mathematics
This paper is divided into two parts: test paper and additional test paper. Test paper 1 to 6 pages, full mark 100. 10 page test paper plus 7, out of 60 points. The full score of the whole paper is 160, and the examination time is 120 minutes.
Examination paper (*** 100 mark)
Precautions:
1. Before answering the first volume, please be sure to scribble your name, admission ticket number and exam subjects on the machine-readable card with 2B pencil.
2. At the moment of answering the paper, after selecting the answer for each question, blacken the answer label of the corresponding question on the machine-readable card with a pencil. If you need to change it, clean it with an eraser and choose another answer.
3. Candidates who only take graduation exams only need to do papers, and candidates who want to take further studies must complete and add papers.
After the exam, take this paper and machine-readable card back.
The first volume (multiple choice questions ***36 points)
First, multiple-choice questions (this big topic * *12 small topic; 3 points for each small question, 36 points for * * *. Only one of the four options given in each small question meets the requirements of the topic. )
1.(20 1 1 Neijiang, Sichuan 1, 3 minutes) Among the following four real numbers, the number less than-1 is
A.-2b . 0c . 1d . 2
Answer a
2.(20 1 1 Neijiang, Sichuan, 2,3 points) As shown in the figure, put the right vertex of the right triangle on one side of the ruler. If ∠ 1 = 32, the degree of ∠2 is.
32 BC to 58 BC
Answer c
(2011Neijiang, Sichuan, 3,3 minutes) The infrared wavelength emitted by an infrared remote controller is 0.0000094m, which is expressed by scientific notation.
a . 9.4× 10-7m b . 9.4× 107m c . 9.4× 10-8md
Answer a
4.(20 1 1 Neijiang, Sichuan, 4,3 points) Some of the following geometric figures must be axisymmetric.
Sector isosceles trapezoid rhombic right triangle
1。
Answer b
5.(20 1 1 Neijiang, Sichuan, 5,3 points) In order to know the weight of 32,000 students who took the senior high school entrance examination in a city, the weight of 1600 students was randomly selected for statistical analysis. The following statement is correct.
A.32000 students as a whole B. 1600 students' weight as a whole sample.
C. Every student is an individual of the whole D. The above survey is a general survey.
Answer b
6.(20 1 1 Neijiang, Sichuan, 6,3 points) Among the following polygons, what cannot be covered by the ground alone is
A. regular triangle B. square C. regular pentagon D. regular hexagon
Answer c
7.(20 1 1 Neijiang, Sichuan, 7,3 points) The age of the members of the math interest group 12 in a middle school is as follows:
Age (years old)1213141516
No. 14322
Then the average age and median age of the members in this group are respectively
A. 15， 16b
Answer d
8.(20 1 1 Neijiang, Sichuan, 8, 3 minutes) The top view of the geometry composed of some small cubes with the same size is shown in the right figure, and the numbers in the box indicate the number of small cubes in this position, so the front view of the geometry is as follows.
Accelerated business collection and delivery system (adopted by the United States post office)
Answer b
9.(20 1 1 Neijiang, Sichuan, 9,3 points) As shown in the figure, ⊙O is the circumscribed circle of △ABC, ∠ BAC = 60, and if the radius oc of ⊙O is 2, the chord length BC is.
a . 1B。 c . 2d . 2
Answer d
10.(20 1 1 Neijiang, Sichuan, 10, 3 minutes) Gao Xiao goes to school by bike from home. He first went uphill to point A, then downhill to point B, and finally took a flat road to school. The relationship between time and distance is shown in the picture. After school, if he goes back the same way, and the speed of going up, up and down is the same as that of going to school, then the time he needs to get home from school is
14 minutes 17 minutes 20 minutes
Answer d
1 1. (2011Neijiang, Sichuan11,3 points) As shown in the figure, in equilateral △ABC, D is a point on the side of BC, and E is a point on the side of AC.
A.b . 15C。 D.
Answer c
12.(20 1 1 Neijiang, Sichuan, 12, 3 minutes) As shown in the figure, in the rectangular coordinate system, the edge OA of the rectangular ABCO is on the X axis, the edge OC is on the Y axis, and the coordinate of point B is (1, 3). Fold the rectangle along the diagonal AC.
A.(，)b .(，)c .(，)d .(，)
Answer a
Neijiang City 20 1 1 year high school entrance examination and junior high school graduation examination papers
mathematics
Volume 2 (non-multiple choice questions ***64 points)
The second and third questions, total score, total score.
17 18 19 20 2 1
score
Precautions:
1. Volume II, section * * *, answer the questions directly on the test paper with a pen or ballpoint pen.
2. Fill in the items in the sealing line clearly before answering the questions.
2. Fill in the blanks (this big question has four small questions, each with 5 points and * * * 20 points). Please fill in the final answer directly on the line in the question. )
13.(20 1 1 Neijiang, Sichuan, 13, 5 points) "Welcome to high school." Welcome to high school. Of all the English letters in this sentence, the frequency of the letter O is.
answer
14.(20 1 1 Neijiang, Sichuan, 14, 5 minutes) If the circumference of the bottom of the cone is 20π, and the central angle of the fan after the side is unfolded is 120, then the length of the generatrix of the cone is.
Answer 30
15.(20 1 1 Neijiang, Sichuan, 15, 5 minutes) If the score is 0, the value of x should be.
Answer -3
16.(20 1 1 Neijiang, Sichuan, 16, 5 minutes) As shown in the figure, when points E, F, G and H are the midpoints of AD, BD, BC and CA in any quadrilateral ABCD, and the sides of the quadrilateral ABCD at least meet the conditions, the quadrilateral EFGH.
Answer AB=CD
Third, answer the question (this big question is ***5 small questions, ***44 points)
17.(20 1 1 Neijiang, Sichuan, 17, 7 points) Calculation:
Original answer =
18.(20 1 1 Neijiang, Sichuan, 18, 9 minutes) As shown in the figure, put an acute angle of 45 at Rt△ABC, ∠ BAC = 90, AC=2AB, and point D as shown in the figure.
Try to guess the relationship between the number and position of the line segment be and EC, and prove your guess.
Answer be = EC, BE⊥EC
AC = 2AB, and point d is the midpoint of AC.
∴AB=AD=CD
∠∠EAD =∠EDA = 45
∴∠EAB=∠EDC= 135
EA = ED
∴△EAB≌△EDC
∴∠AEB=∠DEC,EB=EC
∴∠BEC=∠AED=90
∴BE=EC,BE⊥EC
19. (201/Neijiang, Sichuan,19, 9 points) Xiaoying and Xiaoming are going to watch the dragon boat race together, but because of something at home, they have to stay alone, so they use games to decide who will take part in the dragon boat race. The rules of the game are: put two white and 1 yellow ping-pong balls in opaque pockets, except for the color. During the game, Xiaoying first randomly takes out 1 ping-pong ball from his pocket, records the color, puts it back and shakes it evenly, and then Xiaoming takes out 1 ping-pong ball from his pocket and records the color. If the ping-pong balls touched by the two brothers and sisters are the same color, Xiaoying wins, otherwise Xiaoming wins.
(1) Please use the method of tree diagram or list to represent all possible outcomes in the game.
(2) Are the rules of the game fair to both sides? Please provide a justification for the answer.
Answer (1) White is white, and white is yellow.
White is white, white is white and yellow.
Yellow, yellow, white, yellow, white and yellow.
White, white and yellow
* * * There are nine results.
(2) Both sides are unfair.
Because Xiaoying's probability of winning is 0 and Xiaoming's probability of winning is 0, it is unfair.
20.(20 1 1 Neijiang, Sichuan, 20,9 points) Flying kites is a favorite sport. On Sunday morning, Xiaoming flew a kite in Continental Square. As shown in the picture, when he was in A, he accidentally hung the kite on the top of a tree, and the kite was fixed on D. At this time, the angle between the kite line AD and the horizontal line was 30. In order to facilitate observation, Xiao Ming quickly moved forward and took up the line to reach B, which is 7 meters away from A. At this time, the included angle between the kite line BD and the horizontal line is 45. It is known that three points A, B and C are on the same straight line, ∠ ACD = 90. Please find out the length of the kite string that Xiao Ming took back at this time. (In this question, all kite lines are regarded as line segments, and the final result is accurate to 1 meter. )
The answer is BC=CD=x meters.
, solution
∴ ad-BD = 2x-= (m)
2 1.(20 1 1 Neijiang, Sichuan 2 1, 10) As shown in the figure, the direct proportional function and the inverse proportional function intersect at point A and point B. It is known that the coordinates of point A are (4, n) and BD⊥x axis.
(1) Find the analytic expressions of proportional function, inverse proportional function and linear function;
(2) Find out the value range of x by combining the image.
The answer (1) is B(p, q), then
And S△BDO= =4, so, so.
Get a (4 4,2), get a, so.
Yes, so.
(2) or
Neijiang City 20 1 1 year high school entrance examination and junior high school graduation examination papers
mathematics
Add test paper (***60 points)
First question, second question, total score, total score.
5 6 7
score
Precautions:
Add ***4 pages to the test paper. Please fill in the answers directly on the test paper.
1. Fill in the blanks (this big question has four small questions, each with 6 points and * * * 24 points). Please fill in the shortest answer directly on the horizontal line in the question. )
1.(20 1 1 Neijiang, Sichuan, plus 1, 6 points) If, the value is.
Answer 0
2.(20 1 1 Neijiang, Sichuan, add 2 and 6 points) As shown in the figure, in △ABC, points D and E are respectively the midpoint DF where AB and AC pass through EC midpoint G and BC extension line and intersect at point F, and BE and DF intersect at point O ... If the area of △ADE is S, the area of quadrilateral BOGC is =.
answer
3.(20 1 1 Neijiang, Sichuan, supplemented at 3 and 6 points) If it is known, then.
Answer -2
4. In the rectangular coordinate system (2011Neijiang, Sichuan, plus 4 or 6 points), the squares a1b1c1,A2B2C2C 1, a3. If the coordinates of point B 1 are (1, 1) And the coordinates of point B2 are (3,2), then the coordinates of point an are.
Answer (,)
Second, the answer (this big question ***3 small questions, each small question 12 points, and ***36 points. When answering, you must write the necessary text description, proof process or deduction steps)
5.(20 1 1 Neijiang, Sichuan, plus 5 12) Students, we studied the square grid of n×n, and obtained the expression of the total number of squares in the grid as 12+22+32+…+N2. But n is 100. Let's explore and solve this problem together. First of all, we already know that 0×1+/kloc-0 /× 2+2× 3+…+(n-1)× n = n (n+1) (n-1
(1) Observe and guess:
12+22=( 1+0)× 1+( 1+ 1)×2= 1+0× 1+2+ 1×2=( 1+2)+(0× 1+ 1×2)
12+22+32=( 1+0)× 1+( 1+ 1)×2+( 1+2)×3
= 1+0× 1+2+ 1×2+3+2×3
=( 1+2+3)+(0× 1+ 1×2+2×3)
12+22+32+42=( 1+0)× 1+( 1+ 1)×2+( 1+2)×3+
= 1+0× 1+2+ 1×2+3+2×3+
=( 1+2+3+4)+( )
……
(2) Conclusion:
12+22+32+…+N2 =( 1+0)× 1+( 1+ 1)×2+( 1+2)×3+…+[ 1+(n— 1)]n
= 1+0× 1+2+ 1)×N2+3+2×3+…+N+(N- 1)×N。
=( ) +[ ]
= +
= ×
(3) Practical application:
Through the above query process, we can calculate that when n is 100, the total number of squares in the square grid is.
Answer (1+3)×4
4+3×4
0× 1+ 1×2+2×3+3×4
1+2+3+…+n
0× 1+ 1×2+2×3 ++…+(n- 1)×n
n(n+ 1)(n— 1)
n(n+ 1)(2n+ 1)
6.(20 1 1 Neijiang, Sichuan, with the result of additional test 6 12) A computer dealer plans to purchase a batch of computer cases and LCD monitors at the same time. If you buy 10 computer chassis and 8 LCD monitors, * * * needs 7000 yuan; If you buy 2 computer cases and 5 LCD monitors, * * * needs 4 120 yuan.
(1) What is the purchase price of each computer case and LCD monitor?
(2) The dealer plans to purchase 50 sets of these two commodities, and the funds available for purchasing these two commodities shall not exceed 22,240 yuan. According to the market situation, the profits from selling a computer case and an LCD monitor are 65,438+00 yuan and 65,438+060 yuan respectively. The dealer hopes to make a profit of not less than 465,438+000 yuan after selling these two commodities. Which scheme is the most profitable? What is the maximum profit?
The answer (1) is that the purchase price of each computer case is X yuan, and the purchase price of LCD is Y yuan.
, solution
Answer: The price of each computer case is 60 yuan, and the price of LCD is 800 yuan.
(2) Set up Z sets of computer cases, and get
, the solution is 24≤x≤26.
Because x is an integer, x=24, 25, 26.
The profit is10x+160 (50-x) = 8000-150x. It can be seen that the smaller x is, the greater the profit is, so the maximum profit is 4400 yuan when x=24.
A: The dealer has three purchase plans: ① 24 computer cases and 26 LCD monitors; ② 25 computer cases and 25 LCD monitors; ③ 26 computer cases and 24 LCD monitors. The maximum profit of scheme 1 is 4400 yuan.
7.(20 1 1 Neijiang, Sichuan, additional test score 7 12) As shown in the figure, the parabola intersects with the X axis at points A and B, intersects with the Y axis at point C (0,-1), and the glaze axis X = 1.
(1) Find the analytical formula of parabola and the coordinates of points A and B;
(2) Whether there is a point D on the parabola below the X axis, so that the area of the quadrilateral ABDC is 3. If yes, find out the coordinates of point D; If it does not exist, explain the reason (with figure1);
(3) the point q is on the y axis and the point p is on the parabola. If the quadrilateral whose vertices are Q, P, A and B is a parallelogram, the coordinates of all points P that meet the conditions are required (see Figure 2).
Figure 1 Figure 2
The answer (1) is deduced, and here we go again.
So the analytical formula of parabola is
X =- 1 or x=3.
So a (- 1, 0), b (3, 0)
(2) Suppose that there is a point d that satisfies the condition, and let D(x,).
Let DE⊥x axis be at point E, then OE=x, DE=, BE = 3-X, and we get.
Simplify to get x= 1 or x=2.
So there is a qualified point D, which is D( 1,) or D(2,-1).
(3) When PQ is parallel to AB, PQ = 4；; When P is on the right side of Y axis, the abscissa of P is 4; When p is on the left side of the y axis, the abscissa of p is -4.
When PQ and AB are equally divided, PQ passes through the midpoint of AB (1, 0), and the abscissa of P is 2.
So the coordinates of p are (4,) or (-4, 7) or (2,-1).