2. Hua, a famous mathematician in China, once said: "The combination of numbers and shapes is good in all aspects, but everything is wrong when it is separated." As shown in the figure, on a square cardboard with a side length of 1, rectangular colored papers with an area of,, ... (n is an integer greater than 1) are pasted in sequence. Please use the idea of "combination of numbers and shapes" to calculate = according to the changing law of numbers and shapes.
3. There is a column number: the first number is x 1= 1, the second number is x2=3, and the third number is recorded as x3, x4, …, xn in turn; Starting from the second number, each number is half the sum of its two adjacent numbers. (e.g. x2=)
(1) Find the third, fourth and fifth numbers and write out the calculation process; (2) According to the result of (1), it is inferred that x8 =；;
(3) Explore the law of the number of columns and guess the number of the kth column xk=. (k is an integer greater than 2)
4. Fold a rectangular piece of paper in half, as shown in the figure, to get a crease (dotted line in the figure). Continue to fold in half, and each crease will be parallel to the last one. After folding in half for three times in a row, you can get seven creases, then folding in half for four times can get _ creases. If you fold it n times, you can get a crease.
5. Observe the following rules.
According to this law, the nth number is (n is a positive integer)
6. The number 1, 3,6, 10,15,21,... has certain regularity, so the difference between the 24th triangle number and the 22nd triangle number is.
7. A series of numbers arranged in a certain order is called a series. Generally, a 1, a2, a3, …, an stands for a series, which can be abbreviated as {an}. The existing sequence {an} satisfies the relation: an+ 1 =-nan+ 1, (n = 65438).
8. Observe the following numbers:-1, 2, -3, 4, -5, 6, -7, ... and arrange the column numbers in the following form.
According to the above rules, the ninth number from the left of line 10 is.
9. Observe the following equation 9- 1=8.
16-4= 12
25-9= 16
36- 16=20
…………
These equations reflect some laws between natural numbers. Let n(n≥ 1) represent a natural number, and the equation about n represents this law as follows.
10. The picture shows the trademark pattern designed by Sunshine Advertising Company for a commodity.
The shaded part in the figure is red. If the area of each small rectangle is 1,
Then the red area is.
1 1. As shown in the figure below, from location A to location C, the options are as follows
By water, land and air. There are two waters from a to b.
Highway, 2 land routes, there are 3 land routes to choose from from B to C, while air travel directly from A to C without going through B, so the option from A to C is ().
A.20 species B.8 species C.5 species D. 13 species.
12. A stepped classroom in a school, 1 The number of rows is 12. Starting from the second row, each row has one more seat than the previous row. (1) Please fill in the appropriate algebraic expressions in the blanks in the table below:
Number of seats in line 65438 +0 Number of seats in line 2 Number of seats in line 3 Number of seats in line 4 Number of seats in line n
12 12+a…
(2) It is known that the number of seats in row 15 is twice that in row 5. Find the value of a and calculate how many seats are there in row 2 1?
13. Inquiry: (1) One straight line can divide the plane into two parts, two straight lines can divide the plane into four parts at most, three straight lines can divide the plane into several parts at most, and four straight lines can divide the plane into several parts at most. Try to draw a picture to illustrate; How many parts can a plane be divided by 2 n straight lines at most?
14. Observe first == 1-=
== 1-=
Recalculated value.
15 ... Observe the following equations in order:
9×0+ 1= 19× 1+2= 1 19×2+3=2 19×4+5=4 1
..., guess: Equation 2 1 should be:
16. We call the fraction with the molecule 1 as the unit fraction. For example, any unit score can be divided into the sum of two different unit scores, such as =, =, …
(1) According to the observation of the above formula, you will find =. Please write □, ○;
(2) Further thinking, unit score (n is a positive integer not less than 2) =, please write the formula expressed by △, ☆.
17. Have you ever been to the ramen restaurant in the county? The master of ramen noodle restaurant can first pinch and stretch a rough noodle at both ends, then pinch and stretch it again, and repeat it several times, and then pull this rough noodle into many fine noodles, as shown in the sketch below. Excuse me, can I pull out 256 noodles for the first time?
18. The ancient "river map" in China was composed of 3×3 squares, each with a different number.
The dot graph of, the sum of the dots in each row and column and the three dot graphs on each diagonal.
They are all equal. As shown in the figure, the local dot diagram of "River Map" is given. Please calculate the correspondence at m.
Bitmap of
Asian Development Bank.
19. The result of calculation is ()
A.2008. - 1004C。 - 1D.0
20 16 summer vacation is coming, parents must urge their children to finish their homework carefully and pay attention to holiday safety during the summer vacation. Junior high school channel provides you with homework exercises for seventh grade mathematics in summer vacation for your reference.
I. Fill in the blanks (2 points for each question, 20 points for * * *)
1. The cold storage of food processing factory can reduce the temperature of refrigerated food by 5℃ per hour. If the temperature of beef just put into storage is 10℃, the temperature can reach _ _℃ after 8 hours.
2. When cleaning up the classroom at the beginning of school, the teacher always puts the front and last desks in each column first, then puts the middle desks in turn, and then arranges a column of desks in a row in a short time. This is because _ _ _ _ _ _ _.
3. Calculation: -5× (-2) 3+(-39) = _ _ _.
4. The divisor of1.460×105 is accurate to _ _ _ _, and the effective number is _ _ _ _.
This year, my mother is 30 years old and my son is 2 years old. After _ _ _ _ _, the mother's age is five times that of her son.
6. Place the dining table and chairs as follows:
Number of tables1234 ... n ... n
The seating capacity is 68 10. ...
7. Calculate 72 35 ÷ 2+18 33 ÷× 4 = _ _ _ _ _.
8. Given that point B is on the line AC, AB=8cm, AC= 18cm, and P and Q are the midpoint of AB and AC respectively, PQ = _ _ _ _ _ _
9. As shown in the figure, A, O and B are three points on the same straight line, OC, OD and OE are three rays drawn from point O, and ∠1:∠ 2: ∠ 3: ∠ 4 =1:2: 3: 4.
(9 maps) (10 maps)
10, as shown in the figure. At 8: 00 a.m., Ship A measured that Lighthouse S was 60 northeast and sailed eastward until noon 12. The ship is at point B, and the lighthouse S is measured at 30 northwest (complete the graph by itself). It is known that the speed of the ship is 20 kilometers per hour, so ASB = _
Second, multiple-choice questions (3 points for each question, ***24 points)
1 1, if a
A, aB, b+aC, b-aD, uncertain
12, (-2) 100 is greater than (-2)99 ()
a、2B、-2C、299D、3×299
13, known, +=0, then 2m-n= () ()
a、 13B、 1 1C、9D、 15
14. The charging standard of a taxi is: the starting price is 7 yuan (that is, the distance less than 3km needs to pay 7 yuan fare). 2.4 yuan will be charged for every increase of 1km after 3km (if it is less than 1km, it will be calculated as 1km), and someone will take this taxi to pay from A to B 19 yuan.
a、 1 1B、8C、7D、5
15, as shown in the figure, is an expanded view of a cubic carton. If the three squares A, B and C are filled with appropriate numbers respectively, so that the two numbers on the opposite faces are opposite after they are folded into cubes, then the three numbers filled in the four squares A, B, C and C are () in turn.
a、 1 、-3、0B、0 、-3、 1C 、-3、0、 1D 、-3、 1、0
16. Given the line segment AB, take a point C on the extension line of AB, make AC=2BC, and take a point D on the reverse extension line of AB, make DA=2AB, then the line segment AC is () times that of the line segment DB. ()
A, B, C, D,
17, the ratio of the sizes of the two angles is 7∶3, and their difference is 72, so the relationship between the two angles is ().
A, equal b, complementary c, complementary d, uncertainty
18. The angle that cannot be drawn is () an angle with a known degree on a set of triangles.
a、 15 B、 135 C、 165 D、 100
Iii. Answer questions (5 points for each question, 20 points for * * *)
19,4× (-3) 2-13+(-12)-|-43 | .20, calculation
2 1, solving equation:, 22 solving equation:
Four, (5 points for each question, ***20 points)
23. According to the data, the temperature drops by 0.8℃ every time the height in a certain area increases by 100m. Xiao Ming and Xiao Hong came up with a method to measure the height of mountain peaks. Xiaohong is at the foot of the mountain and Xiaoming is at the top of the mountain. At the same time, they measured the temperature at the foot of the mountain at 2.6℃ and the temperature at the top of the mountain at -2.2℃. Do you know the height of the mountain peak?
24. As shown in the figure, it is a geometry made of a small cube tower. Please look from the front, left and top, and try to draw the plan you see.
25. Grade 7 students go for a spring outing. If one bus is reduced, each bus will take exactly 60 people. If one bus is added, each bus can take exactly 45 people. How many students are there in the seventh grade?
26. The following is a problem that Xiao Ma solved.
Topic: If ∠ BOA = 70 and ∠ BOC = 15 on the same plane, find the degree of ∠AOC.
Solution: You can draw a picture according to the meaning of the problem.
∠∠AOC =∠BOA-∠BOC
=70 - 15
=55
∴∠AOC=55
If you were a teacher, would you get full marks for carelessness? If yes, explain the reasons. If not, please point out the careless mistakes and give your correct solutions.
20. Look at the picture on the right and find the pattern. The number filled in at x is
A.- 136
B.- 150
C.- 158
D.- 162
2 1. If "!" Is a mathematical operation symbol, and 1! = 1,2! =2× 1=2,3! =3×2× 1=6,
4! =4×3×2× 1, …, then the value of is
22. As shown in the figure, there are six rays OA, OB, OC, OD, OE and OF with common endpoints in the plane. Write the numbers 1, 2, 3, 4, 5, 6, 7 ... in counterclockwise order from ray OA, and the number "2008" will be in ().
A. on ray OA B. About ray OB
C. In Ray Oder. In the light of ...
23.
(1) The figure on the left is the top view of the geometry composed of several small cubes with the same size. The number in the small square indicates the number of small cubes in this position. Please draw the front view and the left view of the geometry.
(2) Fibonacci, a famous Italian mathematician, found such a set of numbers when studying rabbit reproduction: 1, 1, 2, 3, 5, 8, 13, …, where each number is equal to the sum of its first two numbers from the third number. Now, every number in this set is the side length of a square.
Then take 2, 3, 4, 5 … squares from left to right to form the following rectangles, which are denoted as ①, ②, ③, ④, …
The perimeter of the corresponding rectangle is shown in the following table:
Serial number 12344 ...
Outside line 6 10
…
Look at the chart carefully.16,26 in the above table.
If you continue to make a rectangle according to this rule, the serial number is 8. The circumference of a rectangle is 178.
24. (The full mark of this question is 10)
As shown, cut a square piece of paper into four small squares, then cut a square into four small squares, then cut a square into four small squares, and so on.
(1) Fill in the following table completely;
(2)
(2) (expressed by the contained algebraic expression).
(3) According to the above method, can we get 2009 squares? If yes, request n; If not, please briefly explain the reasons.
25. Observe the composition of the picture below. According to this law, there is a circle in the eighth number.
26. Observe the picture below and divide it in the "days" box indicated by the two arrows according to the law.
Draw a proper picture.
27. Observe the numbers in the following column and fill in the appropriate numbers on the horizontal line according to certain rules:,,, ...
The number is;
The answer to the special training of legal discovery
1.4n+22. 13。 ( 1)5; 7; 9(2) 15(3)2n- 14. 15； ? 5.n/n(n+2)
6.457.n+ 18.909。 ? 10.5 1 1.D
12.( 1) 12+2a； 12+3a； 12+a(n- 1)(2)a = 2； 54
13.7; 1 1; n/(n+ 1)+ 1
14.n/(n+ 1)
15.9×20+2 1=20 1
16.( 1)6; 30(2)n+ 1； n(n+ 1)
17.8 18.C 19。 B20.D2 1.990022.C
23.(2) 16; 26; 178
24( 1) 13; 16; (2)3n+ 1； (3) No, 3n+ 1=20093n=2008 because 2008 is not a multiple of 3.
25.n×n26。 ? 27.(2n- 1)/n×n
The above is the math test for the seventh grade summer homework for everyone. Have you read it carefully? Come on!
In the competition, we must keep learning. Next, the junior high school channel recommends the first-year mathematics comprehensive test questions for everyone. Please read carefully, hoping to bring help to everyone's study!
First, choose one carefully and you will know gold! (4 points for each question, ***40 points)
1. If the outer angle of a triangle is smaller than its adjacent inner angle, the triangle is ().
A. acute triangle B. obtuse triangle; C. right triangle D. can't be determined
2. In the plane rectangular coordinate system, the line segment A'B' is translated from the line segment AB. It is known that point A'(3-2, 1) corresponds to point A'(3, 1) and point B' (4,0), so the coordinate of point B is: ().
A.(9，0) B.(- 1，0) C.(3，- 1)d .(3，- 1)
3. As shown in the figure, if AB∨CD, ∠B= 1200 and ∠D= 1500 are known, then ∠O is equal to ().
500(B)600(C)800(D)900
4. In △ABC, ∠A=∠B=∠C, then △ ABC is ().
A. acute triangle B. right triangle; C. obtuse triangle D. possible
5. As shown in the figure, the degrees of AB⊥BC and ∠ABD are smaller than those of ∠DBC 15. Let the degrees of ∠ABD and ∠DBC be x and y, respectively, then the degrees of these two angles can get the following equation ().
A, B,
C, D,
6. A triangle with two equal sides is 3 cm long and 5 cm long, so its circumference is ().
A.8cmb. 1 1cmc
7. The sum of the inner angles of a polygon is 180, which is more than twice the sum of its outer angles. The number of sides of this polygon is: ()
A.7B.8C.9D. 10
8. Among the following points, point A (,) parallel to the Y axis is ().
a 、( 2)、B 、( 4，C 、( 2，4)D 、( 4，2)
9. Party A and Party B invest in a company at a ratio of 3: 2, and agree to share the profits according to the investment ratio except various expenses. If the profit of Party A in the first year is 3,000 yuan less than that of Party B, how many thousand yuan will each party get? If Party A gets X,000 yuan and Party B gets Y,000 yuan, the question means ().
A, B,
C, D,
10, giving the following statement:
(1) Two straight lines are cut by a third straight line, and the same angle is equal;
(2) If a straight line in a plane intersects one of two parallel lines, it also intersects the other;
(3) Two equal angles are antipodal angles;
(4) The vertical section from a point outside the straight line to the straight line is called the distance from the point to the straight line;
The correct one is ()
A0 B 1 C2 D3
1 1. As shown in the figure, if AB∨CD, CD∨EF, then ∠BCE= ().
A.∠ 1+∠2B。 ∠2-∠ 1
c . 180-∠ 1+∠2d . 180-∠2+∠ 1
12,,, is the length of three sides of a triangle, and the simplified result is ().
a、0B、C、D、
Second, fill in patiently, you can do it! (3 points for each question, ***30 points)
13. In, if 2=6, then =.
14, P(m-4, 1-m) is on the x axis, then m=.
15, as shown in the figure, AC⊥BC, AC=3, BC=4, AB=5, then the distance from point B to AC is
16. As shown in the figure, AB∨CD intersects with straight line EF, AB, CD is at E, F, F, and EG is divided into ∠BEF, if ∠ 1 = 72, ∠ 2 = _ _ _ _ _ _ _.
17, the equation is a binary linear equation, then,;
18, called the solution of the equations, then =;
19, as shown in the figure, a bridge is to be built between the banks of A and B, and the direction of the bridge is northeast when measured from the bank of A.
50. If both sides of A and B are started at the same time, in order to make the bridge accurately connected, the construction of the second bank should start in the direction of β _ _ _ _ _ _ _.
20. There are the following figures: ① regular triangle; ② Square; ③ Regular hexagon; ④ Regular octagon. Now, we want to choose two of them for plane mosaic. Please write down all your choices (fill in the serial number).
2 1, as shown in the figure, in △ABC, ∠ c = 90, ∠BAD=∠BAE, ∠ABD=∠ABF, then the size of ∠D is.
22. A polygon has 1680 besides an inner corner, so the number of sides of this polygon is _ _ _ _ _.
Reference answers and grading standards
First, multiple-choice questions (4 points for each question, ***48 points)
1——5 bbdbb； 6—— 10 daccb； 1 1、 12DA
Second, fill in the blanks; (3 points for each question, ***30 points)
13、; 14、 1; 15、4; 16、54; 17、,4; 18、;
19、 130; 20、①②,①③,②④; 2 1、90 ; 22、 12.