E, F is a point on AC, FA=FG=FC, GH⊥CD.

Yu Yi made the following statement:

①ag⊥cg； ② ∠ bag = ∠ CGE; ③S△AFG = S△CFG；

④ If ∠ egh ∠ ech = 2 ∠ 7, ∠ EGF = 50.

What is correct is that

①②③④ (B) ②③④

①③④ (D) ①②④

Second, can you fill it out quickly and accurately? (There are 4 questions in this question * * *, 3 points for each small question, *** 12 points)

13. Convert the equation into an algebraic expression.

14, the inequality means "the difference between a and 5 is not a positive number";

15. As shown in the figure, move △ABC to the right along CB edge to get △DFE, and the intersection of DE and AB is at G point.

∠ A ∠ C ∠ ABC = 1 ∠ 2 ∠ 3，AB=9cm，BF=5cm，AG=5cm，

The shaded area in the figure is cm2.

16, observe the coordinates of the following regular points:

A 1( 1， 1) A2(2，-4) A3(3，4) A4(4，-2) A5(5，7) A6(6，)

A7(7， 10) A8(8，- 1)……，

According to this law, the coordinates of A 1 1 are, and the coordinates of A 12 are.

Three, solve the following problems (this question ***9 questions, ***72 points)

17, (6 points in this question) Solve the equation.

18, (6 points in this question) solving inequalities >; X- 1 and represents the solution set on the number axis.

19, (6 points in this question) As shown in the figure, in the quadrilateral, point E is on BC, ∠ A+∠ ADE = 180, ∠ B = 78, ∠ C = 60, and the number of times to find ∠EDC.

20. (7 points in this question) In response to the call of the state, a school requires primary and secondary school students to exercise 1 hour every day and has carried out various forms of "sunshine sports" activities. Xiao Ming has made statistics on the students' participation in exercise in a class and drew the following numbers: 65,438+0,2.

(1) How many students are there in this class? If there are 1200 people in the whole grade, how many people are estimated to take part in table tennis activities in the whole grade?

(2) Please complete the figure of "table tennis" in Figure 1 and find out the degree of the central angle of the sector representing "football" in the sector statistical chart.

2 1, (subject 7 points) as shown in the figure, in the plane rectangular coordinate system:

(1) Write the coordinates of point A;

(2) translate the line segment OA upward twice, each time by 1 unit,

Then translate the line segment to the left by 2 units to get the line segment O'A' and write it out.

Coordinates of points o' and a' corresponding to points o and a;

(3) Draw two different line segments equal to line segment OA.

22. (8 points in this question) As shown in the figure, AD is divided by ∠BAC, ∠EAD=∠EDA.

(1)∠EAC equals ∠B? Why?

(2) If ∠ B = 50, ∠ CAD ∠E = 1 ∠ 3, the number of times to find ∠E. 。

23. (Question 10) Teachers and students of a school actively donated money and materials to the Wenchuan earthquake-stricken area. After learning that tents were urgently needed in the disaster area, they immediately went to a local tent factory to purchase. There are two kinds of tents, which can accommodate three people, and the price is 160 yuan; /kloc-a large tent for 0/0 people, and the price of each tent is 400 yuan. The school spent 96,000 yuan to buy these two tents, which can just accommodate 2,300 people. The school is going to rent 20 trucks of two models, A and B, and transport the purchased tents to the disaster area urgently. It is known that each truck of A can transport 4 small tents and 1 1 large tents at the same time, and B.

(1) asked the school how many small tents for three people and how many tents for 10 people;

(2) How should the school arrange two types of trucks, A and B, to transport these tents to the disaster area at one time? How many schemes are there?

24. (This question 10) It is known that in △ABC and △XYZ, ∠ A = 40, ∠ Y+∠ Z = 95. Put △XYZ as shown in the figure, so that both sides of ∠X pass through point B and point C respectively.

(1) When △XYZ is placed as shown in figure 1, ∠ABX+∠ACX= degrees;

(2) When △XYZ is placed as shown in Figure 2, the degree of ∠ABX+∠ACX is required, and the reasons are explained;

(3) Can you put △XYZ in a certain position so that BX and CX can share ∠ABC and ∠ACB equally? Please write your conclusion directly.

25. (this question 12 points) as shown in the figure, a and b start from the origin o at the same time. Point A moves in the negative direction of X axis with X unit length per second, and point B moves in the positive direction of Y axis with Y unit length per second.

(1) If it is ∣x+2y-5∣+∣2x-y∣=0, try to find out 1 sec respectively.

Coordinates of point A and point B 。

(2) Let the bisectors of adjacent complementary angles of ∠BAO and ∠ABO intersect at point P,

Q: Will the size of ∠P change during the movement of points A and B? If not,

Change, require its value; If there are any changes, please explain the reasons.

(3) As shown in the figure, extend BA to E, so that the point of ray BF within ∠ABO intersects with the X axis.

C if the bisectors of ∠EAC, ∠FCA and ∠ABC intersect at point g, then point g is regarded as BE.

The vertical line of ∠ is h∠AGH and ∠BGC. What is the relationship?

Please write your conclusion and explain the reasons.

Answer:

I. Choice

The title is123455678911112.

Answer A D B D B C B C D C B A

Second, can you fill it out quickly and accurately? (There are 4 questions in this question * * *, 3 points for each small question, *** 12 points)

13，y=。 14，a-5≤0。 15, . 16, ( 1 1, 16), ( 12)

Three, solve the following problems (this question ***9 questions, ***72 points)

17, solution: from ① to ③... 1.

Substitute ③ into ② to get ... 2 points.

..... 4 points

Get ... 5 points (3 points) as a substitute

The solution of the original equation is ... 6 points.

18, solution:1+2x > 3x-3... 1 point

2x-3x >-3- 1 ...2 points

-x & gt； -4 ...3 points

X< four ... four points.

..... 6 points

19, proof: ∵∠ A+∠ ADE = 180.

∴ab∑de...2 points.

∴∠ CED =∠ B = 78...4 points.

∠ c = 60。

∴∠EDC= 180 -∠CED-∠C

= 180 ―78 ―60

= 42 ...6 points

20. Solution: (1)20÷40%=50 (person) ... 1.

50-20- 10- 15=5 (person)

× 1200= 120 (person) ... 3 points.

There are 50 students in this class. It is estimated that there are 120 students participating in table tennis activities in the whole grade ... 4 points.

(2) (omitted), ... 5 points.

= 72 ...6 points

A: The degree of the fan-shaped central angle representing "football" is 72 degrees ... 7 points.

2 1, (1) A (2, 1)...2 points.

(2) O' (-2,2), A' (0,3) ... 5 points.

(3) Slightly ... 7 points

22. Solution: (1) is equal. The reasons are as follows: ... 1.

Advertising split ∠BAC

∴∠ Bud = ∠ CAD...2 points.

Similarly ∠EAD=∠EDA

∴∠EAC=∠EAD-∠CAD

=∠EDA-∠BAD

= ∠ b...4 points

(2) If ∠ CAD = x, ∠ E = 3 x, ... 5 points.

From (1): ∠ EAC = ∠ B = 50.

∴∠EAD=∠EDA=(x+50)

In △EAD，∠ e+∠ EAD+∠ EDA = 180。

∴ 3 x+2 (x+50) = 180...6 points.

Solution: x = 16...7 points.

∴∠ E = 48...8 points.

(Refer to the standard score of binary linear equations)

23. Solution: (1) Suppose the school purchased X small tents and Y large tents ... 1.

Get ... 3 points according to the meaning of the question.

You got ... 4 points for solving this equation group.

A: The school bought 100 small tents for three people, and 200 10 large tents for 0 people ... 5 points.

(2) Assume that truck A has arranged truck A and truck B has arranged (20-a) trucks.

Get ... 7 points according to the meaning of the question.

The score of solving this inequality group is 15 ≤ A ≤ 17.5...8 points.

* The number of vehicles is a positive integer ∴a= 15 or 16 or 17.

∴20-a =5 or 4 or 3...9 points.

Answer: The school can arrange 15a truck, 5 B truck or 16a truck, 4 B truck or 17a truck or 3 B truck, and these tents can be transported to the disaster area at one time. There are three schemes.

..... 10 point

24. Solution: (1) 235; ..... 3 points

(2)ABX+∠ACX = 45。 The reasons are as follows: ... 4 points.

∠∠Y+∠Z = 95

∴∠ X = 180-(∠ Y+∠ Z) = 85...5 points.

∴∠abx+∠acx= 180-∠a-∠xbc-∠xcb

=180-40-(180-85) ... 7 points.

= 45 ...8 points

(3) There is no ... 10 point.

25. Solution: (1) Solve the equation:

Get: ... 3 points.

∴ A (- 1, 0), B (0 0,2) ... 4 points.