mathematics

Volume 1 (30 multiple-choice questions) [Source: Xue Ke | Net]

1. Multiple-choice question: This big question is a small question of *** 10, with 3 points for each small question and 30 points for * * *. Of the four options given in each small question, only one option meets the requirements of the topic.

1.(20 10 Leshan, Sichuan) The result of calculating (-2) × 3 is ().

(A)-6(B)-6(C)-5(D)5

Answer a

2.(20 10 Leshan, Sichuan) In the following figures, the axis symmetry is ().

Answer b

3. In the (20 10 Leshan, Sichuan) function, the value range of the independent variable x is ().

(A)x>2 (B)x≠2 (C)x b, a-2 < b-2 (b) from a > b, -2a.

(c) from A > B, we get > (d) from A > B, we get A2 > B2.

Answer b

5.(20 10 Leshan, Sichuan) A factory produced 654.38+million mascots of the last World Expo: "Haibao", and the quality inspection department randomly selected 500 mascots, 499 of which were qualified. The following statement is true ()

(1) There are 654.38+million overall qualified medals, with a sample of 500.

(2) There are 654.38 million overall qualified medals and 499 samples.

(c) Overall, 500 medals were qualified, and the sample was 500 medals.

(d) There are 65,438+million overall qualified medals, and the sample is 1 medal.

Answer a

6.(20 10 Leshan, Sichuan) In order to measure the height of school flagpole AC, the math interest group of a school erected a benchmark DF with a length of 1 0.5m at point F, as shown in figure (1), and measured the length of DF's shadow EF as1m, and then measured the length of flagpole AC's shadow BC as 6.

(a) 6m (b) 7m (c) 8.5m (d) 9m

Answer d

7.(20 10 Leshan, Sichuan) Figure (2) is three views of a geometric body. It is known that both the front view and the left view are equilateral triangles with a side length of 2, so the total area of this geometry is ().

(A)2л (B)3л(C) л(D)( 1+ )л

Answer b

8.(20 10 Leshan, Sichuan) As shown in the figure, an arc passes through grid points A, B and C. Try to establish a plane rectangular coordinate system in the grid so that the coordinate of point A is (-2,4), and the center coordinate of the circle where the arc is located is ().

A.(- 1，2)B. ( 1，- 1)c .( 1， 1)D. (2， 1)

Answer c

9.(20 10 Leshan, Sichuan) The linear function y = KX+B is known. When 0≤x≤2, the range of the corresponding function value y is -2≤y≤4, and the value of kb is ().

A. 12b。 -6c。 -6 or-12d.6 or 12.

Answer c

10 (Leshan, Sichuan, 20 10). Let a and b be constants, and B > 0, and the parabola y=ax2+bx+a2-5a-6 is one of the four images shown below, then the value of a is ().

A.6 or-1b. -6 or1c. 6D。 - 1+0.

Answer d

Second, fill in the blanks

1 1. (Leshan, Sichuan, 20 10) If the temperature above zero indicated by the thermometer is +5℃, then the temperature below zero should be _ _ _ _ _ _.

answer

12.(20 10 Leshan, Sichuan) As shown in Figure (4), in Rt△ABC, CD is the height on the hypotenuse AB, ∠ ACD = 40, then ∠ EBC = _ _ _ _ _.

Answer 140

13.(20 10 Leshan, Sichuan) If

Answer 3

14.(20 10 Leshan, Sichuan) The following factorization: ①; ② ; ③ ; ④ .

The correct one is _ _ _ _ _. (Fill in serial number only)

Answer ② ④

15.(20 10 Leshan, Sichuan) The side length of the regular hexagon ABCDEF is 2cm, and the point P is a moving point inside the regular hexagon, so the sum of the distances from the point P to each side of the regular hexagon _ _ _ _ _ _ _ _ cm.

Answer 63

16.(20 10 Leshan, Sichuan) Pythagorean theorem reveals the relationship among the three sides of a right triangle, which contains rich scientific knowledge and humanistic value. Figure (6) is a pythagorean tree which is made up of a square and a right triangle with an included angle of 30 degrees. The sum of the areas of the first square and the first right triangle from bottom to top of the tree is S 1. The sum of the areas of the nth square and the nth right triangle is Sn. Let the side length of the first square be 1.

Figure (6)

Please answer the following questions:

( 1)s 1 = _ _ _ _ _ _ _ _ _ _ _ _ _；

(2) Through exploration, if Sn is expressed by an algebraic expression containing n, then Sn = _ _ _ _ _ _ _ _

Answer1+38; ( 1+38)? (34)n-1(n is an integer) (if it is written as 8× 3n-1+32n-122n+1,no penalty will be deducted).

Three. This big question has three small questions, each with 9 points and * * * 27 points.

17.(20 10 Leshan, Sichuan) Solution equation: 5 (x-5)+2x =-4.

Answer: 5x-25+2x = 4.

7x=2 1

x=3。

18.(20 10 Leshan, Sichuan) As shown in Figure (7), take two points E and F on the diagonal AC of the parallelogram ABCD, if AE = cf

Proof: ∠AFD=∠CEB

The answer proves that the quadrilateral ABCD is a parallelogram,

∫AD∨BC，AD=BC，

∴∠DAF=∠BCE

AE = CF

∴AE+EF=CF+EF

That is AF=CE.

∴△ADF≌△CBE

∴∠AFD =∞∠CEB diagram (7)

19.(20 10 Leshan, Sichuan) Simplify first, then evaluate:, satisfy.

Solution 1:

Primitive formula

By, by

∴ Original formula =3- 1=2.

Primitive formula

By, by

When, the original formula =

When, the original formula =

In summary, the original formula =2.

20. (Leshan, Sichuan, 20 10) As shown in Figure (8), the images of the first quadrant of the linear function and the inverse proportional function intersect at point B, the abscissa of point B is 1, the intersection point B is the vertical line of the Y axis, and c is the vertical foot. If,

Find the analytic expressions of linear function and inverse proportional function

.

Solution: ∵ The linear function passes through point B, and the abscissa of point B is 1.

∴

[Source: Zxxk.Com]

The solution is b=6, ∴B( 1,3).

∴ The analytical formula of a linear function is

A little more b,

∴ The analytical formula of inverse proportional function is

2 1.(20 10 Leshan, Sichuan) A proofreader tested the physical education class of all the students in Grade 8 (1). The test results are divided into four grades: excellent, good, qualified and unqualified. The incomplete statistical chart drawn according to the test results is as follows:

The distribution table of the frequency of sports achievements in the eighth grade (1) class; the eighth grade (1) fan chart.

Fractional frequency

Excellent 90- 100?

Good 75-89 points 13

Qualified 60-74 points?

Unqualified 0-59 points 9

According to the information given in the statistical chart, answer the following questions:

(1) How many students are there in Class * * * of Grade 8 (1)?

(2) Fill in the blanks: the frequency of excellent sports performance is, and the frequency of qualified sports performance is;

(3) From the sports scores of all the students in this class, randomly select one student's score, and seek the probability of passing above (inclusive).

Answer: (1) From the meaning of the question:13 ÷ 26% = 50;

That is, there are 50 students in Grade 8 * * * class (1).

(2)2, 26;

(3) Randomly select a classmate's sports performance, and the probability of reaching above the qualification is:

22.(20 10 Leshan, Sichuan) In order to strengthen flood control, the Ministry of Water Resources decided to reinforce the Chengjiashan Reservoir. The original dam section is trapezoidal ABCD, as shown in Figure (9). It is known that the length of the water front surface AB is10m, and the length of the back surface DC is10m. The cross section of reinforced concrete dam is trapezoidal. If the length of CE is 5 meters.

(1) length of dam known to be reinforced100m. How many cubic meters do you need to fill in?

(2) Find the slope of the back water surface DE of the new dam. (The root sign is reserved for the calculation result)

Answer: (1) A and D are AF⊥BC and DG⊥BC respectively, and the vertical points are F and G respectively, as shown in figure (1).

At Rt△ABF, AB = 10m, ∠ B = 60. So sin ∠ b =

DG=5

So s

Need to fill: 100 (m3)

② DC = 10 in the right triangle DGC,

So GC =

So ge = GC+ce = 20.

So the slope I =

Answer: (1) Earthwork is required 1250 cubic meters. (2) The backwater slope is

23. (Leshan, Sichuan, 20 10) As shown in figure (10), AB is the diameter ⊙O, D is a point on the circle, =, connected with AC, and the point passing through D is the parallel line MN with the chord AC.

(1) for reference: MN is the tangent of ⊙O;

(2) Given AB = 10 and AD = 6, find the length of BC.

The answer (1) proves: connect OD and AC to E, as shown in Figure (2).

Because =, so OD⊥AC and AC∨Mn, so OD⊥MN.

So MN is the tangent of ⊙ O.

(2) Solution: Let OE = X, because AB = 10, so OA = 5 ed = 5-x.

Because AD =6 is in right triangle OAE and right triangle DAE, because OA -OE =AE -ED.

So 5-x = 6-(5-x) gives x =

Since AB is ⊙O and ∠ ACB = 90, OD∨BC.

So OE is the center line of △ABC, so BC = 2oe = 2 =

24.(20 10 Leshan, Sichuan) Choose one of the two questions A and B, do both questions, and only score with the question A.

Question A: Does a quadratic equation with one variable have a real root?

The range of (1) real number k;

(2) Assume and find out the minimum value of t 。

Question B: As shown in the figure (1 1), in the rectangular ABCD, P is a point on the side of BC, which connects DP and extends, and the extension line of intersection AB is at point Q.

(1) If, the value of;

(2) If point P is any point on the edge of BC, verify it.

What I chose to do was _ _ _ _ _.

Answer question a

Solution: (1)∵ One-variable quadratic equation has real roots,

∴, .................................................................................................................... 2 points.

That is to say,

Solution ................................................... 4 points.

(3) From the relationship between roots and coefficients, we get: …… 6 points.

Seven points.

∵ ,∴ ,

∴ ,

That is to say, the minimum value of t is -4. ................................................................................................................................................................

Theme b

(1) solution: the quadrilateral ABCD is a rectangle,

AB = CD, AB∨DC, ................................................. 1 min.

∴△DPC ∽△QPB, 3 points.

∴ ,

∴ ,

Leshan 20 10 Senior High School Entrance Examination

Mathematical reference answer

Volume 1 (30 points for multiple-choice questions)

First, multiple-choice questions:

1. answer a.

2. answer b

3. answer c

4. answer b

Step 5 answer a

6.answer d

7.answer b

8. answer c

9. answer c

10. Answer D.

Second, fill in the blanks

1 1.

12. The answer is 140.

13. Answer 3

14. Answer ② ④

15. Answer 63

16. Answer1+38; ( 1+ 38)? (34)n-1(n is an integer) (if it is written as 8× 3n-1+32n-122n+1,no penalty will be deducted).

Three. This big question has three small questions, each with 9 points and * * * 27 points.

17. Answer: 5x-25+2x = 4.

7x=2 1

x=3。

18. The answer proves that the quadrilateral ABCD is a parallelogram.

∫AD∨BC，AD=BC，

∴∠DAF=∠BCE

AE = CF

∴AE+EF=CF+EF

That is AF=CE.

∴△ADF≌△CBE

∴∠AFD=∠CEB

19. Solution 1:

Primitive formula

By, by

∴ Original formula =3- 1=2.

Primitive formula

By, by

When, the original formula =

When, the original formula = [Source: Subject Network]

In summary, the original formula =2.

20. Solution: ∵ The linear function passes through point B, and the abscissa of point B is 1.

∴

The solution is b=6, ∴B( 1,3).

∴ The analytical formula of a linear function is

A little more b,

∴ The analytical formula of inverse proportional function is [Source: Subject Network]

2 1. Answer: (1) From the meaning of the question:13 ÷ 26% = 50;

That is, there are five 0 students in Class * * * of Grade 8 (1).

(2)2, 26;

(3) Randomly select a classmate's sports performance, and the probability of reaching above the qualification is:

22. Solution: (1) Let A and D be AF⊥BC and DG⊥BC respectively, and the vertical points are F and G respectively, as shown in figure (1).

At Rt△ABF, AB = 10m, ∠ B = 60. So sin ∠ b =

DG=5

So s

Need to fill: 100 (m3)

② DC = 10 in the right triangle DGC,

So GC =

So ge = GC+ce = 20[ source: z&; xx & ampk.Com ]

So the slope I =

Answer: (1) Earthwork is required 1250 cubic meters. (2) The backwater slope is

23. The answer (1) proves that OD and AC are connected to E, as shown in Figure (2).

Because =, so OD⊥AC and AC∨Mn, so OD⊥MN.

So MN is the tangent of ⊙ O.

(2) Solution: Let OE = X, because AB = 10, so OA = 5 ed = 5-x.

Because AD =6 is in right triangle OAE and right triangle DAE, because OA -OE =AE -ED.

So 5-x = 6-(5-x) gives x =

Since AB is ⊙O and ∠ ACB = 90, OD∨BC.

So OE is the center line of △ABC, so BC = 2oe = 2 =

24. answer question a.

Solution: (1)∵ One-variable quadratic equation has real roots,

∴, ..................................................................................................................... 2 points.

That is to say,

Solution ................................................... 4 points.

(3) From the relationship between roots and coefficients, we get: …… 6 points.

Seven points.

∵ ,∴ ,

∴ ,

That is to say, the minimum value of t is -4. ................................................................................................................................................................

Theme b

(1) solution: the quadrilateral ABCD is a rectangle,

AB = CD, AB∨DC, ................................................. 1 min.

∴△DPC ∽△QPB, 3 points.

∴ ,

∴ ,

∴ ……………………………………………………………………………………………………………………………………………………………………………………………………………………………… 5 points.

(2) Proof: by △DPC ∽△QPB,

, ... 6 points.

7 points

.......................... 10.

Six, this big question ***2 small questions, the 25th question 12 points, the 26th question 13 points, * * * 25 points.

25.(20 10 Leshan, Sichuan) In △ABC, D is the midpoint of BC, O is the midpoint of AD, and the straight line L passes through the point O, and the three points A, B and C are perpendicular to the straight line L, respectively, and the vertical feet are G, E and F. Let AG=h 1, BE=h2 and CF =

(1) As shown in figure (12. 1), when the straight line l⊥AD (at this time, the point G coincides with the point O), it is verified that H2+H3 = 2h1;

(2) Rotate the straight line L around the point O so that L is not perpendicular to AD.

① As shown in figure (12.2), if point B and point C are on the same side of the straight line L, guess whether the conclusion in (1) holds, please explain your reasons;

② As shown in figure (12.3), when point B and point C are on opposite sides of the straight line L, guess what relation h 1, h2 and h3 satisfy? (Write only the relationship, without giving reasons. )