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First, multiple-choice questions (***6 small questions, 4 points for each small question, out of 24 points)
1, the correct result of calculating (a2)3 is ().
a、a4B、a5C、a6D、a8
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A, the image passing points (1, 2) b and y increase with the increase of x.
C, the image is in the first and third quadrants D. If x > 1, then y < 2.
★★★★★★★★ Display Analysis 3. Among the following equations, the equation with real roots is ().
a、x2+9=0B、C、D、
Display analysis 4. In the plane rectangular coordinate system, move the point P (-2, 1) to the right by one unit, and the coordinate of the corresponding point p' will be ().
a 、( 2，2)B 、( 1， 1)C 、( 3， 1)D 、( 2，0)
Display analysis 5. In △ABC, points D, E and F are on BC, AB, CA, DE∨CA and DF∨BA respectively, so the following three statements are made:
① If ∠ BAC = 90, then the quadrilateral AEDF is a rectangle.
② If AD bisects ∠BAC, then the quadrilateral AEDF is a diamond.
③ If AD⊥BC and AB=AC, then the quadrilateral AEDF is a diamond.
The correct one is ()
a，3 B，2 C， 1 D，0
VIP display analysis 6. As shown in the figure, two equal circles intersect at point A and point B, the intersection at point B is a straight line intersecting at point M and point N of the two circles, and the tangent of the circle intersecting at point M and point N intersects at point C, then the quadrilateral AMCN has the following relationship ().
First, the inscribed circle without circumscribed circle
B, circumscribed circle without inscribed circle
C, both inscribed circle and circumscribed circle.
None of the above is true.
Display parsing
Fill in the blanks (*** 12 small questions, 4 points for each small question, out of 48 points)
7. Calculation: 3-2 =. ☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆?☆☆☆97
Household (Household) 245 1
Monthly water consumption (m3/household) 246 10
Display analysis 14. As shown in the figure, e and f are two points on the diagonal AC of rectangular ABCD. Try to add a condition: so that △ ADF △ CBE. ★☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆97 Then = (denoted by) Display Analysis 17. As shown in the figure, the light P is directly above the crossbar AB, and the shadow of AB under the light is CD, AB∑CD, AB= 1.5m, CD=4.5m, and the distance from point P to CD is 2.7m, so the distance between AB and CD is m.★☆. Point E is on the side of AC, point F is on the side of AB, and it is folded along EF, so that point A falls on the position of point D on the side of BC, and ED⊥BC, then the length of CE is. Display analysis.
Third, answer questions (***7 small questions, out of 78 points)
19, calculation: ☆ ☆ ☆ Display analysis 20, solving inequality: 2 (x+1)-3 (x+2) < 0; The solution set is represented on the number axis. ★☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆97
(2) Find out the degree of the central angle indicating the parents' "approval" in Figure ②;
(3) What is the probability of randomly choosing a student who happens to be "indifferent" from the students surveyed this time? Display analysis 22. As shown in the figure, A and B are blocked by a big mountain, and cars from A to B have to pass through C. In order to promote the economic development of A and B, it is planned to open a tunnel, and cars can directly go from A to B. It is known that ∠ A = 30, ∠ B = 45 and BC= km. If the average speed of the car is (reference data:), display analysis 23. As shown in the figure, AB is the chord of ⊙O, point D is the midpoint, and the vertical line that AB passes through B intersects the extension line of AD at point C..
Proof: AD = DC. Display analysis 24. As shown in the figure, in the right-angled trapezoidal ABCD, ad∨BC, ∠ A = 90, BD⊥DC, BC= 10cm, and CD = 6 cm. There are moving points f and e on line BC and CD, and point f is at the speed of one second. At the same time, point E moves from point C to point D at the speed of 1cm per second on the line segment CD. When point F reaches point C, point E stops moving at the same time. Let point f move t (seconds).
(1) Find the length of AD;
(2) Let the area of quadrilateral BFED be y, find the functional relationship between y and t, and write the function definition domain;
(3) When both point F and point E are moving, if △CEF is similar to △BDC, find the length of line segment BF. Display analysis 25. As shown in the figure, in the rectangular coordinate plane, O is the origin, the parabola y=ax2+bx passes through point A (6 6,0), and the vertex B (m m,6) is on the straight line y=2x.
(1) Find the value of m and the analytical formula of parabola y = ax2+bx；;
(2) If there is a point C on the line segment OB, which satisfies OC=2CB, there is a point D (10/0,0) on the X axis, which connects DC, and the straight line DC intersects the Y axis at point E. 。
① Find the analytical formula of straight DC;
(2) If point M is a moving point on a straight line DC, there is another point N on the plane above the X axis, and the quadrilateral with vertices of O, E, M and N is a diamond, find the coordinates of point N, (write the result directly without processing. )