Math test

1. Multiple choice questions: (This big question includes two groups, I and II, with 6 questions in each group, with 4 points for each question, out of 24 points).

The first group: for candidates who have completed the first phase of curriculum reform.

1. In the following operations, the calculation result is correct.

(1) x? x3 = 2x3(B)x3 \x = x2； (C)(x3)2 = X5； (D)x3+x3=2x6。

2. The newly-built Beijing Olympic Stadium "Bird's Nest" can accommodate 965,438+0,000 spectators, and 965,438+0,000 can be expressed by scientific notation as follows.

(1); (b) and: (c) and: (4).

3. In the picture below, which one is both axisymmetric and centrosymmetric?

(1); (b) and: (c) and: (4).

4. If the parabola intersects the positive semi-axis of the X axis at point A, the coordinates of point A are

(A)(，0)； (B)(，0)； (C)(- 1，-2)； (D)(，0)。

5. If the two roots of a quadratic equation are respectively, then the following conclusion is correct.

(1); (B)，；

(C)，； (4).

6. In the following conclusions, it is true that

(a) The tangent of the circle must be perpendicular to the radius; (b) The straight line perpendicular to the tangent must pass through the center of the circle;

(c) A straight line perpendicular to the tangent must pass through the tangent point; (d) The straight line passing through the center of the circle and the tangent point must be perpendicular to the tangent.

The second group: for candidates who have completed the second phase of curriculum reform.

1. In the following operations, the calculation result is correct.

(1) x? x3 = 2x3(B)x3 \x = x2； (C)(x3)2 = X5； (D)x3+x3=2x6。

2. The newly-built Beijing Olympic Stadium "Bird's Nest" can accommodate 965,438+0,000 spectators, and 965,438+0,000 can be expressed by scientific notation as follows.

(1); (b) and: (c) and: (4).

3. In the picture below, which one is both axisymmetric and centrosymmetric?

(1); (b) and: (c) and: (4).

There are four red balls and eight white balls in a cloth bag, except the colors are exactly the same. So the probability that the ball randomly touched from the bag is a white ball is

(1); (b) and: (c) and: (4).

5. If it is a non-zero vector, then the following equation is correct.

(A)=； (B)=； (C)+= 0； (D) + =0。

6. In the following events, the inevitable events are

(a) Boys must be taller than girls; (b) The equation has no solution in the real number range;

(c) Xiaoming will get full marks in the math exam tomorrow; (d) The sum of two irrational numbers must be irrational.

2. Fill in the blanks: (this big question * *12, 4 points for each question, out of 48 points)

[Please fill in the results directly in the corresponding position on the answer sheet]

7. Inequality 2-3x >; The solution set of 0 is.

8. Decomposition factor xy–x-y+1=.

9. Simplify:

10. The root of the equation is.

The domain of the 1 1. function is.

12. if the function image of the inverse proportional function passes through points P(2, m) and Q( 1, n), the relationship between m and n is: m n (choose to fill in ">", "=", "

13. The equation about x has two equal real roots, so m =.

14. In the plane rectangular coordinate system, the coordinates of point A are (-2,3), and the coordinates of point B are

(-1,6). If point C and point A are symmetrical about X, then the value between point B and point C

The distance is.

15. As shown in figure 1, translate the straight line OP downward by 3 units to get the functional analysis of the straight line.

The formula is.

16. At ⊿ABC, a straight line passing through the center of gravity G and parallel to BC intersects AB at point D,

Then ad: db =

17. As shown in Figure 2, circle O 1 and circle O2 intersect at point A and point B, with both radii of 2.

When the circle O 1 passes through the point O2, the area of the quadrangle O 1A02B is.

18. As shown in Figure 3, rectangular paper ABCD, BC=2, ∠ Abd = 30.

Diagonal BD folds, point A falls on point E, EB crosses DC at point F, and then point F goes straight.

The distance of DB is.

Three. Solution: (There are 7 questions in this big question, out of 78 points)

19. (The full mark of this question is 10)

Simplify first, then evaluate.

20. (The full mark of this question is 10)

Solve equations.

2 1. (The full score of this question is 10, (1) is 6, and (2) is 4).

As shown in Figure 4, in trapezoidal ABCD, AD‖BC, AC⊥AB, AD=CD, cosB=, BC = 26.

Find the value of (1)cos∠DAC; (2) the length of the line AD.

22. (The full score of this question is 10, (1) is 3, (2) is 5, and (3) is 2).

In recent 50 years, the spread area of land desertification and the number of sandstorms in China are shown in table 1 and table 2.

Table 1: land desertification area expansion

The fifties and sixties, the twenties, the eighties, the seventies and the nineties 10 years.

The average annual desertification area (km2) is 1560 2 100 2460.

Table 2: Frequency of sandstorms

50s 65438+60s 65438+70s 65438+80s 65438+90s 10.

The number of sandstorms per decade is 5 8 13 14 23.

(1) Calculate the average annual area of land desertification in the past 50 years;

(2) Draw a line chart of the number of sandstorms in different years in Figure 5;

(3) Observe the line chart obtained in Table 2 or (2). Do you think sandstorms will happen?

Frequency shows the trend (select "Increase", "Stable" or "Decrease").

23. (The full score of this question is 12, and the full score of each small question is 6.)

As shown in fig. 6, at ⊿ABC, point D is on the AC side, DB=BC, and point E is the midpoint of CD.

Point f is the midpoint of AB. (1) proof: EF = AB；;

(2) Take point A as AG‖EF and pass through the extension line of BE at point G to verify: ⊿ Abe ≌ ⊿ Age.

24. (The full score of this question is 12, and the full score of each small question is 4 points.)

As shown in Figure 7, in the plane rectangular coordinate system, point O is the coordinate origin and point A (0, -3) is the center of the circle.

5 is the radius of circle A, intersecting with X axis at points B and C, and intersecting with Y axis at points D and E. 。

(1) Find the coordinates of points B, C and D;

(2) If a quadratic function image passes through points B, C and D,

Find this second resolution function;

(3)P is a point on the positive semi-axis of the X axis, and the passing point P is separated from the circle A and coincides with the circle A..

The straight line perpendicular to the x axis intersects the quadratic function image at point f,

When the tangent of the internal angle of ⊿CPF is, find the coordinates of point P.

25. (The full score of this question is 14, (1) is 3, (2) is 7, and (3) is 4).

The side length of the square ABCD is 2, e is the moving point on the ray CD (not coincident with point D), the straight line AE intersects with the straight line BC at point G, and the bisector BC of ∠BAE intersects with the ray at point O. (1) As shown in Figure 8, when CE=, find the length of the line segment BG;

(2) When point O is on line BC, let BO=y and find the resolution function of y about x;

(3) When CE=2ED, find the length of line segment BO.

In 2008, Shanghai junior high school graduates took the unified academic examination.

Key points and grading standards of answers in mathematical simulation test papers

Description:

1. Answers only list one or more answers to the questions. If the candidate's answer is different from the listed answer, you can score according to the scoring standard in the answer.

2. If the first question and the second question are not specified, the score of each question is only full or zero;

3. The score marked at the right end of each question in the third big question indicates the score that the candidate deserves to do this step correctly;

4. When correcting the test paper, we should insist on correcting every question to the end, and we should not interrupt the correction of this question because of the wrong answer of the candidate. If the candidate answers incorrectly at a certain step, the content and difficulty of this question will remain unchanged, and the score of the subsequent part will be determined according to the degree of influence, but in principle it will not exceed half of the score because of the subsequent part;

5. When scoring, the basic unit of scoring or deduction is 1.

1. Multiple choice questions: (This big question includes two groups, I and II, with 6 questions in each group, with a full score of 24)

Group I 1, b; 2、D； 3、C； 4、D； 5、A； 6、d。

Group 2 1, b; 2、D； 3、C； 4、C； 5、A； 6、b。

2. Fill in the blanks: (This big question is *** 12, out of 48 points)

7、 ; 8、 ; 9、 ; 10、 ;

1 1, and; 12、 ; 13、4; 14、 ;

15、 ; 16 (or 2); 17、 ; 18、 .

Three. Solution: (There are 7 questions in this big question, out of 78 points)

19. solution: original formula =-(3 points)

-(2 points)

-(2 points)

When, the original formula =-(3 points)

20. Solution: [Method 1] Hypothesis,-(2 points).

Then the original equation is changed and sorted out,-(2 points)

∴ , ; -(2 points).

When, and,-(1 min)

When, get,-(1 min)

Prove to be the root of the original equation. -(2 points)

[Method 2] If the denominator is removed,-(3 points)

Finishing,-(2 points)

Solution,-(3 points)

It is proved to be the root of the original equation. -(2 points)

2 1. solution: in Rt△ABC: (1), and cosb =. - ( 1).

bc = 26，∴ AB = 10。 -(1 min)

∴ AC =。 -(2 points)

∫ad//BC，∴ DAC = ∠ ACB。 -(1 min)

∴cos∠dac= cos∠ACB =； - ( 1)

(2) The intersection point D is marked as DE⊥AC, and the vertical foot is marked as e .( 1).

∫AD = DC，AE = EC =。 - ( 1)

In Rt△ADE, cos∠DAE=,-(1)

∴ AD = 13。 -(1 min)

22. Solution: (1) The average annual land desertification area is

(2 points)

(square kilometers),-(1)

A: The average annual land desertification area1956km2;

(2) the right picture; -(5 points)

(3) Increase ...-(2 points)

23. Proof: (1) links to BE,-(1)

Db = bc, point e is the midpoint of CD, and ∴ is ⊥ CD. (2 points)

∵ point f is the midpoint of the hypotenuse in Rt △ABE, ∴ ef =;

-(3 points)

(2) [Method 1]-(3 points) of △,, ∴.

When △ and △, ∠ AEB = ∠ AEG = 90, ∴△abe≌△age；; ; -(3 points)

[Method 2] Obtained from (1), EF=AF, ∴∠ AEF = ∠ FAE. - ( 1).

∫ef//ag，∴∠ AEF = ∠ EAG。 -(1 min)

∴∠ EAF = ∠ EAG。 -(1 min)

Ae = ae, ∠ AEB = ∠ AEG = 90, ∴△Abe?△ age. -(3 points)

24. Solution: (1) The coordinates of point ∵ A are the coordinates of line segment and point ∴ D. (1).

Connect AC, at Rt△AOC, ∠ AOC = 90, OA=3, AC=5, ∴ OC = 4. -( 1)

∴ The coordinates of point C are; - ( 1).

Similarly, the coordinate of point B is ...-(1).

(2) Let the analytic expression of quadratic function be,

Because the image of quadratic function passes through three points, b, c and d, then

-(3 points)

The analytical formula of the quadratic function obtained by solving ∴ is: -( 1)

(3) Let the point P coordinate be, which is derived from the meaning of the question,-(1)

The coordinates of point f are,,,

∵∠CPF = 90°, ∴ When the tangent of the internal angle in △CPF is,

(1) If, that is, the solution, (give up); -( 1)

(2) When, the solution (up), (up), -( 1 min)

Therefore, the coordinate of point P is (12,0) ...................................... (1).

25. Solution: (1) In a square with a side length of 2,

∵, that is ∴, got it. -(2 points)

∵ ,∴ ; - ( 1).

(2) When a point is on a line segment, it is a point if it passes through it.

Is the angular bisector of ∴ -( 1 min)

In a square.

∵, ∴ - ( 1)

And:, ...-(1)

∵ at Rt△ABG,,,

∴ .

∵, ∴ - ( 1)

∵, that is, get,; (2 points) (1 minute)

(3) When,

① When the point is on the line segment, it is obtained from (2); -( 1)

② When the point is on the extension line of the line segment,

In Rt△ADE,

Let the intersecting line segment be at this point, then the bisector of ? is, that is,

Do it again.

∴.∴-(1 min)

∵, ∴, that is to get. (2 points)

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