I. Fill in the blanks (1×28=28)

1, in the following algebraic expression:13x+5Y2X2+2x+Y2304-XY253x = 06, there are _ _ _ _ monomials and _ _ _ _ polynomials.

2. The coefficient of the monomial -7a2bc is _ _ _ _ _, and the degree is _ _ _ _.

3. Polynomial 3a2b2-5ab2+a2-6 is a _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

4、3b2m？ (_ _ _ _ _ _ _)= 3b4m+ 1-(x-y)5(x-y)4 = _ _ _ _ _ _ _ _(-2a2b)2 \\) = 2a

5 、(-2m+3)(_ _ _ _ _ _ _ _ _ _ _ _)= 4 m2-9(-2ab+3)2 = _ _ _ _ _ _ _ _ _ _ _ _ _

6. If ∠ 1 and ∠2 are complementary angles, then ∠ 1=72? ,∠2=_____? , if ∠3=∠ 1, the complementary angle of ∠3 is _ _ _ _? The reason is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

7. In the picture on the left, if ∠A+∠B= 180? ，∠C=65？ , then ∠1= _ _ _? ,

A 2D ∠ 2 = _ _ _ _ _? .

B.C.

8. In biology class, the teacher told the students: "Microorganisms are very small, and the diameter of dendrites is only 0. 1 micron", which is equivalent to _ _ _ _ _ _ _ _ meters (1 meter = 106 micron, please use scientific notation).

9. In the group's self-editing and self-answering activities, Xiao Fang gave the group members such a question: Zu Chongzhi, an ancient mathematician in China, found that pi = 3. 14 15926 ..., the approximate value was 3. 14, and the accuracy was _ _ _ _ _ _.

Xiao Ming, Xiao Gang and Xiao Liang are playing games. Now, if one of them is helping Grandma Wang, P (Xiaoming is selected) = _ _ _ _ _, P (Xiaoming is not selected) = _ _ _ _ _.

1 1. Throw a dice at will, calculate the probability of the following events and mark them in the figure below.

(1) The number of throwing points is even (2), and the number of throwing points is less than 7.

(3), the number of throwing points is two digits (4), and the number of throwing points is a multiple of 2.

0 1/2 1

Impossible, inevitable.

Second, multiple-choice questions (2×7= 14)

1. In math class today, the teacher talked about polynomial addition and subtraction. After school, Xiao Ming came home and took out his class notes. He carefully reviewed what the teacher said in class. He suddenly found a problem: (-x2+3xy- y2)-(- x2+4xy- y2)= ah.

The space of-x2 _ _ _+y2 is stained with ink, so one of the spaces is ().

a、-7xy B、7xy C、-xy D、xy

2, the following statement, the correct is ()

A, the complementary angle of an angle must be obtuse B, and the two acute angles must be complementary angles.

C, the right angle has no complementary angle d, if ∠MON= 180? Then m, o and n are in a straight line.

3. In math class, the teacher gave the following data, () is accurate.

In 2002, the American war in Afghanistan cost $654.38 billion per month.

B, the coal reserves on the earth exceed 5 trillion tons.

C, the human brain has 1× 10 10 cells.

D, you got 92 points in this midterm.

4. The probability that the puppy walks around on the square brick as shown in the figure and finally stops on the shadow square brick is ()

A, B,

C, D,

5. If ∣ x ∣ = 1 and ∣ y ∣ = are known, then the value of (x20)3-x3y2 is equal to ().

A,-or -B, or c, d,-

6, the following conditions can't get a‖b is () C ..

a、∠2=∠6 B、∠3+∠5= 180？ 1 2 a

c、∠4+∠6= 180？ d、∠2=∠8 5 6 b

7. Among the following four figures, ∠ 1 and ∠2 are diagonal figures ().

a、0 B、 1 C、2 D、3

Third, the calculation problem (4×8=32)

⑴ -3(x2-xy)-x(-2y+2x) ⑵ (-x5)？ x3n- 1+x3n？ (-x)4

⑶(x+2)(y+3)-(x+ 1)(y-2)⑷(-2m2n)3？ mn+(-7m7n 12)0-2(mn)-4？ m 1 1？ n8

5] (5x2y3-4x3y2+6x) ÷ 6x, where x =-2 and y = 2 [6] (3mn+1) (3mn-1)-(3mn-2) 2.

Calculate by multiplication formula:

⑺ 9992- 1 ⑻ 20032

Fourth, fill in the blanks by reasoning (1×7=7)

A known: as shown in the figure, DG⊥BC AC⊥BC, EF⊥AB, ∠ 1=∠2.

Verification: CD⊥AB

F certificate: ∵⊥ DG, BC, AC ⊥ BC (_ _ _ _ _ _ _).

∴∠DGB=∠ACB=90？ (definition of vertical)

∴DG‖AC(_____________________)

∴∠2=_____(_____________________)

∠ ≈1= ∠ 2 (_ _ _ _ _ _ _) ∴1= ∠ DCA (equivalent substitution)

∴ef‖cd(______________________)∴∠aef=∠adc(____________________)

∵EF⊥AB ∴∠AEF=90？ ∴∠ADC=90？ Namely CD⊥AB

V. Answer questions (1 question 6 points, 2 questions 6 points, 3 questions (1) 2 points, 2 points, 3 points, a total of 19 points)

1, Xiaokang village is undergoing green space transformation. There used to be a square green space, but now each side of it has increased by 3 meters, and the area has increased by 63 square meters. What is the side length of the original green space? What is the area of the original green space?

2. Known: as shown in the figure, AB‖CD, FG‖HD, ∠B= 100? FE is the bisector of ∠CEB,

Find the degree of ∠EDH

A F pt

E

B H

G

D

3. The figure below is the statistical chart of pocket money expenditure for one week (unit: yuan).

Analyze the picture above and try to answer the following questions:

(1) On which day of the week do you spend the least pocket money? how much is it? How much did he spend on the day when he spent the most pocket money?

On which days did he spend the same amount of pocket money? What is the difference?

Can you help Mingming figure out how much pocket money he spends on average every day for a week?

Ability test paper (50 points)

(Volume II)

I. Fill in the blanks (3×6= 18)

1. There is a rectangular wooden box one meter long, two meters wide and three meters high in the room. It is known that the thickness of the board is x meters, so the volume of this wooden box is _ _ _ _ _ _ _ _ _ _ cubic meters. (Unexpanded)

2. The maximum value of Formula 4-a2-2ab-b2 is _ _ _ _ _.

3. If 2×8n× 16n=222, then n = _ _ _ _ _ _

4. Known = _ _ _ _ _ _.

5. If a little boy throws a uniform coin twice, the probability is _ _ _ _ _ _ _.

6, a as shown in the figure, ∠ABC=40? ，∠ACB=60？ , BO and CO share equally ∠ABC and ∠ACB,

D E DE passes through point O and DE‖BC, then ∠ BOC = _ _ _ _ _ _ .

B.C.

Second, multiple-choice questions (3×4= 12)

1, the complementary angle of an angle is its complementary angle, then this angle is ()

60? b、45？ c、30？ d、90？

2. For a polynomial of degree six, the degree of any term ()

A, all less than 6 B, all equal to 6 C, all not less than 6 D, all not more than 6.

3. The correct judgment of formulas -mn and (-m)n is ().

A, these two formulas are opposite. B, these two formulas are equal.

C. when n is odd, they are reciprocal; When n is an even number, they are equal.

D, when n is even, they are reciprocal; When n is odd, they are equal.

4. It is known that the sides corresponding to two angles are parallel to each other, and the difference between these two angles is 40? , then these two angles are ()

a、 140？ And 100? b、 1 10？ There are still 70? c、70？ What about 30 years old? d、 150？ And 1 10?

Fourth, solving problems (7×2= 14)

1. If the product of polynomial x2+ax+8 and polynomial x2-3x+b does not contain x2 and x3 terms, find the value of (a-b)3-(a3-b3).

The sun god has a herd of cows, which are white, black, colored and brown.

Among the bulls, the number of white cattle is more than that of brown cattle, and the extra number is equivalent to1/2+1/3 of the number of black cattle; The number of black cattle is more than that of brown cattle, and the extra number is equivalent to1/4+1/5 of the number of flower cattle; The number of flower cattle is more than that of brown cattle, and the extra number is equivalent to 1/6+ 1/7 of the number of white cattle.

Among the cows, the number of white cows is1/3+1/4 of all black cows; The number of black cattle is1/4+1/5 of all flower cattle; The number of flower cattle is1/5+1/6 of all brown cattle; The number of brown cattle is 1/6+ 1/7 of the total number of white cattle.

How is this herd made up? Question 02: The weight of Bachet de Meziriac A businessman had a 40-pound thing, which was smashed into four pieces because it fell to the ground. Later, each piece was weighed by the whole pound, and these four pieces can be used to weigh any integer pound from/kloc-0 to 40 pounds.

How much do these four weights weigh? Problem 03 Newton's Grassland and Cow Newton's Field and Cow's Problem A cow ate up B piece of grass in C days;

A' A cow ate up B' s grass on C' day;

A "the cow ate up the grass in B" on day C ";

Find the relationship between 9 quantities from A to C "? Question 04 Seven Questions of Bewick Seven Questions of Bewick In the following division example, the dividend is divided by the dividend:

* * 7 * * * * * * * ÷ * * * * 7 * = * * 7 * *

* * * * * *

* * * * * 7 *

* * * * * * *

* 7 * * * *

* 7 * * * *

* * * * * * *

* * * * 7 * *

* * * * * *

* * * * * *

Numbers marked with an asterisk (*) were accidentally deleted. What are the missing figures? Question 05: Female students in Kirkman and female students in Kirkman. There are fifteen girls in a boarding school. They often walk in groups of three every day and ask how to arrange for each girl to walk a line with other girls once a week. Question 06 Bernoulli-Euler problem of mispronouncing letters The Bernoulli-Euler problem of mispronouncing letters seeks the arrangement of n elements, which requires that no element is in its proper position. Question 07 Euler Polygon Division How many methods are there to divide triangles with diagonal lines for N-polygons (planar convex polygons)? Question 08 Lucas' question to the married couple. The couple sat around the round table. The seating order is that a man sits between two women, but no man sits with his wife. How many sitting postures are there? Question 09: Kayam binomial expansion Omar Khayyam binomial expansion When n is an arbitrary positive integer, find the n power of binomial a+b expressed by the powers of A and B. The Cauchy mean value theorem in question 10 proves that the geometric average of n positive numbers is not greater than the arithmetic average of these numbers. Bernoulli's power sum problem in the problem 1 1 When the exponent p is a positive integer, the sum of the p powers of the first n natural numbers is S= 1p+2p+3p+…+np. Problem 12 Euler number Euler number function φ(x)=( 1+ 1/x)x and φ (x) = (65438+) X+ 1 are the limit values when x increases infinitely. Newton's exponential series in 13 transforms the exponential function ex into a series whose term is the power of x, and Nicola US Mercator's logarithmic series in 14 does not need a logarithmic table. Calculates the logarithm of a given number. Problem 15 Newton sine and cosine series to calculate sine and cosine trigonometric functions with known angles without looking up the table. Question 16 Andre's derivation of secant and tangent series. The Gent series is n numbers 1, 2, 3, ..., n, and if there is no element whose value is between two adjacent values ci- 1 and ci+ 1, it is called c 1, c2, ...

Deriving the series of secant and tangent by the method of inflectional arrangement. The number 17 Gregory arctangent sequence has three sides, so it is not necessary to look up the table to find the angle of the triangle. The number 18 Buffon Buffon's needle problem Draw a set of parallel lines with a distance of d on the table, and throw a needle with a length of l (less than d) on the table at will. Fermat-Euler Prime TheoremNo. 19 Every Fermat-Euler Prime Theorem can be expressed as a prime number in the form of 4n+ 1, and can only be expressed in the form of the sum of squares of two numbers. Fermat equation 20 finds the integer solution of equation x2-dy2 = 1. Where d is a non-quadratic positive integer. The Fermat-Gauss possibility theorem in question 2 1 proves that the sum of two cubes cannot be a cube. Question 22 Legendre Reciprocity Symbols of Odd Prime Numbers P and Q The quadratic reciprocity law depends on the formula.

(p/q)。 (q/p)=(- 1)[(p- 1)/2]。 [(q- 1)/2) Question 23: Basic Algebraic Theorem of Gauss Every equation of degree n Zn+c1Zn-1+C2Zn-2+…+CN = 0 has n roots. Question 24: Sturm problem of the number of roots. The number of real roots of algebraic equations with real coefficients in known intervals. Question 25: Abel's impossibility theorem Generally, equations with Abel's possibility theorem higher than quartic cannot have algebraic solutions. Question 26: Hermite-Lin Deman Transcendence Theorem Hermite-Lin Deman Transmission Theorem. The coefficient A is not equal to zero, and the exponent α is the expression A1eα1+A2eα 2+A3eα 3+... which can't be equal to zero. Question 27: Euler Straight Line In all triangles, the center of the circumscribed circle, the intersection point of the middle lines and the intersection point of the heights are all on a straight line-Euler Line. Moreover, the distance between the three points is: the distance from the intersection of each high line (vertical center) to the intersection of each middle line (center of gravity) is twice the distance from the center of the circumscribed circle to the intersection of each middle line. Question 28: The three midpoints of three sides in Feuerbach's circular triangle, and the three midpoints of the line segment from the intersection of three vertical feet and heights to each vertex are on a circle. Question 29: Castillon's problem is inscribed with a triangle, and each side passes through three known points and becomes a known circle. Question 30: marfa's question draws three circles in a known triangle. Each circle is tangent to the other two circles and two sides of the triangle. Question 3 1 gaspard monge Question Gaspard Monge's question is circled. Make it orthogonal to three known circles. Question 32: Tangency between Apollonius and Apollonius. Draw a circle tangent to three known circles. Question 33: Maceroni's compass problem. Prove that any diagram that can be made with compasses and straightedge can only be made with compasses. Question 34: Steiner. The problem of straightedge Steiner's problem of straightedge proves that any figure that can be made with compasses and straightedge can be made only with straightedge if a fixed circle is given on the plane. Deliaii cube doubling problem in question 35 draws one side of a cube whose volume is twice that of a known cube. The bisection of the angle in question 36 divides an angle into three equal angles. The positive he in question 37 is a regular heptagon. Ptadecagon draws a regular heptagon. Question 38: Determination of Archimedes π value The determination of Archimedes logarithm pi assumes that the perimeters of circumscribed and inscribed regular 2vn polygons are av and bv respectively, and then the perimeters of Archimedes series polygons are obtained in turn: a0, b0, a 1, b 1, a2, B2, … where av+ 1 is the harmonic median of av and bv, bv+/kloc. This method is called Archimedes algorithm. Fuss Chord-tangent Quadrilateral Question 39 Find the relationship between the radius of a bicentric quadrangle and the circumscribed circle and inscribed circle. (Note: A bicentric or chordal quadrilateral is defined as inscribed on a circle at the same time. A quadrilateral tangent to another circle) Question 40 Measurement Additional Question An attachment to a survey uses the position of a known point to determine the position of an unknown but reachable point on the earth's surface. Question 4 1 The billiards problem in Alhazen is in a known circle. Make an isosceles triangle with two waists passing through two known points in the circle. Question 42: Make an ellipse from the radius of the yoke. We know the size and position of the two yoke radii and draw an ellipse. Question 43: Make an ellipse in a parallelogram. Make an inscribed ellipse in the specified parallelogram, which is tangent to the parallelogram at the boundary point. Question 44: Make a parabola with four tangents and know the four tangents of the parabola. Make a parabola. Question 45: Make a parabola from four points. Draw a parabola from four known points. Question 46: Make a hyperbola from four points. It is known that there are four points on a right-angled (equidistant) hyperbola. Do this hyperbola. Question 47 Van Short's Trajectory Problem Two vertices of a fixed triangle slide along two sides of an angle on the plane. What is the trajectory of the third vertex? Question 48: The spur gear problem of cardan. When a disk rolls along the inner edge of another disk whose radius is twice as large, what is the trajectory drawn by a point marked on this disk? Question 49 Newton elliptic problem. Determine the center trajectories of all ellipses inscribed in a known (convex) quadrilateral. Question 50 The Poncelet-Brianxiong hyperbola problem determines the intersection of the top vertical lines of all triangles inscribed with the right-angled hyperbola. Trajectory Parabola A Parabola, as an envelope, intercepts any line segment E from the vertex of the corner n times in succession, and intercepts line segment F from the other side n times in succession. The end points of the line segments are marked with numbers, starting from the vertex, which are 0, 1, 2, ..., n and n, n-65438 respectively.

It is proved that the envelope of the line connecting points with the same sign is a parabola. Question 52: Two calibration points on the straight line of the star line slide along two mutually perpendicular fixed axes. Find the envelope of this straight line. Question 53 Steiner's trident hypocycloid determines the envelope of the Wallace line of the triangle. Question 54: The nearest circumscribed ellipse of a quadrilateral and the nearest circle ellipse draw a quadrilateral, which one has the smallest deviation from the circle? The curvature of the conic in question 55 determines the curvature of the conic. Archimedes calculated the area of parabola in question 56, and determined the area contained in parabola. The area of hyperbola in question 57 is calculated by squaring a hyperbola. El Bora determined the area contained in the cut section of hyperbola. Question 58 is to find the long division of a parabola to determine the length of the parabola arc. The 59th question is Gilad Girard Desargues's homology theorem (homology triangle theorem). If the corresponding vertices of two triangles pass through a point, the corresponding edges of the two triangles intersect on a straight line.

On the other hand, if the intersection of the corresponding sides of two triangles is on a straight line, the connecting line of the corresponding vertices of two triangles passes through a point. Question 60 Steiner's two-element construction is an overlapping projection given by three pairs of corresponding elements. Make it a binary element. Question 6 1 Pascal's hexagon theorem proves that the intersection of three pairs of opposite sides of a hexagon inscribed with a conic curve is on a straight line. Question 62 Briante's Hungarian Hexagon Theorem proves that it is circumscribed within the hexagon of a cone. Three pairs of vertex lines pass through a point. Question 63 Descartes involution theorem Dasaga involution theorem The intersection of three pairs of opposite sides of a straight line and a complete quadrilateral * forms a involution four-point pair with the conic curve circumscribed by the quadrilateral. The connecting line between a point and three pairs of vertices of a complete quadrilateral * and the tangent drawn from the conic curve tangent to the point form a involutory four-ray pair.

* A complete quadrilateral actually contains four points (lines) 1, 2, 3, 4 and their six connection points 23, 14, 3 1, 24, 12, 34; Where 23 and 14, 3 1 and 24, 12 and 34 are called opposite edges (opposite vertices). The conic curve obtained by five elements in question 64 is a conic curve. Its five elements-point and tangent-are known. Question 65 Conic Curve and Straight Line A known straight line intersects a conic curve and has five known elements-points and tangents. Find their intersection. Question 66: A conic curve and a point are known. A point and a conic curve have five known elements-points and tangents. Tangents are made from points to curves. Question 67: How many parts can Steiner divide the whole space into by plane division method? Question 68 The Euler tetrahedron problem represents the volume of a tetrahedron with six sides. Question 69: The shortest distance between diagonal lines Calculate the angle and distance between two known diagonal lines. Question 70. The circumscribed sphere of tetrahedron. Re-circumscribe the tetrahedron to determine the radius of the circumscribed sphere of the tetrahedron with all six sides known. Question 7 1, five regular solids divide a sphere into congruent spherical regular polygons. In question 72, the square is a quadrilateral image and the square is Im. The age of quadrilateral proves that every quadrilateral can be regarded as a perspective image of a square. Question 73 Polk-Siegel Theorem Any four points on the plane of Polk-Schwartz Theorem that are not all on the same straight line can be regarded as an oblique mapping of each corner of a tetrahedron similar to a known tetrahedron. Question 74 Basic Theorem of Gauss Basic Theorem of Axonometry: If in an orthogonal projection of three corners, the image plane is regarded as a complex plane, the projection of the vertices of the three corners is regarded as a zero point, and the projection of the endpoints of the sides is regarded as a complex number of the plane. Then the sum of the squares of these numbers equals zero. Question 75: Hipparchus's stereographic projection attempts to give an example of a conformal map projection method that transforms a circle on the earth into a circle on a map. Question 76: Mercator projection painting conformal geographical map. The coordinate grid consists of rectangular grids. Oblique course Question 77 Determine the longitude of the oblique course between two points on the earth's surface. Question 78. Determine the position of a ship at sea. The position of the ship at sea is determined by the astronomical meridian deduction algorithm. Question 7: The two heights of Gauss determine the time and position according to the known heights of two planets. Problem 80 Gauss's Three Highs problem obtains the time interval of the same altitude moment from the known three-star sphere and determines the observation moment. The latitude of the observation point and the height of the planet. Kepler equation 8 1 calculates eccentricity and true perigee angle according to the average perigee angle of the planet. The star setting in question 82 calculates the time and azimuth of the known star setting for a given place and date. Question 83: The problem of the sundial. Make a sundial. Question 84: When the straight pole is placed at the latitude φ, the shadow curve when the declination of the sun is δ, determine the curve described by the projection of the pole at one point in a day. Question 85: Eclipse and Eclipse If we know the right ascension, declination and radius of the sun and the moon at two moments near the eclipse time, we can determine the beginning and end of the eclipse. And the maximum value of the hidden part of the sun's surface. Question 86: "The star of a star and the rendezvous period of revolution" Determine the rendezvous period of two * * * plane rotating rays with the known star operation period. Question 87: "Forward and Backward Motion of Planets" When did the planet change from forward motion to backward motion (or vice versa)? Question 88: Prolem of Lambert Comet, the problem of Lambert Comet, expressed the time required for the comet to move an arc along a parabolic orbit by means of focal radius and chords connecting the two ends of the arc. Question 89 Steiner problem about Euler number If X is a positive variable, what is the value of X and the square root of X is the largest? The height base point problem of fagnano The 90th question is the inscribed triangle with the smallest circumference among the known acute triangles. Torricelli's 9 1 problem Fermat problem tries to find a point. Minimize the sum of the distances from it to the three vertices of a known triangle. Question 92: How can a sailboat sailing against the wind sail due north at the fastest speed against the north wind? Question 93: Beehive (Reaumur's problem) tries to close a regular hexagonal prism, the top cover of which is made of three congruent diamonds, so that the obtained solid has a predetermined volume and the surface area is the smallest. Question 94: The biggest problem of Reggio Montanus is where there is a vertical boom on the earth's surface? (that is, where is the largest viewing angle? Question 95: The maximum brightness of Venus. Where is the maximum brightness of Venus? Question 96: How many days can a comet stay in Earth orbit at most? Question 97: The shortest morning light problem is at a known latitude. Which day of the year has the shortest morning light? Question 98 Steiner Ellipse Problem Among all the ellipses that can be circumscribed (inscribed) in a known triangle, which ellipse has the smallest (largest) area? Question 99 Steiner circle problem In all plane figures with equal perimeters, the circle has the largest area.

On the contrary, in all plane figures with equal areas, the circumference of a circle is the smallest. Problem 100 Steiner sphere problem Among all solids with the same surface area, the sphere has the largest volume.

Among all solids of equal volume, the surface area of the ball is the smallest.