46. The number of solutions of the equation sinπx= is.

47. If the equation 4x+(4+A) 2x+4 = 0 has a solution, the range of the real number a is.

48. If the function f(x) is odd function on R, the period T=5 and f (3) = 0, then the equation f (x) = 0 has at least one root in the interval (0, 10).

49. If | |=3, | |=5 and | |=7, the included angle is.

50. Known = (3,4), when || takes the maximum value, =.

55. It is known that | |=2, | |=3, and the included angle with is, the short diagonal length of the parallelogram is, and the adjacent side is.

52. The parabola x2=2y is just tangent to the straight line 2x-y+6 = 0 after being translated by the vector (-3,2), and the coordinates of the tangent point are.

53. If O is the origin of coordinates, y2=2x and the straight line of focus intersect at point A and point B, it is equal to.

54. For x∈R, the range of function y= is.

55. The maximum value of the function f (x) = 3x+2+4 is. The maximum value of the function f(x)=5 is.

56. Let M= and a+b+c= 1 (where a, b, c∈R+), then the range of m is.

57. If the inequality about x | x-2 | +| x-a |≥ a is constant on R, then the maximum value of A is.

58. Known-1 59. It is known that P is the moving point on a straight line 3x+4y+8=0, PA and PB are two tangents of a circle x2+y2-2x-2y+ 1 = 0, A and B are tangents, and C is the center of the circle, so the minimum value of the quadrilateral PACB area is.

60. Let f (x) = x2+ax+b, and 1 ≤ f (- 1) ≤ 2, and 2≤f( 1)≤4, then the area of point (a, b) on the aob plane is.

6 1. If known, the minimum value of (x+ 1)2+(y+ )2 is.

62. The equation x2+ax+2b=0 about X has two roots in the interval (0, 1) and (1, 2) respectively, so the value range is.

63. It is known that the function f (x) = Asinx-BCOSX and a symmetric equation of the image is x =, then the inclination angle AX-BY+C = 0 is.

64. Let the coordinates of point A and point B be (1, 1) and (4,3) respectively, and point P is the point on the X axis, then the minimum value of |PA|+|PB| is

65. Fold a drawing once so that point (0,2) coincides with point (4,0) and point (7,3) coincides with point (m, n), then m+n =.

66. If the straight line y =-x+m and the circle x2+y2 = 1 have two different intersections in the first quadrant, then the range of the real number m is.

67. If the eccentricity of the ellipse = 1 is 0, then the distance between the two directrix is 0.

68. Equation = 1 represents an ellipse whose focus is on the X axis, so the range of real number A is.

69. The parabolic equation is called y2 = 4px (P >; 0), where a is the point on the parabola and f is the focus. If | af | = 4p, the value of |OA| is.

70. When the point P(x, y) moves on the curve (x-2) 2+2Y2 = 1, the maximum value of x+2y2 is.

7 1. Real numbers x and y satisfy x2+y2=5, and x≥0, m =, then the minimum value of m is.

72. It is known that point P is the moving point on the parabola y2=2x, and the projection of point P on the Y axis is m. If the coordinate of point A is (4), the minimum value of |PA|+|PM| is.

73. Given that point F is the right focus of hyperbola, point M is the fixed point on the right branch of hyperbola, and the coordinate of point A is (5,4), the maximum value of 4 | MF |-5 | Ma | is.

74. Let F 1, F2 be the focus of the ellipse = 1, P be its upper point and | pf1| | pf2 | =1,then tan∠F 1PF2=.

75. Let p be the moving point of the ellipse = 1, F 1 and F2 be the focus of the ellipse, then the minimum value of cos∠F 1PF2 is.

76. If the ellipse = 1 passes through point A (3,4), the minimum value of a2+b2 is _ _ _ _.

77. Let p be any point on an ellipse = 1, then the maximum distance from p to a straight line is 2x-3y+8 = 0.

78. Given the ellipse = 1 and point A (0,5), find a point B on the ellipse to maximize the value of |AB|, then the coordinates of point B are.

79. It is known that A (- 1, 0), B A(- 1, 0) and c point (x, y) are satisfied, then |AC|+|BC| is equal to _ _.

80. Knowing two points M (-5,0) and N M (-5,0), the following linear equations are given: ① 5x-3y = 0; ②5x+3y-32 = 0； ③x-y-4 = 0； ④ 4x-3y+ 15 = 0, there is a point p on the straight line, and all linear equations satisfying |MP|=|PN|+6 are. Fill in all the serial numbers you think are correct.

8 1. Any point on the hyperbola m = 1 Take the vertical line of one of its asymptotes, the vertical foot is n, and the o is the origin, then the area of △MON is.

82. The four planes of space intersect, and the set consisting of the number of intersecting lines is.

83. In the tetrahedron P-ABC, the three sides are perpendicular to each other, m is a point in the curved surface ABC, and the distances from the point m to the three curved surfaces PAB, PAC and PBC are 2, 3 and 6 respectively, so the distance from the point m to the vertex P is _ _ _ _ _.

84. It is known that in a regular tetrahedron A-BCD, AE= AB, CF= CD, E and F are on the sides of AB and CD, respectively, so the cosine of the angle formed by the straight line DE and BF is.

85. in ABC-a1b1c1,AA 1=AB=AC, ∠ BAC = 90, m is the midpoint of CC 1, q is the midpoint of BC, and p is a/.

86. In △ ABC, ∠C is a right angle, there is a point P outside the plane ABC, PC=4cm, and the distance from point P to straight lines AC and BC is equal to cm, so the angle formed by PC and plane ABC is.

87. cross the square ABCD? The vertex a of is a line segment of the ⊥ plane a ′ cd. If ⊥ A = AB, the included angle between plane A ⊥ AB and plane A ⊥ CD is.

88. It is known that there are PA=BC, PB=AC and PC=AB in the triangular pyramid P-ABC, and the dihedral angles formed by the three sides and the bottom are α 1, α2, α3, then cosα 1+cosα2+cosα3=.

89. In the cube ABCD-A1B1C1D1,where O is the intersection of AC and BD, the angle formed by C 1O and A 1D is (expressed as anti-cosine).

90. The three sides of a parallelepiped intersecting with the same vertex are all A, and the included angle between every two of these three sides is 60, so the volume of the parallelepiped is.

9 1. In tetrahedral ABCD, AC=2, S△ADC=6, S△ABC=4, and the dihedral angle formed by surface ABC and surface ADC is, then the volume of tetrahedral ABCD is.

92. The three opposite sides of the tetrahedron SABC are equal, respectively, and the volume of this tetrahedron is.

93. Five of the six sides of the tetrahedron are equal to A, so the maximum volume of the tetrahedron is.

94. As shown in the figure, it is an expanded diagram of a cube with a side length of 1. In the original cube, the following four propositions are given: ① The distance from point M to AB is; ② The distance between straight line AB and ED is: ③ The volume of triangular pyramid CDNE is: The angle between AB and EF is. The serial number of the correct proposition is (fill in the serial number of all correct propositions).

95. If there are four rays at a point in space, and the angle formed by every two rays is equal, then the cosine of this angle is.

96. The sphere with radius r is tangent to all six sides of the regular tetrahedron, so the side length of the regular tetrahedron is.

97. Choose a subset of five numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} so that the sum of any two of these five numbers is not equal to 1 1. Such a subset * * has

98. If the natural number n consists of several of the nine numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and the order from high to low happens to be from small to large, there are four such natural numbers n. 。

99.8 identical balls are arranged in a row in sequence, with red and white colors, three of which are painted red and the rest are painted white. If at least two balls are required to be painted red in succession, then * * * has a painting method (answer with numbers).

100. Five programs scheduled for a New Year's party in a class have been arranged in the program list, and two new programs have been added before the performance. If these two programs are inserted into the original program list, the number of different insertion methods is.

10 1. Dye each vertex of a pyramid with one color and make two vertices on the same side with different colors. There are five different colors to choose from, so the total number of different dyeing methods is.

102. Take two cards from 50 cards with 1, 2, 3, …, 50 written on them, and the product can be divisible by 6.

103. Choose three different numbers from 0, 1, 2, 3, 4, 5 and 6 as the coefficients A, B and C of the quadratic function y=ax2+bx+c, which meets the requirements of A >; B, so the number of different quadratic functions is.

104. Put nine identical footballs into three boxes numbered 1, 2, 3. It is required that the number of balls put in each box is not less than its number, so there are different ways to put them.

105.3 people sit in a row with 8 seats, and everyone has seats around, so the number of different sitting methods is.

106. Arrange the nine numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 into a square with three horizontal and three vertical lines. Three numbers in each column are required to be arranged from front to back, so the different arrangement numbers are (divided by numbers).

107. In the cube AC 1, the diagonal of each side, each face and the diagonal of the body * * * can form a pair of straight lines in different planes.

108.( 1-3a+2b) 5 The sum of the coefficients of the items without B is.

109. let (2x-1) 5 = A0+a1x+a2x2+a3x3+a4x4+a5x5, then | a1|+a2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

1 10. It is known that {an} is a geometric series with the first term as 1 and the common ratio as 2, then a1cn1+A2CN2+…+ANCN =.

1 1 1. Given (2x2+1) 6 = A0+a1x2+a2x4+…+a6x12, then a0+a2+a4+a6.

1 12. If a student randomly arranges the spelling order of the letters in the word "error", the probability that he just writes correctly is.

1 13. There are five balls numbered 1, 2,3,4,5 and five boxes numbered 1, 2,3,4,5. Now put these five balls into five boxes, and each box is required to put a ball, so there are exactly two ball numbers and box numbers.

1 14. In a shooting competition, if "someone shoots 8 shots in a row, only 4 shots hit, of which 3 shots hit in a row", the probability of this event is.

1 15. As shown in the figure, an electronic device is a loop consisting of three resistors, in which * * * has six solder joints A, B, C, D, E and F. If one solder joint falls off, the whole circuit will be blocked, and the probability of each solder joint falling off is. Now that the circuit is out of order, the probability that at least two solder joints will fall off is.

1 16. A product produced by a factory is packed in a box of 10 pieces, and each box of products can only leave the factory after passing the inspection. The quality inspection method stipulates that a box of products 10, 4 pieces are randomly selected for inspection, and if the number of defective products does not exceed 1 piece, the box of products is considered as qualified, otherwise it is considered as unqualified. If this box of products is inspected twice, the probability that the two inspection results are inconsistent is.

1 17. If you choose 4 pairs of 6 different gloves, the probability of at least one pair is.

1 18. A building has nine floors, and six people take the elevator from the first floor to the upstairs, but only one person can't get off halfway, so the probability that there are just two people on the top floor is (just write the expression).

1 19. There are the following propositions: ① the opposition of two events is a necessary and sufficient condition for the mutual exclusion of these two events; (2) If two events are independent of each other, then they must not be mutually exclusive events; ③ If P (AB) ≠ P (A) P (B), then A and B must not be independent events; (4) Let the probability of events A and B be greater than zero. If A+B is an inevitable event, then A and B must be opposite events, where the true proposition is (fill in the serial numbers of all true propositions).

120. The given function has an extreme value at x=3, and the monotone interval of the function is.

12 1. If the function f (x) = kx3+3 (k-1) x2-k2+1(k >; 0) is (0,4), then the value of k is.

122. The number of real roots of the equation x3-6x2+9x- 10 = 0 is.

123. At some point during the festival at the railway station, a certain amount of passengers still arrived. If only three ticket gates are opened, it will take half an hour for all stranded passengers to pass through the ticket gates. If six ticket gates are opened, it only takes 10 minutes for all stranded passengers to pass. Now all stranded passengers are required to pass within 5 minutes, so at least one ticket gate needs to be opened at the same time.

124. If the curve y =-x3+3 is tangent to the straight line y =-6x+b, then b=.

125. Among the tangents of the curve Y = x3+3x2+6x- 10, the tangent equation with the smallest slope is.

126. Known A >；; 5. The number of roots in the interval (0,3) of equation x3-AX2+ 1 = 0 is.

127. Given the image with function f (x) = AX3+Bx2+CX+D, the range of b is.

Second, multiple choice questions

128. the functions F(x) = 2x- 1, g (x) = 1-x2 and the constructor F(x) are defined as follows: when |f(x)|≥g(x), f (x) =| F.

C. there is a maximum value of 1 and no minimum value. D. there is no minimum value and no maximum value.

129. the function y=f(x) defined on r is the increasing function on (-∞, 2), and the symmetry axis of the image of the function y=f(x+2) is the straight line x=0, then

a . f(- 1)f(3)c . f(- 1)= f(3)d . f(2) 130。 Given the function f (x) =, the image of f (1-x) is.

A B C D

13 1. It is known that f (x) = ax (a >; 0 and a ≠ 1), f- 1 (3)

A B C D

132. The coordinate of the image symmetry center of the function y=2cosx(sinx+cosx) is

A.(，0) B .(， 1) C .(， 1) D. (-，- 1)

133. The image of function y = sin (1-x) is

A B C D

134. Function f (x) = msin (ω x+ψ) (ω >; 0) in the interval

7.-4 8.2a2-M 9。

10.6,-6 1 1. 12.3,4

13.-2 14.(-∞, ) 15.(- 1,2)

16. 17.f(4.5) 19。 20.(0,3) 2 1.-2

22.y=- 23。 -3 24.65

25.5 12 26.350 27.

28. 100 29.30.

3 1.32.33.3 1

34. The third quadrant 35. 1 36. -

37. (-4,38.6 39.7)

40.-4 4 1.-2 42.5

43.4π 44.45.30

46.7 47. (-∞,-8) 48.7

49.60 50.( ) 5 1. 15

52.(- 1,4) 53.- 54.(- 1, 1)

55. 12,3 56. The above is increasing function, and the following judgment about f(x): ①f(x) is a periodic function; ② The image of f (x) is symmetrical about the straight line x= 1; ③f(x) is a decreasing function; ⑤f(2)=f(0), where the correct judgment is (fill in the serial numbers of all the judgments you think are correct). Senior three mathematics hundred questions training (second set)