mathematical problem

First, judge the problem. (*** 50 points)

1.(2 points) true or false:

If α> 2,

2.(2 points) True or false:

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3.(2 points) True or false:

Calculation ()

4.(2 points) True or false:

The solution of the system 3x-y = 9 is x = 3.

x-2y=3 y=0

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5.(2 points) True or false:

Calculation: (-2a+5a)-[(3a-8a)-(6a-2a)] =-12a.

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6.(2 points) True or false:

In, the cardinality is-and the exponent is 3. ()

7.(2 points) True or false:

This equation has no solution.

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8.(2 points) True or false:

Decomposition factor: x2+6xy+9y2-4m2+4mn-N2 = (x+3y+2m-n) (x+3y-2m-n).

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9.(3 points)

Multiple choice questions: judging right or wrong

Decomposition factor: x4-14x2+25 = (x2+2x-5) (x2-2x+5) ()

10.(3 points) true or false:

Decomposition factor: 343m6-125n12 = (7m2-5n4) (49m4+35m2n4+25n8).

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1 1.(3 points)

Judge right or wrong

It is known that the symmetry axis of parabola is parallel to the Y axis, and its two intersections with the X axis are A (3 3,0) and B (- 1 0) respectively, and the distance from the vertex C to the point A is, and the analytical formula of this parabola is Y = x2-2x-3 or Y =-x2+2x+3.

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12.(3 points) true or false:

Denominators are physical and chemical (in a simple way)

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13.(3 points) true or false:

When x =-3 and y = 5.

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14.(3 points) true or false:

In a factory, there are workers A in the first workshop, 4 fewer workers in the second workshop and 7 more workers in the third workshop than the 13 times of the first workshop, so the number of workers in the third workshop is [( 13a-4)-7].

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15.(3 points)

True or false:

a3m-a3m+3 = a3m( 1-a)( 1+a+a2)

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16.(3 points) true or false:

Decomposition factor: x4+2x2-3 = (x+1) (x-1) (x2-3).

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17.(3 points) true or false:

Simplification: x-(x-4y-6z)+2(-2x-2y+z) is -4 x+8z.

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18.(3 points) Choose a topic: judge whether it is true or not.

Decomposition factor: 2x3+x2-4x-12 = (x-2) (2x2+5x+6)

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19.(4 points) true or false:

The distance between a and b is 20 kilometers. A and B leave from A and B at the same time and meet on the road two hours later. Then A returns to A and B moves on. When A returned to A, B was still 2 kilometers away from A..

The speed of (1) A is 5.5 km/h.

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(2) The speed of B is 4.5 km/h..

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Second, multiple choice questions. (*** 49 points)

20.(2 points) When AC < 0 and AB < 0, the image with linear function y = x- will not pass.

[ ]

A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant

The solution of 2 1.(2 points) equation: Yes.

[ ]

A. or -B.- C.- D.- or-

22.(2 points) The image as shown in figure Y = │ A │ X+│ B │ (A and B are non-zero constants) should be

[ ]

23.(2 points) The value of the vertex of a given parabola Y = AX2+BX+C in the third quadrant.

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

24.(2 points) the solution of the equation is

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a2，-B- 2，-C2，d-2，

25.(2 points) The solution of the equation 12x2+3 = 13x is

[ ]

26.(2 points)

The number is

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A. Equal numbers B. Reciprocal

C. reciprocal D. reciprocal negative number

27.(2 points) If point P(m, 3-m) is a point in the second quadrant, then m satisfies.

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< 0 b.m > 3 c.0 < m < 3 d.m < 0 or m > 3 in the morning.

28.(2 points) If the sum of three consecutive even numbers is 6 times greater than the smallest even number, then these three numbers are

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A.0，2，4 B.0，-2，-4 C.2，4，6 D.-2，0，2

29.(2 points)

Then, the two roots of the unary quadratic equation x-3 = 0 are

[ ]

A.=-3, = 1

30.(2 points)

Equation set: 3x-2y = 10 ① The solution is

5y-3x= 12 ②

[ ]

A.x= B. x=8 C. x= D. x=-

y= y= y=7 y=-7

3 1.(3 points)

If there are two equations-17x+9 = 0, the following correct relationship is

[ ]

A.B.

C.D.

32.(3 points) It is known that y-(m-3) is directly proportional to X (m is a constant), when X = 6, Y = 1, when X =-4, Y =-4, then the functional relationship between Y and X is

[ ]

a . y =-2x+2b . y = x+4c . y = x-2d . y =-x-4

33.(3 points) A polynomial is divided by (3am+ 1)2. As a result, then this polynomial is

[ ]

A.am+5-3a2m+3+9a2m+2b . a2m+5-3a2m+ 1+9a2m+3

C.a2m+5-3a2m+3+27a2m+2d . a2m+5-3a2m+3+9a2m

34.(3 points)

The output value of a factory in January was 654.38 million yuan, and the total output value in the first quarter was 700,000 yuan, with an average monthly growth rate of

[ ]

A. 10% B.20%

C.50% D. 100%

35.(3 points) The following calculation results are wrong.

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A.(a2+4)2-(a+2)(2-a)(a2+4)= 2 a4+8 a2

B.8 1(x+2)2(x-2)2-(3x-5)2(3x+5)2 = 67 1- 198 x2

C.2(2x+3y)(3y-2x)-(3x+2y)2-(3x-2y)2 =-36x 2

36.(3 points)

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A.2+a B.a C.-2-a D.-a

37.(3 points) The variance of given data x 1, x2, …, xn is s2, and the variance of new data 2x 1, 2x2, …, 2xn is

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A.s2 B. s2 C.2s2 D.4s2

Third, fill in the blanks. (*** 5 1 min)

38.(2 points) ABCD, AB ‖ DC, up to ⊥ AB, AB = 13, CD = 8, AD = 12, then the distance from A to BC is _ _ _ _ _ _ _.

39.(2 points) The solution of equation = 2x is X = _ _ _ _ _ _

40.(2 points)

If a is negative, | a | = _ _ _ _ _ _

4 1.(3 points)

Someone is walking by the streetcar. Note that every 6 minutes, a tram comes from the back to the front, and every 2 minutes, a tram comes from the opposite side. If the speed of people and trams is always the same, the time interval of tram departure is _ _ _ _ _ _ _ _.

42.(3 points) If x =-2 is known, the value of x4+4x3+2x2+4x+4 is _ _ _ _ _ _ _.

43.(3 points) If x and y are the integer part and decimal part of 8- respectively, 2xy-y2 = _ _ _ _ _ _

44.(3 points) As shown in the figure, AB is the diameter of a semicircle, O is the center of the circle, P is a point on the extension line of AB, PC cuts a semicircle on C, CD⊥AB is on D, PC: Pb = 2: 1, AB = 6. Then the length of the CD is _ _ _ _ _ _ (.

45.(3 points) When x = 3 and y =- 1, the value of 8x2-5x(3y-x)+4x(-4x- y) is _ _ _

46.(3 points)

A container is filled with 64 liters of pure liquid medicine. After pouring out some pure liquid medicine for the first time, it was filled with water. The liquid medicine poured out for the second time is half of that poured out for the first time, and then filled with water. At this time, the remaining pure liquid medicine in the container is 42 liters, so the liquid medicine poured out for the first time is _ _ _ _ _ _ _ _ _ _ _.

47.(3 points) Calculation:

48.(3 points) The difference between the polynomial 3x3+ 10x2-6x+ 1 and _ _ _ _ _ _ _ is divisible by x2+3x-3, and the quotient 3x+ 1 is obtained.

49.(3 points)

Equation about X: If the two real roots of x2+(2m+3) x+m2-3m-3 = 0 are reciprocal, then the value of m is _ _ _ _ _ _.

50.(6 points) There is a pasture where the grass grows at a constant speed every day (the amount of grass growth every day is equal). If you graze 24 cows, you will eat the grass in 6 days, and if you graze 2/kloc-0 cows, you will eat the grass in 8 days. Let each cow eat the same amount of grass every day. (1) If you graze 16 cows,

5 1.(6 points)

There are 94 people in Class A and Class B. After-class math groups are organized by grade. It is known that there are students in Class A and Class B, *** 16, so the number of people participating in the math group is _ _ _ _ _ _ _ _ _ _ _.

52.( 12 points) Write the frequencies from top to bottom in the frequency distribution table below.

First, judge the problem. (*** 49 points)

1.(2 points) t

2.(2 points) f

3.(2 points) t

4.(2 points) t

5.(2 points) f

6.(2 points) t

7.(2 points) t

8.(2 points) f

9.(3 points) f

10.(3 points) t

1 1.(3 points) t

12.(3 points) t

13.(3 points) f

14.(3 points) f

15.(3 points) t

16.(3 points) f

17.(3 points) t

18.(3 points) t

19.(4 points) TT

Second, multiple choice questions. (*** 49 points)

20.(2 points) c

2 1.(2 points) d

22.(2 points) b

23.(2 points) b

24.(2 points) A.

25.(2 points) d

26.(2 points) b

27.(2 points) A.

28.(2 points) A.

29.(2 points) c

30.(2 points) A.

3 1.(3 points) c

32.(3 points) c

33.(3 points) c

34.(3 points) d

35.(3 points) c

36.(3 points) c

37.(3 points) d

Third, fill in the blanks. (*** 5 1 min)

38.(2 points) 12

39.(2 points) 0

40.(2 points)-A.

4 1.(3 points) 3

42.(3 points) 3

43.(3 points) 5

44.(3 points) 12/5

45.(3 points) 48

46.(3 points) 16

47.(3 points) 1

48.(3 points) 4

49.(3 points) 4

50.(6 points)18; 12

5 1.(6 points) 9; seven

52.( 12 points) 0.08; 0. 10; 0.20; 0.36; 0.26; 1

Junior high school mathematics self-test questions

(Total score: 100)

Check the answer

First, judge the problem. (*** 33 points)

1.(2 points)

True or false:

If A+B = 1, A2+B2 = 1.

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2.(2 points) True or false:

Decomposition factor: m15+m12+M9+M6+m3+1,and the result is (m+1) (m2-m+1) (M6+m3+/kloc-0.

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3.(2 points) True or false:

Decomposition factor: a12+a10-a7+2a6-a5-2a11,and the result is a5 (a-1) 3 (a4+a3+a2+/kloc-0.

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4.(2 points) True or false:

The decomposition factor x4+y4+(x+y) 4 = 2 (x2+y2+xy) 2.

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5.(2 points) True or false:

The minimum value of the function y = 3+1 is+1 (where x >-5).

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6.(2 points)

True or false:

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7.(2 points) If "*" stands for operation symbol, indicating that a * b =, then 5 * (3 * 2) = _ _ _ _. (expressed in decimal)

8.(2 points)

True or false:

If a+b = 1

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9.(2 points) True or false:

If, and A, B, C are not equal, then X+Y+Z = 0.

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10.(2 points) true or false:

As we all know, x, y and z are three unequal real numbers.

Then = 1

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1 1.(2 points) true or false:

If x =, y =, z =,

Then (1+x) (1+y) (1+z) = (1-x) (1-y) (1-z).

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12.(2 points)

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13.(3 points)

True or false:

If a≥, then = 1

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14.(6 points)

If the vertex of the parabola y = x2+2 (cos α) x+sin2α is (m, n),

The relationship between m and n is 2m2+n = 1.

( )

The value range of n is-1≤n≤ 1.

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Second, multiple choice questions. (*** 33 points)

15.(2 points) In the following methods to prove that a graph is a trajectory, it is incorrect.

[ ]

A. Every point on the trajectory meets the conditions, and every point not on the trajectory does not meet the conditions.

B. None of the points that do not meet the conditions are on the trajectory, and all the points on the trajectory meet the conditions.

C. Every point that meets the conditions is on the trajectory, and every point on the trajectory meets the conditions.

D. Every point that is not on the trajectory does not meet the conditions, and every point that does not meet the conditions is not on the trajectory.

16.(2 points) Given real numbers A, B and C satisfy A+B+C = 0 and ABC = 8, the value is.

[ ]

A. positive number B. zero C. negative number D. positive and negative can not be determined

17.(2 points) The smallest product of AB=a, CD=b (a C > 0, =, L2, L 1, L2 L3, L 1, L22 is

[ ]

A.L2 L2 L3

C.L3 L 1 D.L22

19.(2 points) d is a point on the bisector of ∠A in △ABC. Let m = AB+AC and n = DB+DC, then the relationship between m and n is

[ ]

A.m > nb.m = n.c.m < n.d. Not sure.

20.(2 points) The perimeter of a triangle is even, and the two sides are 4 and 1997 respectively, so the number of triangles satisfying the above conditions is

[ ]

A. 1 B.3 C.5 D.7

2 1.(2 points)

As a result of simplification,

[ ]

a . 1 b . 2 c . 1d .- 1

22.(2 points) The inner angle of a convex N polygon has exactly four obtuse angles, so the maximum value of N is

[ ]

A.5 B.6 C.7 D.8

23.(2 points) As shown in the figure, in the convex pentagonal ABCDE, ∠ A = ∠ B = 120, and EA = AB = BC = 2, CD = DE = 4, then its area is

[ ]

A.5 B.6 C.7 D.8

24.(3 points) The two sides of an equilateral triangle are two of the equation X2+PX+ 1 = 0, and the length of the third side is 2, so the range of p is

[ ]

A.-2 < p

C.-2 B > C, 22B = A+C, 3A2+B2+C2 = 84, and 4B is a positive integer, then the value of b is _ _ _ _ _ _ _ _.

38.(3 points) The value of simplification is equal to _ _ _ _ _ _ _ _ _.

39.(3 points)

A and B go from A to B at the same time. Party A rides a bike to C first, and then walks. B walk to c first, and then ride a bike. As a result, they both arrived at B at the same time. If the walking speed of A and B is 15km/h and 10km/h respectively, and the cycling speed is 20km/h, then their average speed during this journey is _ _ _ _ _ _ _ _ km/h. 。

40.(3 points) In △ABC, ∠ BAC = 120, and p is any point in the isosceles triangle ABC. If M = PA+Pb+PC and N = AB+AC, then the relationship between m and n is m _ _ _ _ N. (Use

4 1.(6 points)

According to the regulations on civil electricity charges, each household charges 20.7 cents per degree per month. If it exceeds 24 degrees, the excess will be charged at 6 cents per degree. After a month, a household pays 8.8 cents more than B household (the electricity fee is charged in full). How much is the electricity bill paid by Party A and Party B respectively? A _ _ _ _ _ _ _ _ _ _ _ points, B _ _ _ _ _ _ _ _ (unit)

First, judge the problem. (*** 33 points)

1.(2 points) t

2.(2 points) t

3.(2 points) t

4.(2 points) t

5.(2 points) t

6.(2 points) t

7.(2 points) t

8.(2 points) t

9.(2 points) t

10.(2 points) t

1 1.(2 points) t