There are four options for each question below, and only one of them fits the meaning of the question.
The absolute value of 1.2 is
A.2 B.2 C. D
2. The following operation is correct
A.B. C. D。
3. As shown in the figure, it is known that the straight line AB∨CD intersects CE at point F, ∠ DCF = 1 10, AE=AF, then ∠A is equal to.
A.B. C. D。
4. If every outer angle of a polygon is equal to, then the number of its sides is
a . 6b . 7c . 8d . 9
5. Randomly select a number from the six numbers 1, 2, 3, 4, 5 and 6. The probability that the selected number is a multiple of 3 is
A.B. C. D。
6. Factorizing algebraic expressions, the following results are correct.
A. The second century BC
7. Convert the quadratic function into the form of, and the result is
A.B. C. D。
8. The following figure shows the whole process of folding an isosceles right-angled triangular piece of paper (Figure 1) with a right-angled side length of 2: firstly, fold it in half, as shown in Figure 2, and the crease CD intersects AB at point D; After opening, it will be folded at will after passing through point D, so that the crease line DE intersects with point E, as shown in Figure 3; After opening, as shown in Figure 4; Then fold along AE, as shown in Figure 5; After opening, the crease is shown in Figure 6. Then the minimum value of the sum of the crease lengths DE and AE is
A. 1+ C.2 D.3
Fill in the blanks (***4 small questions, 4 points for each small question, *** 16 points)
9. In the function, the range of independent variables is.
10. If the unary quadratic equation Mx2-3x+ 1 = 0 about x has real roots, then the range of m is.
1 1. As shown in figure, where is the midpoint of sum, a point on the extension line, sum, and EG=CG, then.
12. As shown in the figure, points E and D are points on the extension line of one side with point C as the vertex in regular triangle ABC, regular quadrangle ABCM and regular pentagon ABCMN, respectively, and BE=CD, and the extension line of DB intersects AE at point F, then the number of times of ∠AFB in figure 1 is; If the condition "regular triangle, regular quadrilateral and regular pentagon" is changed to "regular n-polygon", and other conditions remain unchanged, the degree of ∠AFB is. (expressed by algebraic expression of n, where ≥3 is an integer).
III. Answer questions (***6 small questions, 5 points for each small question, 30 points for * * *)
13. Calculation:.
14. Solving inequality groups:
15. Known, find the value of () (x+2).
16. As shown in the figure, △ACB and △ECD are isosceles right triangles, ∠ ACB = ∠ ECD = 90,
D is a point on the side of AB. Verification: AE = BD.
17. As shown in the figure, a known straight line passes through points and points, and another straight line.
Pass through this point and intersect the axis at this point.
Find the analytical formula of straight line;
(2) If the area of is 3, find the value of.
18. Solving application problems with column equations (groups)
A clothing factory received an order to process 720 pieces of clothes. The original plan is to make 48 pieces a day, which can be delivered smoothly. But before it started, it received the customer's delivery request five days in advance. Therefore, it is necessary to process more clothes every day to deliver the goods on time. How many more clothes are processed than planned every day?
Fourth, answer questions (***4 small questions, 5 points for each small question, ***20 points)
19. in trapezoidal ABCD, DC∨AB, AB =2DC, diagonal AC and BD intersect at point o, BD=4, the midpoint h passing through AC is EF∨BD, and AB and AD intersect at points e and f respectively, so find the length of EF.
20. As shown in the figure, it is known that point C is on ⊙O, and the diameter AB is extended to point P to connect PC, ∠ Cob = 2 ∠ PCB.
(1) Verification: PC is the tangent of ⊙O;
(2) If AC=PC, PB=3, and M is the midpoint of the lower half arc of ⊙O, find the length of MA.
2 1. A middle school held a keynote speech contest on "Be honest". The schedule is divided into three stages: preliminaries, semi-finals and finals. The preliminaries are conducted by each class, and all participants are graded according to the unified standard. After statistics, a "preliminary statistics table (incomplete)" was made. From the preliminaries, 10 players from all grades participated in the semi-finals. Look at the results.
(1) If the grade 9 preliminary test results are made into a fan-shaped statistical chart, then the degree of the central angle corresponding to "the number of people with points on it" is _ _ _ _ _ _.
(2) If the number of people with grade 8 semi-final scores above points is similar to those with preliminary results, please fill in the preliminary results statistics table.
(3) In the semi-final results, the median score of the seventh-grade players is _ _ _ _ _ _ _ _ _ _; The performance mode of the ninth grade players is.
22. As shown in the figure, an object with a cross section of Rt△ABC, ∠ ACB = 90, ∠ CAB = 30, BC= 1 m, the master wants to move this object to the wall, first put the AB edge on the ground (on the straight line M), and then turn it clockwise around point B to the position of △B (B is in.
(1) Write the lengths of AB and AC directly;
(2) Draw the trajectory of point A in the whole process of moving this object,
And find the length of the path.
V. Answer questions (***3 questions, 6 points for 23 questions, 8 points for 24 and 25 questions, and 22 points for * * *).
23. As shown in the figure, in △ABC, BC=3, AC=2, P is a moving point on the side of BC, the intersection point P is PD∨AB, and AC crosses BD at point D..
(1) as shown in figure 1, if ∠ C = 45, please write directly: When =,
△BDP has the largest area;
(2) As shown in Figure 2, if ∠C=α is an arbitrary acute angle, when point P is on BC,
△BDP has the largest area?
24. On-the-spot investigation: We know that if the trigonometric function value of acute angle α is sinα = m, the size of angle α can be calculated by a calculator. At this time, we use arc sin m to represent α, which is recorded as: α = arc sin m; If cos α = m, write α = arccos m; If tan α = m, write α = arc tan m.
Solution: As shown in the figure, it is known that the square ABCD, point E is the moving point on the AB side, point F is on the AB side or its extension line, and point G is on the AD side. Connect ED and FG, and the intersection point is H.
(1) as shown in figure 1, if AE=BF=GD, please write ∠ EHF = directly;
(2) As shown in Figure 2, if EF =CD and GD=AE, let ∠EHF = α. Please judge whether ∠ EHF changes when point E moves on AB. If there are any changes, please explain the reasons; If there is no change, request alpha.
25. As shown in figure 1, in the plane rectangular coordinate system, the hypotenuse of the isosceles right triangle OMN is on the X axis, the coordinate of the vertex M is (3,3), and MH is the height on the hypotenuse. Parabola C: A straight line perpendicular to the X axis intersects with point N at point D, point P (m, 0) is a moving point on the X axis, and the intersection point P is a parallel line of the Y axis.
(1) Write the coordinates of point D and the value of n directly;
(2) Judge whether the vertex of parabola C is on the straight line OM? And explain the reasons;
(3) When m≠3, find the functional relationship between S and M;
(4) As shown in Figure 2, let the straight line PE intersect the ray OD at R and the parabola C at Q,
Take RQ as one side and make a rectangle RQfg on the right side of rq, where RG=,
Write the overlapping part of rectangle RQFG and isosceles right triangle OMN directly as follows.
The value range of m in axisymmetric graphics.
Reference Answers and Grading Criteria of Mathematics Test Paper 20 1 1.5
First, multiple-choice questions (***8 small questions, 4 points for each small question, ***32 points)
Title 12345678
Answer b a b c b a d a
Fill in the blanks (***4 small questions, 4 points for each small question, *** 16 points)
9 10 1 1 12
x≠ 1 2 60，
22. solution: (1) AB = 2m, AC = m.
(2) The path of point A is shown by the thick line in the figure.
The path length is () meters.
V. Answer questions (***3 questions, 6 points for 23 questions, 8 points for 24 and 25 questions, and 22 points for * * *).
23. Solution: (1) 2 points for ....................................
(2) As shown in Figure 2, point D is marked as DE⊥BC, and e ....................................................................... has 3 points.
∴∠DEC=90。
Let Pb = X.
BC = 3，
∴PC=3-x.
∫PD∨AB，
∴.
∴.
∴.
In Rt△DEC, ∠ dec = 90, ∠ c = α,
Germany = .............................. 4 points.
∴ s △ BDP = 5 points for .....................................
∵ α is an arbitrary acute angle,
∴0