The sum of 1.6 and -9 is ().
A.-3 B. 3 C. 15 D. - 15
2. The following operation is correct ().
A.x3？ x2 = x6b . 4x 2÷x2 = 4x c . x3+x2 = X5 D 2x-x = x
3. Translate the parabola upward by 2 units, and the analytical formula of the parabola after translation is ().
A.B. C. D。
4. Among the following figures, the figure that is not central symmetry is ()
A.B. C. D。
5. In △ABC, D and E are the midpoint of AB and AC respectively. If DE=2cm, the length of BC is ().
A.2cm, B.3cm, C.4cm, D.5cm
6. As shown in the figure, the top view of a three-dimensional graphic frustum is () in the fourth picture on the right.
A.B. C. D。
7. Choose two numbers from 4, 5 and 9, and the probability that the sum is even is ().
A.B. C. D。
8. As shown in the figure, the quadrilateral ABCD is a square, and e is a point on the edge CD. If △ADE rotates α clockwise around point A and then coincides with △ABF, the value of α is ().
A. 90 BC to 60 BC
9. As shown in the figure, diagonal AC and BD of trapezoidal ABCD intersect at O, and G is the midpoint of BD. If AD = 3 and BC = 9, then Go: BG = ().
1:2 b . 1:3 c . 2:3d . 1 1:20
10. As shown in the figure, when the water in the drinking bucket drops from the position shown in Figure ① to the position shown in Figure ②, if the water volume decreases and the water level drops by 0, then the image that can express the functional relationship between and is ().
① ②
Fill in the blanks (3 points for each question, 30 points for * * *)
1 1. Plants are one of the main forms of life, including about 350,000 species such as trees, shrubs, vines, grasses, ferns, lichens and green algae. The figure of 350,000 is expressed by scientific counting.
12. In the function, the range of the independent variable x is.
13. Calculation: =.
14. Decomposition factor:.
15. If the image of the inverse proportional function passes through point P (-2,3) and point Q (1, b), then the value of b is _ _ _ _ _.
16. Given that the generatrix length of a cone is 5cm and the side area is 15πcm2, the radius of the circle at the bottom of the cone is.
17. As shown in the picture, Xiaoxu plays an origami game with a rectangular piece of paper ABCD that is broken on both sides. After he folded the paper along EF, D and C fell at D ′ and C ′ respectively. When measured with a protractor, ∠ EFB = 65, ∠ AED ′ equals degrees.
18. Observe the following figure, which is arranged according to certain rules. Then in the sixth figure, there is a pentagram and a cross star.
19. As shown in the figure, in Rt△ACB, ∠ ACB = 90, AC=BC= 12, D is the point on the side of BC, CD=4, and K is the point on the straight line BC.
∠ DAK = 45, then the length of CK is.
20. As shown in the figure, in the rectangular ABCD, AB=4, AD=, point Q is a point on the edge CD, DQ=3, connected with AC, and the passing point Q is PQ∑AC. Fold △DPQ along PQ to get △PQN, and edges PN and QN intersect AC at points E and F, then the length of EF is.
Three. Problem solving (2 1 ~ 24 6, 25, 26 8, 27, 28 10).
2 1. Simplify before evaluating:, where a = tan 60+ 1.
22. As shown in the figure, every small square in the grid paper is a square with a side length of 1. We call a polygon with lines connecting grid points a "grid polygon". As shown in figure (1), quadrilateral ABCD is a "grid quadrilateral".
(1) Find the area of quadrilateral ABCD in the graph (1);
(2) Draw a grid point △EFG on the grid paper in Figure (2) so that the area of △EFG is equal to the area of quadrilateral ABCD, which is an axisymmetric figure.
Figure (1) Figure (2)
23. It is known that, as shown in the figure, in quadrilateral ABCD, AB=CB and AD=CD. Verification: ∠ c = ∠ a.
24. In a small production activity, a team will make a rectangular frame with a thin wire with a length of 48 cm. As shown in the figure, if AB=BC, let the area of rectangular ABFE be S square centimeters and the side length AB be X centimeters.
(1) Find the functional relationship between S and X (it is not required to write the range of the independent variable X);
(2) According to production requirements, the area s of rectangular ABFE is 16 cm2, BF >；; AB, what is the length of AB?
25. Four classes of grade six in a middle school in Harbin carried out recycling activities of old newspapers, made statistics on the recycling results in April, and drew the following histogram.
And fan charts.
100?
80?
60?
40?
20?
(1) How many kilograms of old newspapers were recycled by four classes in April?
(2) The median of this set of data is _ _ _ _ _ kg.
(3) Recycling1000kg of waste paper is equivalent to cutting down 20 big trees. So how many big trees were cut down by four classes in grade six in April to recycle old newspapers?
26.a exceeds the plan to buy 80 pieces of A and B, and the price of each piece of A is 15 yuan; The price of each commodity of commodity B is 40 yuan, and the purchase price of commodity A is less than that of commodity B by 20 yuan.
(1) If the profit (profit = selling price-purchase price) of selling 20 pieces of Class A goods is the same as that of selling 10 pieces of Class B goods, what are the purchase prices of the two kinds of goods respectively?
(2) In order to make the total profit of 80 commodities A and B not lower than that of 600 yuan, but not more than 6 10 yuan, how many commodities A should be purchased?
27. The straight line y=-2x+b intersects with the X axis and Y axis at points A and C, and points B (-2,0) and AB= CO respectively.
(1) Find the coordinates of point A;
(2) Starting from point A, the moving point P moves along the line segment AC to the end point C at the speed of 1 unit/second. When passing through P, the positive semi-axis of the Y axis intersects with PH⊥AC at point H, the PH length of the line segment is Y, and the moving time is T. Find the functional relationship between Y and T (and write the range of independent variables);
(3) Under the condition of (2), the ray BK bisects ∠CBP, the intersecting line segment AC is at point K, and the vertical ray BP passing through point C is at point Q. When t is what value, AC? QK？ BC, and directly write the position relationship between the circle with P as the center and the line segment PH as the radius and the X axis.
28. As shown in the figure, the straight line PD is the vertical line of △ABC on BC side, the point D is the vertical foot, the point F connects CP and extends the CP intersection AB, and the point E is the ray BP intersection AC.
(1) If ∠A=∠BPF, then verify: BF = CE.
(2) Under the condition of (1), if ∠ a = 60, the quantitative relationship among the line segments PD, PE and PF is _ _ _ _ _ _ _ _ _ _;
(3) Under the condition of (2), if BC=, EF = 7, PF >；; PE, find the length of AF.
1. Multiple choice questions: 1, A 2, D 3, B 4, C 5, C.
6、D 7、A 8、A 9、A 10、C
Second, fill in the blanks:
1 1、3.5× 105 12、x≥3 13、 14、2(m+2)(m-2) 15 、-6
16,317,5018,2119,24 or 6 20,4.
Third, answer questions:
2 1, solution: original formula = ……………………………………………………………………………………………………….
22. Solution: As shown in the figure, 3 points for each question.
Solution: (1) 12 (2)
23. Solution: certificate △ CDB △ ADB ... 6 points.
24. solution: (1) from the meaning of the question, S =...3 points (2) AB = 2...3 points.
25, (1)300 kg ... 2 points; (2) 3 points for 75 trees (3) 3 points for 6 trees.
26. solution: (1) A 10 yuan, B 30 yuan ... 4 points.
(2) If the purchase of a commodity is X pieces, then the purchase of a commodity is (80-x pieces), which can be obtained according to the meaning of the question:
600 ≤( 15- 10)x+(40-30)(80-x)≤6 10
Solution: 38 pieces purchased for 38≤x≤40. A...4 points.
27. (1) A (3,0) ... 2 points.
(2) y = (< t < 3)...4 points.
(3)t=, 4 points for separation.
28.( 1) let BM⊥CF be in m, CN⊥BE in m, ∠ BMF = ∠ CNE = 90.
△ BME ≌ CMEBF = CE...3 points
(2) PE+PF = 2pd...3 points.
(3) ...4 points