First, multiple-choice questions (3 points for each small question, 30 points for * * *)

1. Among the following triangles with side lengths, the one that can form a right triangle is ().

A.3、4、6 B. 15、20、25 C.5、 12、 15 D. 10、 16、25

2. Assuming that the distance from point P to X axis is 3 and the distance from point P to Y axis is 2, the coordinates of point P must be

A, (3,2 2) B, (2,3 3) C, (-3, -2) D, none of the above answers are correct.

3. The main view of the geometry in the figure below is

4. It is known that point P(3, -2) and point Q are symmetrical about X axis, so the coordinate of point Q is ().

A.(-3，2) B.(-3，-2) C.(3，2) D.(3，-2)

5. If the image of the proportional function y = (1-2m) x passes through point A (x 1, y 1) and point B (x2, y2), if X 1 < X2, Y 1 > Y2, then

A.m < 0 b . m > 0 c . m < 12d . m > 12

6. As shown in the figure, ∠ 1 and ∠2 are complementary, ∠ 3 = 130, so the degree of ∠4 is ().

A.50 years ago, 60 years ago, 70 years ago and 80 years ago

7. In the figure below, the straight line y=x- 1 is ().

8. In the picture below, what can't be folded into a square is ().

(A) (B) (C) (D)

9. The two sides of an isosceles triangle are 4 and 5 respectively, so its circumference is ().

A.12b.13c. 14d.13 or14.

10. The following judgment is correct ()

A. Two isosceles triangles with equal vertex angles are congruent.

B. Two isosceles triangles with equal waist are congruent.

Two right triangles with one side and an equal acute angle are congruent.

Two isosceles triangles with equal vertices and bases meet.

Fill in the blanks (4 points for each small question, 24 points for * * *)

1 1. Given the sample: 3, 4, 0, -2, 6, 1, then the variance of this sample is _ _ _ _ _ _ _.

12. Inequality 2x- 1

13. Given the image passing point (-1 2) of a function, the value of function y decreases with the increase of independent variable X. Please write the function relation that satisfies the above conditions: _ _ _ _ _ _ _.

14. If the right side of an isosceles right triangle is 1 cm, then the high line on its hypotenuse is _ _ _ _ _ cm.

15. in Rt△ABC, AB = 5 and BC = 3, then AC = _ _ _ _ _ _ _ _

16. move the point P(-3, y) down by 3 units and to the left by 2 units to get the point Q(x,-1), then xy = _ _ _ _ _ _ _ _ _ _ _ _

Third, answer questions.

17. Solve the inequality group and express its solution set on the number axis: (The full mark of this question is 6 points)

18. As shown in the figure, BD and CE are the high lines of △ABC, BD = CE, and △ABC is an isosceles triangle? Please explain your reasons. (The full mark of this question is 6 points)

19. Teacher Wang gives exercise books to the students in Class 2, Grade 2 (1). If four copies are given to each student, there are still 24 copies left.

Ben; If each student is assigned five copies, then only one student is assigned less than five exercise books.

Please count the number of people in this class. (The full mark of this question is 6 points)

20. (The full mark of this question is 8) It is known that the image of a linear function passes through (2,5) and (-1,-1).

(1) Find the analytical expression of this linear function.

(2) Draw the image of this function.

2 1. (The full mark of this question is 8) A middle school held a speech contest of "Eight Honors and Eight Disgraces". Five players from Class 9 (1) and Class 9 (2) will participate in the semi-finals. The results of the semi-finals of the five players selected by the two classes (full marks are 100) are shown in the figure below. (1) Fill in the following table according to the picture on the left.

Average score (score), median score (score) and mode score (score)

Category 9 (1) 85 85

Nine (Class Two 85 80

(2) Combining the average score and median score of the two classes, analyze which class has better score in the rematch.

(3) If each class chooses two players to participate in the semi-finals, which class do you think is stronger, and explain the reasons.

22. (The full mark of this question is 10) Write the coordinates of each vertex as shown in figure △ABC, and work out the area of this triangle.

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

As shown in the figure, EF‖AD, ∠ 1 =∠2, ∠ BAC = 70, and find the degree of ∠AGD.

24. (The full mark of this question is 12) In order to encourage Xiao Qiang to do housework frequently and cultivate his labor consciousness, Xiao Qiang's monthly expenses are obtained from his parents according to the reward he got for doing housework last month and the basic living expenses. If Xiao Qiang spends x hours doing housework every month, and the total sum he can get this month (that is, next month) is Y yuan, then the function image between Y (yuan) and X (hours) is as shown in the figure.

(1) Please write down the basic monthly living expenses in Xiao Qiang according to the pictures; How do parents reward Xiao Qiang for doing housework?

(2) Write the corresponding functional relationship between Y and X when 0≤x≤20;

(3) If Xiao Qiang needs 250 yuan's expenses in May, how much time does Xiao Qiang need to do housework in April?

1. Fill in the blanks: (2 points for each question, ***28 points)

1, if x+y=0 and xy=7, then x2y+xy2 = _ _ _ _ _ _ _ _ _ _

2. The lengths of two sides of an isosceles triangle are 25cm and 12cm respectively, so the length of the third side is _ _ _ _ _ _ _ _ cm.

3.4x2x2+2kxy+9 is a completely flat pattern, so the value of k is _ _ _ _ _ _ _.

4. In △ABC, AB=AC, ∠ A = 40, BD⊥AC in D, then ∠ DBC = _ _ _ _ _ _ degrees.

5. Factorization: (1) 9a2-B2 = _ _ _ _ _ _. (2)9x2- 12xy+4y2=________ .

(3)x6-64y3=_______________ .

6. When x _ _ _ _ _ _ (x-3)/(x2-5x+6) is meaningful.

7. When x _ _ _ _ _ _ the value of (x2-x-2)/(x-2) is zero.

8. The inverse proposition of "right angles are all equal" is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

9. in △ABC, AB=AC. If AD is high and ∠ DAB = 40, ∠BAC is _ _ _ _ _.

10, as shown in figure. In △ABC, AB=AC, BD is the bisector of △ABC, BD=BE, ∠ A = 100, then ∠ DEC = _ _ _ _ degrees.

1 1, the sum of three internal angles of an isosceles triangle and an external angle of the top angle is equal to 260, then its base angle is equal to _ _ _ _ _ _ _.

2. True or false questions: (65438+ 0 points for each question, ***4 points)

1. Two triangles with two sides and an angle are congruent. ( )

2. The midline of two sides and one of them corresponds to the coincidence of two equal triangles. ( )

3. Two isosceles triangles with a vertex angle of 80 are congruent. ( )

4. Two triangles whose two sides are equal in height and one of them is identical. ( )

Three, multiple choice questions: (2 points for each question, ***20 points)

1, when m=a-4 and n=2a-3, the value of 4m2-4mn+n2 is _ _ _ _.

A, 25 B, 12 1 C, 49 D, all of the above are wrong.

2. The common factor of algebraic expressions x4- 16, x3-8, x2-7x+ 10 is _ _ _ _.

a、x+2 Bx2+4 C、x2-4 D、x-2

3. When △ABC, ∠ A = 70, BO and CO are bisectors of ∠B and ∠C respectively, which intersect at point O ... then ∠BOC is _ _.

A, 100 b, 1 15 c, 125 d, uncertain.

4, the following proposition is correct _ _ _ _.

A. Two equilateral triangles have an angle corresponding to each other. B, there is an angle corresponding to the congruence of two right triangles.

C, two equilateral triangles with one side corresponding to the same are congruent. D, two triangles with the same height as the third side are congruent.

5. If A, B and C are the three sides of △ABC, the value of the algebraic formula a2-2ab-c2+b2 is _ _ _ _ _ _ _ _.

A, greater than B, less than zero C, equal to zero D, uncertain.

6. If a/b=c/d and m≠0, the following equation is _ _ _ _.

a 、( a-m)/b=(c-m)/d B、a/b=(c+m)/(d+m) C、a/bm=cm/d D、a/b=cm/dm

7. Rational formulas are 3/y, 1/2(a+b), x/π- 1, 5/(x- 1), (x+y)/2, (1/x)+X.

a， 1 b，2 c，3 d，4

8. As shown in the figure: AB=AC, BE=CD, BD=CF, then ∠ EDF = _ _ _ _ _

a、 180 -2∠B B、 180 -∠B C、90 -∠B D、∠B

9. If the top angle of an isosceles triangle is 36, then the bisector of a bottom angle and the original triangle bisect to form _ _ _ _ _.

A, two equilateral triangles B, two isosceles triangles C and two right triangles D are all wrong.

10, if the factorization result of x2-px+mn is (x+m)(x+n), then p is _ _ _ _ _.

a、m-n B、m-n C、m+n D 、-m+n

Fourth, answer the following questions

1, decompose the following polynomial factors (4 points for each question, *** 16 points)

( 1)a6-3 a4+2 a2(2)(x2-x)2-5(x2-x)+6

(3)(a2+B2- 1)2-4a2b 2(4)-(x-y)2n+x6y 2(y-x)2n

2. As shown in the figure, in △ABC, ∠B=∠C, D is the midpoint of BC, DE⊥AB is in E, DF⊥AC is in F, and verification: AD divides ∠EDF equally. (5 points)

3. Calculation: (4 points for each small question *** 12 points)

( 1)(-x2y/4a)2 \u(-y/2a3x)2？ (-2x/ay)4(2) 1/(x+3)-6/(x2-9)-(x- 1)/(6-2x)

(3)[a+a/(a2- 1)]⊙[a+ 1/(a- 1)- 1/(a+ 1)]

4. Given a hypotenuse and a right-angled side, find a right-angled triangle (you need to draw with a ruler and ruler, you don't need to write and prove) (4 points).

└———————————┘a

└————————┘b

Five (3 points for each question, ***6 points)

1, known as: x+y=3, xy=-5, find the value of: 1/x2+ 1/y2.

2. Given that a2+b2-8a+6b+25=0, find the value of (2a2-ab-6b2)/(a2-4ab+4b2).

Six, as shown in the figure: It is known that in △ABC, AC=BC, ∠ C = 90, D is the midpoint of AB, EF is on BC and CA respectively, and be = CF

Verification: (1) de = df; (2)DE⊥DF。 (6 points)

Answers to Math Test Paper in Lower (Upper) Term of Shahe No.2 Middle School

I. Fill in the blanks:

1、0

2, 25 cm

3、 6

4、20

5 、( 1)(3a+b)(3a-b)(2)(3x-2y)2(3)(x2-4y)(x4+4x2y+ 16 y2)

6、x≠2，x≠3 .

7、x=- 1

8. Equal angles are right angles, which is a false proposition.

9、80

10、 100

1 1、40

Second, the judgment:

1、×2、√3、×4、×

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

Four. 1，( 1)A2(A+ 1)(A- 1)(A2-2)

(2)(x-2)(x+ 1)(x2-x-3)

(3)(a+b+ 1)(a+b- 1)(a-b+ 1)(a-b- 1)

(4)(a-y)2n(x3y+ 1)(x3y- 1)

2. Omission

3. Omission

4 、( 1)4x 10/y4

(2)(x+7)/2(x+3)

(3) A /2

5、( 1) 19/25 (2)- 1/ 10

Sixth, ellipsis

1. Fill in the blanks: (3 points for each small question, ***60 points)

1, calculation:-(-5)+3 = _ _ _ _ _ _

2. Factorization: ab3-a3b=.

3. Calculation:-=.

4. Factorization: x2-3x-4 =.

5. When x, the score is meaningful.

6. If one factor of polynomial a2-ab-3a+3b is a-3 and the other factor is.

7. The polynomial a3-3a2+2a is decomposed into factors, and the result contains the factors.

8. The circumference of an isosceles triangle is 10cm, and one side is 3cm, so the waist length of this isosceles triangle is _ _ _ _ _.

9. Equation about X: The solution of 2ax-a = 0 (A0) is X = _ _ _ _ _ _ _

10, when x, the value of the score is positive.

1 1, as shown in the figure: there is a triangle in the figure.

A triangle with an internal angle of ∠C is.

12, Party A and Party B contract a project, which can be completed in 10 day; If it takes 2 days for A to do it alone, and X days for A to do it alone, then the equation can be listed as _ _ _ _ _ _ _.

13, the lengths of two sides of the triangle are 2 and 9 respectively, and the third side is odd, so the length of the third side is.

14. In an isosceles triangle, if the lengths of two sides are 4 and 9 respectively, then its circumference is.

15. Given that the degree ratio of the three internal angles of a triangle is 2: 3: 4, the degree of the three internal angles of this triangle is.

In 16 and △ABC, BD and CD are bisectors of ∠ABC and ∠ACB, respectively, and ∠ BDC = 1 10, then the degree of ∠A is.

17, as shown in the figure: △ ABC △ EFC, AB=EF, ∠ABC=∠EFC.

Then corresponding to the edge, corresponding to the angle.

18, as shown in figure AO bisects ∠BAC, AB=AC, and there is a triangle congruence in the figure.

19, calculation: () 2 = _ _ _ _ _ _

20. in rt △ ABC, if pheasant side AB=5 and right-angled side BC=4, the other right-angled side CA is.

Second, multiple-choice questions: (3 points for each small question, ***45 points)

2 1, the following factorization deformation, the correct is ()

a . ab(a-b)-a(b-a)=-a(b-a)(b+ 1)b . 6(m+n)2-2(m+n)=(2m+n)(3m+n+ 1)

c . 3(y-x)2+2(x-y)=(y-x)(3y-3x+2)d . 3x(x+y)2-(x+y)=(x+y)2(2x+y)

22, the following polynomial can't be decomposed by the square difference formula is ().

A.a2 B2- 1 b . 4-0.25 y4 c . 1+a2 d .-x4+ 1

23, the following polynomial can be decomposed by the complete square formula is ()

a . m2-Mn+N2 b . 1-4ab c . x2+2x+d . x2+2x- 1

24. It is known that a2+ma+4 is completely flat, so the value of m is ().

a 、+ 1 B 、- 1 C 、+4 D、4

25, (a+b)2+8(a+b)-20 factorization ().

A.(a+b+ 10)(a+b-2)b .(a+b+4)(a+b-5)c .(a+b+5)(a+b-4)d .(a+b+2)(a+b- 10)

26. The following statement is correct: ()

A, the square root of 16 is 4 B, and that of-15)2 is-15.

The arithmetic square root of c and 4 is 2 D. If x2 = 1 1, then x =

27, all of the following belong to factorization is ()

A.(3x+ 1)(3x- 1)= 9 x2- 1 b . x2-2x+4 =(x-2)2

c . a4- 1 =(a2+ 1)(a+ 1)(a- 1)d . 9 x2- 1+3x =(3x+ 1)(3x- 1)+3x

28. The decomposition factor adopts the grouping decomposition method, and the correct grouping is ()

A.(x2-y2)+(6y-9)； b .(x2-9)-(y2-6y)； c . x2-(y2-6y+9)； D.(x2+6y)-(y2+9)

29, ①, ② x2y-3xy2, ③, ④ ⑤, all have scores ().

A.①③④ B. ①②③ C. ③⑤ D. ①④

30, in the following categories, the incorrect deformation is ()

A.=- B. =-

C.=- D. =-

3 1.Rt△ABC, if the difference between two acute angles is 16, the larger acute angle is equal to ().

a、53 B、37 C、56 D、42

32. The lengths of two sides of a triangle are 5 and 7 respectively, so the value range of the third side is ().

A.a & lt 12b . a & gt； 2 C.2 & lta & lt 12 D.2≤a≤ 12

33. If the degree ratio of three internal angles of a triangle is 6: 1: 5, then the triangle is ().

A. acute triangle B. right triangle C. obtuse triangle D. uncertainty

34, as shown in figure AB‖CD, ∠ A = 35, ∠ C = 75, then ∠ E.

The degree is ()

35 BC to 40 BC

As we all know, A, B and C are three sides of a triangle. The result of simplifying A+B-C-B-A-C is ().

A.0 B.2a C.2(b-c) D.2(a+c)

Three. Answer: (45 points)

36. Factorization: (12, 6 points for each small question)

( 1) (2)、a2+8a+ 16

37. Calculation or evaluation: (6 points for each small question. *** 12 points)

(1) calculation: (2) calculation:

38. As shown in the figure, draw the center line on the side of BC.

The bisector of ∠ B (don't write, but keep the trace) (8 points)

39. Students from Class 3, Grade 2 of Weixin Middle School visited a place 15km away from the school. Some of them ride bicycles first. After 40 minutes, the others set off by car. As a result, they arrived at the same time. As we all know, the speed of a car is three times that of a bicycle. What are the speeds of the two cars? (13)

First, multiple-choice questions (3 points for each question, ***30 points)

The arithmetic square root of 1.4 is ()

A.2b–2c . d . 2

3. Enlarge the three sides of a right triangle by the same multiple, and the triangle is ().

A. acute triangle B. obtuse triangle C. right triangle D. arbitrary triangle

4. Every regular polygon with an internal angle of 120 is ().

A. square b regular pentagon c regular hexagon d regular octagon

5. The regular polygon that can be densely laid separately is ()

A. regular pentagon, regular hexagon, regular heptagon and regular octagon

8. The following is a part of the table of food nutrients (the nutrient content of the edible part per100g of food). In the data composed of grams of carbohydrates provided in the table, the median and mode are () respectively.

Vegetables: mung bean sprouts, Chinese cabbage, rape, cabbage, spinach, leeks and carrots.

Carbohydrate 4 3 4 4 2 4 7

A.4，3 B. 4，4 C. 4，7 D. 2，4

9. It is known that the proportional function y =-kx and the linear function y=kx-2 (x is the independent variable) are images in the same coordinate system.

Roughly ()

A B C D

10. If in △ ABC, AB= 13, AC= 15 and AD= 12, the length of BC is ().

A. 14

Fill in the blanks (3 points for each question, 30 points for * * *)

1 1. Suppose that the average of the five numbers 7, 4, 3, a and 5 is 5, then a=.

12.p (3,–4) is symmetrical about the origin.

13. It is known that the image of linear function y=kx+b passes through point (0,–5) and is parallel to the image of straight line y= x, then the linear function table.

The expression is.

14. Suppose+| 2x–y | = 0, then x–y =

15. As shown in the figure, the ABCD of the small fish is rhombic, and the known fish length BD=8 and AB=5. Take the straight line where BD is located as the X axis and the straight line where AC is located as the Y axis, and establish a rectangular coordinate system, then the coordinate of point C is.

(Question 15) (Question 16) (Question 20)

16. As shown in the figure, given the isosceles trapezoid ABCD, AD‖BC, AD=5cm, BC= 1 1cm, and the height DE=4cm, then the ladder.

The circumference of the shape is.

18. The area of the triangle enclosed by the straight line y=2x+8 and the coordinate axis is.

20. Fold a rectangular piece of paper as shown. After folding along AE, point D falls on point F on BC side, which is known.

AB=8cm, BC= 10cm, then S△EFC=.

Third,

22.(5 points) Calculation: -2+(- 1) 2.

24.(6 points) As shown in the figure, is it known that in the parallelogram ABCD, E and F are on the diagonal AC, AE=CF, and the quadrilateral EBFD is a parallelogram? Try to explain why.

26.(8 points) As shown in the figure, l 1 represents the relationship between the sales volume of notebook computers in a shopping mall, and l2 represents the relationship between the sales cost and the sales volume of notebook computers in the shopping mall:

(1) When x=2, the sales amount = _ _ ten thousand yuan, the sales cost = _ _ ten thousand yuan and the profit (income-cost) = ten thousand yuan. (3 points)

(2) When a table is sold one day, the sales amount is equal to the sales cost. ( 1)

(3) The corresponding function expression of l1is. (2 points)

(4) Write the functional expression between profit and sales. (2 points)