Class name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

I. Selection (3 points for each small question *** 10 small question)

1. The following statement is incorrect ()

The center of a triangle is the intersection of three bisectors of the triangle.

B the point where the three vertices of a triangle are equidistant is the intersection of the perpendicular lines of the three sides.

Of the three internal angles of any triangle, there are at least two acute angles.

D. Two right-angled triangles with a common hypotenuse are congruent.

2. If all three sides of a triangle are integers, the perimeter is 1 1, and one side is 4, then the longest side in this triangle is ().

a7 b . 6 c . 5d . 4

3. Factorization is ()

A.B.

C.D.

4.a and B are rational numbers of (a≠b), and the value of is ().

A.B. 1 C.2 D.4

5. If the angle between the height and the bottom of an isosceles triangle is 45, then the triangle is ().

A. acute triangle B. obtuse triangle C. equilateral triangle D. isosceles right triangle

6. It is known that x should satisfy ()

A.x < 2 b.x ≤ 0 c.x > 2 d.x ≥ 0 and x≠2

7. As shown in the figure, in △AB=AC, AB = AC, DE is the middle vertical line of AB side, the circumference of △BEC is 14cm, and BC = 5cm, then the length of AB is ().

a . 14cm b . 9cm c . 19cm d . 1 1cm

8. The following calculation is correct ()

A.B.

C.D.

9. If ... is known, the value of is ()

A. 15

10. There are four propositions, of which the correct one is ().

(1) congruence of an isosceles triangle with an angle of 100.

(2) Among the straight lines connecting two points, the straight line is the shortest.

(3) A triangle with two equal angles is an isosceles triangle.

(4) In △ABC, if ∠ A-∠A-∠B = 90°, △ABC is an obtuse triangle.

A.( 1)(2)b .(2)(3)c .(3)(4)d .( 1)(4)

Fill in the blanks (2 points for each small question *** 10 small question)

1. If known, then _ _ _ _ _ _ _ _ _ _ _ _

2. Decomposition coefficient _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

3. When x = _ _ _ _ _ _ _ _ _ _ _ _ _ _ minute value is zero.

4. If X = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

5. Calculate _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

6. The circumference of an isosceles triangle is = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

7. If the outer angle of the top angle of an isosceles triangle is 30 smaller than the outer angle of the bottom angle, then the inner angle of this triangle is _ _ _ _ _ _ _.

_____________________

8. As shown in △ABC, if AD⊥BC is in D, ∠ B = 30, ∠ C = 45, CD = 1, then AB = _ _ _ _ _ _ _ _ _

9. As shown in △ABC, BD bisector ∠ABC, BD⊥AC at D, DE‖BC, AB at E, AB = 5cm, AC = 2cm, then the circumference of △ADE = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

10. In △ABC, ∠ c = 1 17, the perpendicular line on the side of AB intersects BC in D, and AD is divided into ∠CAB. ∠ CAD: ∠ DAB = 3: 2, then ∠.

Third, the calculation problem (***5 small questions)

1. decomposition (5 points)

2. Calculation (5 points)

3. Simplify and re-evaluate, where x =-2 (5 points)

4. Solve the equation (5 points)

In order to alleviate the traffic jam, it is decided to build a light rail from the city center to the airport. In order to finish the project three months ahead of schedule, it is necessary to improve the original planned work efficiency by 12%. How many months will it take to plan this project? (6 points)

Fourth, proof calculation and drawing (***4 small questions)

1. As shown in the figure, when △AB=AC, AB=AC, ∠ A = 120, DF divides AB, AB, F and BC vertically, D. Verification: (5 points)

2. As shown in Figure C, a point on AB is an equilateral triangle with △AMC and △CNB. Verify that An = BM (6 points).

3. Find a point P so that PC = PD and the distance from point P to ∠AOB is equal. (No writing method) (5 points)

4. As shown in Figures E and F, on the BD line, AB = CD, ∠ B = ∠ D, BF = de. (8 points).

Verification (1) AE = cf

(2)AE‖CF

(3)AFE =∠CEF

Reference answer

I. Selection (3 points for each small question *** 10 small question)

1.D 2。 C 3。 D 4。 B 5。 D 6。 B 7。 B 8。 C 9。 B 10。 C

Fill in the blanks (2 points for each small question *** 10 small question)

1.2 2.3. 1 4.5 5.

6.7 7.80 50 50 8.2 9.7 cm 10. 18

Third, the calculation problem (***5 small questions)

1. solution:

2. Solution:

.

3. Solution:

party history

The value of the original formula.

4. Solution:

.

Test: X = 4 is the root of the original equation.

It was originally planned that this project would take x months.

Test is the root of the original equation.

A: It was originally planned to be completed in 28 months.

Fourth, proof calculation and drawing (***4 small questions)

1. Certificate: even AD.

∫∠A = 120

AB=AC

∴ ∠B=∠C=30

∫fd⊥ Divide AB equally.

∴ BD=AD

∠B=∠ 1=30

∠DAC=90

∫In Rt△ADC

∠C=30

∴

that is

2. Certificate: Point ∵ C is on AB.

A, b and c are in a straight line.

∠ 1+∠3+∠2= 180

∵ △AMC and△△△ CNB are equilateral triangles.

∴ ∠ 1=∠2=60

That is ∠ 3 = 60.

AC=MC，

CN=CB

In △MCB and △ACN.

∵

∴△MCB?△ACN(SAS)

∴ Ann =MB.

3.

4. Syndrome ① is in △ABF and △DCE.

∵

∴△abf?△DCE(SAS)

∴ AF=CE，∠ 1=∠2

B, f, e and d are in a straight line.

∴∠ 3 = ∞∞∠∠ 4 (complementary angles of the same angle are equal)

That is ∠ AFE = ∠ cef.

② in △AFE and △CEF.

∵

∴△AFE?△cef(SAS)

∴ AE=CF ∠5=∠6

∵ ∠5=∠6

∴ AE‖CF

③ ∵ ∠3=∠4

That is, ∠ AFE = ∠ cef.

Mid-term examination paper of junior two mathematics

Fill in the blanks: (20')

1._ _ _ _ _ _ is called factorization.

2.

3.

4.

5. When x _ _ _ _ _, the score is meaningful, and when x _ _ _ _ _, the value of the score is equal to 0.

6. In the formula, R 1, R2 is known; Then r = _ _ _ _ _ _

7. One side of an isosceles triangle is 4cm long and the other side is 9cm long, so the circumference of this isosceles triangle is _ _ _ _ _

8. In △ ABC, ∠ BAC = 50 and ∠ ABC = 60, then ∠ ACB = _ _ _ _ _ degrees. The external angle adjacent to ∠ABC is equal to _ _ _ _ _ _ degrees.

9. In a right triangle, the acute angle formed by the intersection of bisectors of two acute angles is equal to _ _ _ _ degrees.

10. If known, then _ _ _ _

2. Multiple choice questions: (30')

1. Among the following polynomials, the factor that can be decomposed by the square difference formula is () within the range of rational numbers.

A.B C D

2. If the factor of is, then P is ()

A B C D

3. In the rational formula, the number of fractions is ()

A b, two c, three d and four d.

4. Divided by the score, the result is ()

A B C D

5. If the value of the score is 0, it must be ().

A B C D

6. If the side lengths of an isosceles triangle are 10 and 12, then its perimeter is ().

A 32 B 34 C 32 or above 34 D is not.

7. In △ABC, AD is the angular bisector. If BC intersects at point D, ∠ B = 60, ∠ C = 48, then ∠ADB= ().

A 84 B 96 C 72 D 108

8. In 8.△ ABC, the lengths of the three sides are A, B, C and A >； respectively; B>c If b=8 c=3, the range of A is ().

a3 & lt； a & lt8 b5 & lt； a & lt 1 1 c8 & lt； a & lt 1 1d 6 & lt； a & lt 10

9. If it is completely flat, the value of k is ().

A 6 B 6 C 12 D 12

10. The condition that the score is meaningful is ()

A B C D

3. Factorization: (12')

( 1) (2)

(3) (4)

Four. Calculation: (8')

( 1)

(2)

5. Simplify before evaluating: (5')

In ...

6. Equation: (5')

7. Assuming that this equation has an increasing root, find the value of k .. (5')

Eight. As shown in the figure: It is known that ∠ A = 70 in △ABC, BD and CE are bisectors of △ABC, and BD and CE intersect at O, so find the degree of ∠BOC. (5′)

9. As shown in the figure, it is known that △ABC and △CDE are equilateral triangles and ∠ 1=∠2. Verification: AE=BD.

10. A ship goes downstream 105km, and goes upstream for 60km, which takes 9 hours. On another occasion, it sailed 84km downstream and 75km upstream in the same time, thus calculating the sailing speed and current speed of the ship in still water. (5′)

References:

【url=/plug-ins/ad/get.asp？ Get= 142003] Good place for free courseware, course plans, papers, papers and online exams [/url]