A..① B.①② C.①②③ D.②③
2. Mathematics education in compulsory education stage is (B)
A. Basic education B. Handsome education C. Elite civic education D. Civic education
3. The result of calculating-3 2 is (a)
A.- 9th century BC-6th century BC
4. The result of factorizing (X- 1) 2-9 is (d).
A.(x-8)(x+ 1)b .(x-2)(x-4)c .(x-2)(x+4)d .(x+2)(x-4)
5. The position of the point A.B.C.D.E in the square grid is as shown in the figure, so sina is equal to (c).
A.BE/DC· B.AE/AC· C.AD/AC· D.BD/BC
6. The solution set of inequality set 2x-4 < 0 is (a)
X+ 1≥0
A.- 1≤x < 2 b .- 1 < x≤2 c .- 1≤x≤2d .- 1 < x < 2
7. As shown in △ABC, BE/ /BC, if AD:= 1:3, BE=2, then BC is equal to (a).
A8 b . 6 c . 4d . 2
8. As shown in the figure, the vertex coordinates of △ABO are A( 1, 4) and B(2 1). If △ABO rotates 90 counterclockwise around point O to get △ A 'b 'o, then the coordinate (d) of point A 'b'
A.(-4，2)(- 1， 1)b .(-4 1)(- 1，2)c .(-4 1)(- 1， 1) D.(-4，2)(- 1，2)
9. In a circle with radius r, the ratio of the side lengths of inscribed squares to circumscribed regular hexagons is (b).
a . 2:3 b . 2:√3 c . 1:√2d .√2: 1
10. If the unary quadratic equation (k- 1) x 2+2x-2 = 0 about x has two unequal real roots, then the value range of k is (c).
A.k >1/2b.k ≥1/2c.k >1/2 and k≠ 1 D. k≥ 1/2 and k ≠/kloc-.
12. The image of the linear function y 1=kx+b and y2=x+a is shown in the figure, and the following conclusions are drawn: ① k < 0; ②a > 0； ③ when x < 3, the correct number in y 1 < y2 is (b).
A.0 B. 1 C. 2 D.3
13. Translate the parabola y = x 2 down by 1 unit, and then translate the unit to the left to get the new parabola equation (d).
y=(x- 1)^2+2 y=(x-2)^2+ 1
y=(x+ 1)^2+ 1 y=(x+2)^2- 1
14. The ages of the players of a basketball team 12 are as follows, so the modes and median ages of the players of this 12 are (a) respectively.
a . 2 19 b . 18 19 c . 2 19.5d . 18 19.5
15. The distance between the centers of two intersecting circles is 5. If the radius of a circle is 3, then the radius of another circle is (b).
A.2 B.5 C.8 D. 10
16. Regarding the image of quadratic function y = 2-(x+ 1) 2, the following statement is correct (D).
A. the image opening is upward
The symmetry axis of B image is a straight line x= 1.
C. the image has the lowest point.
D. Vertex coordinates of the image (-1, 2)
17. when a≠0, the functions y=ax+ 1 and y=a/x are on the same coordinate, and the image may be (c).
18. As we all know, each face of a cube is filled with several displacements, and the books filled on the opposite faces are reciprocal. If the surface of this cube is unfolded as shown in the figure, the values of AB are (a) respectively.
A. 1/3， 1/2 B. 1/3， 1 c . 1/2 1/3d . 1， 1/3
19. Put 10 soldier balls with the same shape and size. The target number is 1.2.3... 10 in a box, shake them evenly, and then grab a ping-pong ball casually. The probability that the extracted number is an exponent less than 7 is (a)
A.3/ 10
2 1. The three basic attributes of mathematics education in compulsory education stage are (b)
A. fundamentals, competition and universality
B. fundamentals, universality and development
C. competitiveness, universality and development
D. Foundations, competition and development
22. The organization design or attempt of mathematics teaching should handle some relations well, and the wrong statement is (D).
A. The relationship between process and result B. Only talk about abstract relationship
C. Relationship between direct experience and indirect experience D. Relationship between methods and steps
23. "Compulsory Education" lists nine basic facts about "graphic nature and proof", and the following do not belong to (a)
A. Two straight lines intersect with only one intersection point.
B there is one and only one straight line perpendicular to this point.
C. Two points determine a straight line
D, two triangles with equal included angles are equal.
24. in the ruler drawing, according to the following conditions, can't make a suitable triangle is (c)
The included angles between two sides of three sides, the diagonal angles between two sides and one side, and their clamping edges are all known.
25. In △ABC, BD shares equally)
a . 100 b . 1 15 c . 120d . 125
26. Use a fan-shaped piece of paper, the central angle ∠AOB= 120, AB=2√3CM, and enclose a conical edge, and the radius of the bottom of the cone is (A).
A.2/3cm b. 2/3π cm C.3/2cm d. 3/2π cm
27. In rectangular ABCD, AB= 16CM, AD=6CM, moving points P and Q start from A and B respectively, point P moves to point B at a speed of 3cm/s until point B, point Q moves to point D at a speed of 2cm/s, and the distance between p and Q is 10cm, and points P and Q.
A.7/3s B.7/3 or 14/3 C.8/5 or 24/5 D.8/5
28. On a chessboard with two rows and three columns (1 and 6, 2 and 5, 3 and 4 respectively), roll along one side of the dice.
In each reaction mode, the sieve can't retreat, as shown in figure 1 at the beginning, with 2 faces up, or at the end as shown in figure 2, and the number of points to be considered at this time can't be (d).
A.5 B.4 C.3 D. 1
29. Known rectangular ABCD, AD=5cm, AB=7CM, BF is)
A. 2 cm B.2 or 3 cm C.5/2 or 5/3 cm d. 5/3 cm.
30. It is known that BD is the diagonal of square ABCD, m is the moving point on BD different from d, AB is the equilateral triangle ABE on the side of ABCD, and BM is the equilateral triangle BMF on the lEFt of BD, which is the shortest when ef, AM, AM+BM+CM are connected. )
A. 15 B. 15 C.30 D
3 1. Let A={ x | x? -7x+ 10 ≤ 0}, b = {x |㏒ 2 (x- 1) ≥ 1}, then A∩(CrB)= ()
A. empty set B. {x | 3 ≤ x ≤ 5} C. {x | 2 ≤ x ≤ 3} D. {x | x ≥ 3}
32. Let {An} be a stroke ratio series, and its common ratio is q, then q > 1 is {An is an increasing series} (d&; nb sp)
A. sufficient and unnecessary conditions B. necessary and insufficient conditions C. necessary and sufficient conditions D. neither sufficient nor necessary conditions
33.x obeys orthogonal normal distribution N (0, 1), and p (x > 1) = 0.2, then p (- 1 < x < 1) = (c).
A.0. 1 b 0.3 c 0.6d 0.8
34. Let a= ㏒3(6), B = ㏒ 0.2 (0. 1) and C = ㏒ 7 (14), then the relationship among A, B and C is (D).
a c > b > a b > b b > c > a c a > c > b d . a > b > c
35. If the negative number z satisfies (3-4i )z= | 1- √3i |, then the imaginary part of z is (c).
A.-8∕25i·8∕5·8∕25·8∕25i
36. A proposition is related to a positive integer, if n= k (k ∈ N? ), the proposition holds, then it can be deduced as n = k+ 1. Now it is known that when n=5, the proposition does not hold, then (d) can be deduced.
A.N=6, the proposition is invalid; B. N=6, C. N=4, D. N=4, the proposition is invalid.
37. The operation on R is defined as xy=x(2-y). If the inequality (x-a) (x+a) < 4 holds for any real number x, then A is | (A).
A.- 1 < a < 3 b .-3 < a < 1 c .- 1 < a < 1/3d .- 1/3 < a < 1
38. The figure on the right is the flow chart of1/2+1/4+1/6+...+1/20, in which (a) should be filled in the judgment box.
a . I > 10 b . I < 10 c . I > 9d . I < 9
39. It is known that m and n are two different straight lines, and α and β are different planes. Give the following four propositions (c).
① If m⊥α,n⊥β,m⊥n, then α ⊥ β ② If m∥α,n∥β,m⊥n, then α ∧β.
③ If m⊥α,n∥β,m⊥n, then α ⊥β④ If m⊥α,n∥β,α∥β, then m⊥n 。
The real proposition is:
A.①④ B. ②④ C. ①③ D. ③④
40. A three-view geometry is shown in the figure, so its volume is (B).
A.4 B. 14/3 C. 16/3 D. 6
4 1. Let the opposite sides of internal angles A, B and C of ABC be A, B and C respectively, and a = b cos C +c sin B, then ∠B is equal to (B).
42. Functions defined on r? (x)= 1，？ (x) yes? Derived function of (x), known function? X), as shown in the figure, if two positive numbers A and B satisfy? (2a+b) < 1, then the value range of b+ 1/a+2 is ().
A.(2/3，3) B.( -∞， 1/3) C.( 1/3，3/2) D. (-∞，3)
43. In order to get the image of the function Y=sin3x +cos3x, the image (a) of the function Y√2 cos3x can be
A. shift π/ 12 units to the right B. shift π/4 units to the right.
C. shift π/ 12 units to the left. D. move π/4 units to the left.
44. If the general term formula of series {an} is α n = if the first n terms are Sn, then Sn is ().
45. If the function? (x) = (k- 1) a x-a x (a > 0 and a≠ 1) is both a odd function and a subtraction function on R, then g (x) = ㏒ a (the image of x+k) is (a).
46. In the known space quadrilateral ABCD, AB=CD=3, points E and F are points on BC and AD respectively, BE: EC = AF: FD = 1: 2, EF=√7, then the angle formed by straight lines of AB and CD on different planes is (B).
.30 caliber? B. 60？ C. 120？ D. 150？
47. The false proposition in the following proposition is (b)
48. At present, there are two boys and girls standing in a row. If boy A doesn't stand at both ends and only two girls out of three are adjacent, then the total number of different tactics is (b).
A.36 B. 48 C. 72 D. 78
49. A shooter has five bullets, and the probability of one in the lifeline is 0.9. If he hits it, stop shooting, or at most three bullets will be used. The probability is (d).
A.0.729 B 0.9 C 0.99 D 0.999
56. The angle θ between the straight line L: x+y+3z = 0 and the plane x-y+2z+ 1=0 is ().
X-y-z=0
A.π/6 B.π/4 C.π/3 D.π/2
57. Let A = I+2J-K and B = 2J+3K. Then the cross product of a and b (c).
a . I-j+2k b . 8i-j+2k c . 8i-3j+2k d . 8i-3j+k
58. Let x 1 x2 x3 be the three roots of the equation X 3+PX+Q = 0, then the determinant X 1 X2 X3=( C).
A.-6q
b6q
C.0
D.P
59. The parallel equation between the intersection point p(2.0. 1) and the straight line 4x-2y+3z-9=0 is ().
2x-3y+z-6=0
A.(x-2)/7=y/2=(z- 1)/8
B.(x-2)/7=y/2=(z- 1)-8
C.(x-2)/7=y=(z- 1)-8
D.(x+2)/7=y/2=(z- 1)-8
60. The total differential of the function z = e xy at point (2, 1) is (b).
A.e^2dx+e^2dy
B.e^2dx+2e^2dy
C.2e^2dx+e^2dy
D.2e^2dx+2e^2dy
1. As shown in the figure, when Rt△ABC = 90°, the edges of the circle O with diameters of AC and AB intersect at point D, and the tangent of the circle O passing through point D intersects with points BC and E. ..
1. Verify EB=EC.
2.2. If the quadrilateral whose vertex is O.E.D.C is a square, it is the shape of △ABC, and explain the reasons.
Solution: 1 Indicates the outside diameter of the connection. OE.CD
Tangent first
∴OD⊥DE
In Rt△DCE and △ODE.
DE=OE
OE=OC
∴Rt△OCE=Rt△ODE
∴DE=CE
AC is the diameter.
∵CD⊥AB
∴
∴
∴DE=BE
∴CE=BE
2.△ABC is an isosceles Rt triangle.
∫OE is the center line of △ABC.
∴OE≠ 1/2AB
∵
△ ABC is an isosceles Rt triangle.
Second, probability.
(1) Find the probability that the daily sales volume will be no less than 100 for two consecutive days and no less than 50 for the other.
(2) Use X to represent the number of days in the next three days when the daily sales volume is not less than 100, and find the distribution list number, expected E(X) and variance D(X) of the random variable X..
Iii. Case analysis (the full mark of this question is 14)
The following is a teaching clip of Pythagorean Theorem:
The new course introduces listening to stories and thinking: It is said that Pythagoras, a famous mathematician in ancient Greece, visited a friend's house more than 2,500 years ago. At the banquet, all the other guests were in high spirits, but Pythagoras stared at a friend's house.
Bricks in a daze. It turns out that the floor tiles are paved with many right-angled triangles, black and white, very beautiful. While the master was wondering, Pythagoras suddenly realized that he had found three squares in the pattern.
There is some quantitative concern about the area, so we also find some quantitative relations between the three sides of an isosceles triangle through this relationship. Students, what kind of quantitative relationship is contained in the pattern of floor tiles? Let's explore together.
Follow-up teaching Next, under the guidance of the teacher, in group cooperation, the students found that the sum of the areas of the small squares of the two right sides of an isosceles right triangle is equal to the big positive with the hypotenuse as the side length.
The area of a square has a special relationship with the three sides of an isosceles triangle: the square of the hypotenuse is equal to the sum of the squares of two right-angled sides. Then it is found that other right-angled triangles in the grid also have the above properties, and the hook is guessed.
Strand theorem.
According to the above materials, please answer the following questions:
1, analyze the teaching methods and rationality of introducing new courses into this discipline from the perspective of teaching methods;
2. Analyze the position and function of Pythagorean theorem in junior high school mathematics teaching from the perspective of grasping teaching materials;
3. From the perspective of three-dimensional curriculum objectives, what teaching objectives have been implemented in the above teaching design?
Expert analysis
1, the new curriculum standard points out that mathematics teaching activities should stimulate students' interest, arouse their enthusiasm, stimulate their thinking, and pay attention to the use of heuristic teaching methods. The above materials are introduced into the new lesson by telling stories.
This teaching method shows students' cognitive level and existing experience, and can better stimulate students' interest in learning. Through the exploration of the quantitative relationship contained in floor tile patterns, it reflects that ancient Greece paid attention to heuristic teaching methods.
2. The position and function of Pythagorean theorem in junior high school mathematics are as follows:
Pythagorean theorem is learned on the basis of students mastering the related properties of right triangle, which plays a connecting role in junior middle school mathematics and paves the way for the study of the inverse theorem of Pythagorean theorem.
It lays a foundation for learning "quadrilateral" and "solving right triangle" in the future. The exploration and frontier of Pythagorean theorem contains such rich mathematical ideas and scientific research methods, which is the carrier of cultivating students' good thinking quality.
Learning plays an important role in the development process and is a model of the combination of numbers and shapes.
3, from the above teaching design to implement the following teaching objectives:
(1) knowledge and skills, experienced the exploration process of observation, conjecture and verification, and mastered the Pythagorean theorem.
(2) Mathematical thinking: In the exploration of Pythagorean theorem, understand the idea of combining numbers with shapes and develop the ability of rational reasoning.
(3) Problem solving: Experience the rigor of mathematical thinking and develop thinking in images through activities.
(4) Emotional attitude, in the inquiry activities, cultivate students' awareness of cooperation and communication and exploration spirit.
Fourthly, teaching design.
Content: Explore and prove "triangle interior angle sum theorem"
Student foundation: I have learned the nature and judgment of intersection and parallel lines. )
Requirements: 1. Write only the instructional design fragments of exploration and proof.
2. Explain the design intention of each teaching link.
education
1. Explore the teaching clip of "Internal Angle and Constant Force of Triangle"
Teacher: We know that a triangle has three angles. Which student tells the teacher what the sum of the three angles is?
Health: 180
Teacher: How do you know?
Student: I guess.
Health: You can write down two angles and put them together with the third angle to form a straight angle, which is 180.
Teacher: (Courseware Language)
Health: You can also measure each angle with the measuring angle and add it up.
Teacher: Great. Let's measure it by hand and add it up to see if it is 180.
Teacher: Today, the teacher didn't bring a goniometer and didn't want to borrow it from anyone. Then can you prove that the sum of the internal angles of the triangle is 180 with what you have learned?
Health: No.
Teacher: We already know that a flat angle is 180, and we have also learned the nature and judgment of parallel lines. Let's imagine if it works. Let's write in groups.
Design intention: In this teaching session, students can say that the sum of the internal angles of the triangle is 180 according to their existing knowledge, and then guide them to verify it through hands-on operation and hands-on measurement, so as to cultivate students' independent thinking and exploration ability.
The ability to learn, and then guide students to use what they have learned to transform, explore and prove through writing exchange, stimulate students' curiosity and thirst for knowledge, and mobilize students' enthusiasm for learning, which is in line with the new curriculum standards.
Students are the main body of learning, and teachers are the organizers, guides and collaborators of learning.
2. Teaching fragment to prove "triangle interior angle sum theorem"
Teacher: Which group sent a watch to prove your group's achievements?
the first group
Student: Drawing Student: Writing proof process
Make a straight line EF//AB to connect point a.
∴
Yes
∴
Teacher: This group has proved the method of transforming three internal angles of a triangle into a straight angle by using the properties of parallel lines. But we proved a proposition.
The sum of the interior angles of the triangle is 180. Write what is known first and then prove it.
Please write it out (one-man performance board). Teachers and students should standardize it together.
Writing method
Teacher: Let's think about it. Is there any other way to prove it?
the second group
Student: Drawing Student: Writing proof process
Teacher: In this group, three angles of a triangle are converted into equal internal angles, and then proved by the properties of parallel lines. It is a good idea to make visible parallel lines and prove them by their properties. Here are some ways for you to think.
Method 1: extend BC to d as CE//AB.
Method 2: BD//AE//CF
Method 3: Take a little D from BC as DE//AB, DF//AC.
Design intention: Heuristic teaching is mainly used to prove the triangle interior angle theorem, guide students to use the transformed teaching ideas and knowledge to prove it, organize students to teach in the form of cooperative group report, and cultivate students' innovative thinking ability and cooperative spirit. Teaching activities advocated by the new curriculum are the process of active participation, interaction and development of teachers and students.