20 10 Bengbu Mathematics Senior High School Entrance Examination

Anhui province 200 1 ordinary high school science experimental class entrance examination

Math test questions

(There are two tests in this volume * * *, the full mark is 150, and the answer time is 120).

The total score of the first test and the second test

One two three four five six seven

13 14

score

Reference formula:

(a+b)3=a3+3a2b+3ab2+b3，(a-b)3 = a3-3ab 2+3ab 2-B3，

a3+b3 = (a+b)(a2-ab+b2)，a3-b3 = (a-b)(a2+ab+b2). '

First attempt

A, multiple-choice questions (this question ***4 small questions, 5 points for each small question, out of 20 points. Each question gives four conclusions, code A, B, C and D, and only one is correct. Please put the code of the correct answer in brackets after the question. )

1. The number of solutions of the unary quadratic equation x2-|x| -6 = 0 is ....................................................... []

A. 1

2. In △ABC, ∠C is a right angle, and if Sina =, TGB = ………………………………………………………… []

A.B. C. D。

[13] The original wood stock of a forest farm is am3, the annual growth rate of wood is P, and the total amount of wood felled every year is bm3, so the wood stock of the forest farm is ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

A.[a( 1+p)2-(2+p)b]m3 b .[a( 1+p)2+BP]m3

C.[a( 1+p)2+(2+p)b]m3 d .[AP( 1+p)-( 1+p)b]m3

3. As shown in the figure, in the acute triangle ABC, points D, E and F are the midpoints of sides BC, CA and AB respectively, and the midpoints of each side are the perpendicular lines of the other two sides, and these six perpendicular lines form a hexagonal DPEQFR. Let the area of hexagonal DPEQFR be S 1 and the area of ABC be s, then S 1: S = ...

A.3:5 B.2:3 C. 1:2 D. 1:3

Fill in the blanks (this topic is ***8 small questions, 5 points for each small question, out of 40 points)

5. Calculation:-=.

6. It is known that when x=2, the value of algebraic expression x2+ax+3+ is 16, so when x=-2, the value of x2+ax+3+ is.

As shown in the figure, in △ABC, AB=AC, D is a point on BC, and ∠ Bad = 30, E is on AC, and AD=AE, then ∠EDC is a degree.

⒏ known inequality about x (2a-b) x >; The solution of b is X.

As shown in the figure, AB is the water pipe of automatic sprinkler irrigation equipment, with point A on the ground and point B higher than the ground1.5m.. There is an automatic rotating nozzle at B. Every moment, the sprayed water flow is parabolic. The connecting line between the nozzle B and the highest point C of water flow forms an angle of 45 with the horizontal line. The highest point C of water flow is 2m higher than the nozzle B. In the coordinate system shown in the figure, the distance from the falling point D of water flow to the point A is meters.

⒑ Known: As shown in the figure, if the radius ⊙O is R, op = L, AB = A., CD = B, then a2+b2=.

5. It is known that, as shown in the figure, in the right angle △ABC, AD=DE=EB, CD2+CE2= 1, then the length of hypotenuse AB is.

5. It is known that if A, B and C are integers, the inequality A2+B2+C2+3.

Third, answer the question (two small questions in this question, each 15, out of 30 points)

13, it is known that x, y and z are integers, and x

14. It is known that in the regular triangle ABC, P is the midpoint of AB, Q is the midpoint of AC, R is the midpoint of BC, M is any point on RC, and △PMS is a regular triangle. Verification: RM=QS.

A second attempt

Four, (full mark of this question 15)

Let max{a, b} represent the larger number of a and b, such as max{2, 3}=3.

(1) verification: max{a, b}=

⑵ If the function y 1 = 2x+ 1, y2 = x2-2x+4, try to draw the image of the function max{y 1, y2}.

Verb (abbreviation of verb) (the full mark of this question is 15)

It is known that AD=BD=CD=m, AB=n, BC=p, BC//AD, M and N are rational numbers.

Prove: P is also rational.

Six, (full mark for this question 15)

Known: 0

X<y. Verification: 0

Vii. (Full score for this question 15)

It is known that the diagonal of the inscribed quadrilateral ABCD of ⊙O as shown in the figure intersects with point M, and points E and F are the midpoint of AB and CD respectively.

Verification: ∠OEM = ∠OFM.

Reference answers and grading standards of mathematics test questions

First attempt

First, multiple-choice questions (this question is ***4 small questions, 5 points for each small question, out of 20 points)

1、B 2、D 3、A 4、C

Fill in the blanks (this topic is ***8 small questions, 5 points for each small question, out of 40 points)

5、 6、-2 7、 15 8、-3

9、2+ 10、8R2 - 4l2

1 1、 12、a = 1、b = 2、c = 1

Iii. (There are * * * two small questions in this question, each small question 15, out of 30 points)

13, solution:

Substituting (1) and z = -(x+y) into equation (2), you get ……3 points.