The whole volume is divided into test paper 1, test paper 2, answer sheet and answer sheet. There are 3 big questions and 27 small questions in the test paper. The perfect score is l 20. The examination time is 120 minutes.
Calculators are allowed, but there is no approximate calculation requirement, and the results cannot be expressed by approximate numbers. The vertex coordinates of parabola y=ax2+bx+c are.
Test paper 1
1. Multiple choice questions (3 points for each question, * * 36 points, only one of the four options given in each question meets the requirements of the topic)
The absolute value of 1 -Equal to ()
(A)-2 (B)2 (C) - (D)
2. If the real number is meaningful, the value range of x is ().
(A)x & gt； 1(B)x≥l(C)x & lt； 1 (D)x≤ 1
3. In the following calculation, the correct one is ()
(1) a3? a4 = a 12(B)(a2)3 = a5(C)a6÷a2 = a3(D)(-ab)3 =-a3 B3
According to the statistics of Ningbo Finance Bureau, the fiscal revenue of our city has exceeded 50 billion yuan in 2006, which can be expressed as () by scientific notation.
(A)5×l0 10 yuan (B)50× 109 yuan (c) 0.5×1kloc-0/65438 0 yuan (d) 5× 1065438+.
5. It is known that the radii of two circles are 3 and 5 respectively, and the center distance is 4, so the positional relationship between the two circles is ().
(a) inscribed (b) circumscribed (c) intersected (d) separated.
6. The solution set of the inequality group is expressed on the number axis, and the correct one is ().
7. The following events are random events ()
(a) winning the lottery. (b) At standard atmospheric pressure, heat it to 100℃ and water will boil.
(c) At the Olympic Games, the result of the 100 meter race was 5 seconds. (d) Throw an ordinary dice with 8 points on the top.
8. As shown in the figure, it is known that the two diagonal lines AC and BD of □ABCD intersect at the origin of the plane rectangular coordinate system, and the coordinate of point A is (-2,3), then the coordinate of point C is ().
(A)(-3，2) (B)(-2，-3) (C)(3，-2) (D)(2，-3)
9. A, B, C and D each get 10, with an average of 8 rings. The mode and variance are shown in the table, so the level of the four players is the most stable ().
Hand-selected EPDM
Mode (ringing) 9 8 8 10
Variance (second loop) 0.035 0.0 15 0.025 0.27
(a) A (B) B (C) C (D)
10. as shown in the figure, it is a linear function y=kx+b and an inverse proportional function y=, then the solution of the equation kx+b= about x is ().
(A)xl= 1，x2=2 (B)xl=-2，x2=- 1
(C)xl= 1，x2=-2 (D)xl=2，x2=- 1
1 1. As shown in the figure, the geometry corresponding to the three views is ().
12. As shown in the figure, there is an iron tower AB at the top of the slope, where B is the midpoint of CD and CD is horizontal. In the sun, Tayingde stayed on the slope. It is known that the tower base CD= 12 m, the tower shadow length DE= 18 m, and the heights of Xiaoming and Xiaohua are both 1.6m, which are the same.
(a) 24m (b) 22m (c) 20m (d)18m
Fill in the blanks (3 points for each small question, ***2 1 point)
13. Calculation = ▲.
14. The solution of equation x2+2x=0 is ▲
15. As shown in the figure, if AB cuts ⊙0 to point B, AB=4 cm, AO=6 cm, then the radius of ⊙O is ▲ cm.
16. There are three red balls, six white balls and five black balls in a box, all of which are the same except the color. The probability that 1 ball is white after stirring is ▲.
17. As shown in the figure, in △ABC, AB=AC, CD bisects ∠ACB at point D, and AE ∠ DC at point E. If ∠ E = 36, then ∠B= ▲ degrees.
18. As shown in the figure, in the plane and rectangular coordinate system xOy, a parabola y=x2+bx+c intersects with the X axis at two points A and B. Point A is the negative half axis of the X axis, and point B is the positive half axis of the X axis, which intersects with the Y axis at point C. tan∠ACO=, CO=BO, AB=3, then this line.
19. A regular triangle with an area of L square units is called a unit regular triangle. Each small triangle in the figure below is a unit regular triangle, and the vertices of the triangle are called grid points. In figure 1, 2 and 3, a parallelogram, a trapezoid and a convex quadrilateral with non-parallel opposite sides are drawn respectively, and the vertices of these three figures are required to be l2 square units in grid points and areas.
Three. Problem solving (5 points for the 20th question, 6 points for each of 2 1 ~ 23 questions, 8 points for the 24th question 10, 8 points for the 25th question, 26 points 10, 27 points 12, * * 63 points).
20. simplify a (a-2b)-(a-b) 2.
2 1. Solve the equation.
22. As shown in the figure, the rectangular ABCD is folded in half, and the crease is MN. Rectangular DMNC is similar to rectangular ABCD, and AB = 4 is known.
(1) Find the length of AD.
(2) Find the similarity ratio between rectangular DMNC and rectangular ABCD.
23. As shown in the figure, AB is ⊙O in diameter, BC=5 in chord, ∠ BOC = 50, OE⊥AC, and E in vertical foot.
(1) Find the length of OE.
(2) Find the length of the bad arc AC (the result is accurate to 0. 1).
24. At the end of April this year, the State Bureau of Surveying and Mapping and the Ministry of Construction set the "height" (unit: meter) for China 19 Mountain for the first time. The following figure shows the statistical chart of 10 mountain "height". Please answer the following questions according to the information provided on the map:
(1) What is the range and median of the "heights" of these famous l0 mountains?
(2) How often do the "heights" of these famous l0 mountains appear between 1000m and 2000m?
(3) Mount Tai, Huashan, Hengshan, Hengshan and Songshan are also called "Five Mountains", and the average height of the "Five Mountains" is sought.
25. Enclose a nursery with a fence with a length of l2 meters and a wall long enough. As shown in the figure, the enclosed nursery is pentagonal ABCDE, AE⊥AB, BC⊥AB, ∠ C = ∠ D = ∠ E, let CD=DE=xm, and find the maximum value of S.
26. From May 19, 2007, the People's Bank of China raised the deposit interest rate.
RMB deposit interest rate adjustment table
Annual interest rate before adjustment% after adjustment%
Demand deposit 0.72 0.72
Two-year fixed deposit 2.79 3.06
The net interest income of depositors is the interest after deducting interest tax, and the interest tax rate is 20%.
(1) On May 9, 2007, Xiaoming deposited the lucky money of 3,500 yuan in the bank regularly for one year. What is his actual interest income at maturity?
(2) Xiaoming had a one-year fixed deposit before the interest rate adjustment, and the interest was calculated at an annual rate of 2.79% before the adjustment. The sum of principal and realized interest income is 2555.8 yuan. Ask him what the principal of this deposit is.
(3) Xiaoming's father has a one-year time deposit certificate of 10000 yuan, which was deposited before May 9, 2007. In order to get more interest income, he wants to convert this deposit into a one-year fixed deposit with adjusted interest rate. Should he transfer it? Please explain the reason.
Agreement:
① The number of deposit days is calculated by integer days, and the interest is calculated by 360 days a year.
② Comparative interest refers to the comparison of interest earned within one year from the date of first deposit. If the deposit is not transferred, the interest shall be calculated according to the fixed interest rate of the previous year; If you deposit, the interest will be calculated at the current interest rate for the days before deposit, and at the adjusted one-year fixed interest rate for the days after deposit (the principal will remain unchanged before and after deposit).
27. If the distance from a point on the diagonal of a quadrilateral to both ends of the diagonal is not equal, but the distance from both ends of the other diagonal is equal, the point is called a quasi-equidistant point. As shown in Figure L, point P is a point on the straight line of diagonal AC of quadrilateral ABCD, and PD=PB, PA≠PC, then point P is a quasi-equidistant point of quadrilateral ABCD.
(1) As shown in Figure 2, draw the quasi-equidistant points of rhombic ABCD.
(2) As shown in Figure 3, make the quasi-equidistant points of quadrilateral ABCD (draw with a ruler, keep the drawing traces, and do not require the writing method).
(3) As shown in Figure 4, in quadrilateral AB CD, P is a point on AC, PA≠PC, extending BP intersection CD to point E, and DP intersection BC to point F, and ∠CDF=∠CBE, CE = CF It is proved that point P is a quasi-equidistant point of quadrilateral ABCD.
(4) Try to study the quasi-equidistant points of quadrilateral (name the characteristics and quasi-equidistant points of the corresponding quadrilateral without proof).
Reference Answers and Grading Criteria of Mathematics Examination Questions in Ningbo City, Zhejiang Province in 2007
First, multiple-choice questions (3 points for each small question, 36 points for * * *)
The title is123455678911112.
A: DBD, DBD, BCA, DBD, BCB, BCB.
Fill in the blanks (3 points for each small question, ***2 1 point)
Title:13141516171819.
Answer 1 0, -2 2
3/7 72 y=x2-x-2 is below.
Every painting that is right (in no particular order) will get an L, and the answer is not unique. The following figure is for reference:
Iii. Answering questions (***63 points)
Note: L. Grading should be graded step by step, and only integral points should be set for each step;
2. If there are other solutions, as long as they are correct, you can refer to the scoring standard and score each step accordingly.
20. solution: original formula = A2-2ab-(A2-2ab+B2) ...........................................................................................................................................
= A2-2ab-A2+2ab-B2 ............................................ 3 points.
=-B2 ....................................... 5 points.
2 1. solution: both sides of the equation are multiplied by (x-2)(x+2), so.
X(x+2)-(x2-4)= 1, 2 points for .....................................................
For simplicity, 2x =-3 .................................................................... 4 points.
X=-3/2, 5 points.
After testing, x=-3/2 is the root ...................................... score of the original equation.
22. solution: (1) is known, MN=AB, MD = ad = BC.
∫ Rectangular DMNC is similar to rectangular ABCD,
............................., two points.
∴ AD2=AB2，
∴ From AB=4, AD = 4, 4 points.
(2) The similarity ratio between rectangular DMNC and rectangular ABCD is
23? Solution: (1) ∵OE⊥A C, and the vertical foot is E.
..AE=EC， 1
∫A O = B0，
∴ OE = BC = 5/2 ..................................... 3 points.
(2) ∠ A = ∠ BDC = 25, ................................ 4 points.
At Rt△AOE, sinA=OE/OA, at
∫≈AOC = 180-50 = 130
∴ The length of arc AC = ≈13.4 ................................................... 6 points.
24. Solution: (1) The "height" range of this 10 famous mountain is 3079.3-286.3 = 2793 (m). ..............................................................................................................
The median is 1572.4 (m). .........................................................................................................................................................
(2) The frequency of 10 of these mountains between 1000m and 2000m is 6.
So the frequency is 0.6 ............. for seven minutes.
(3) ( 1532.7+2 154.9+ 1300.2+20 1+ 149 1.7) ...9
= 1699 438+02 (m), .................... 10.
∴ The average "height" of "Five Mountains" is1698.02m.
25. solution: the connection EC is DF⊥EC, and the vertical foot is F.
∠∠DCB =∠CDE =∠DEA，∠EAB=∠CBA=90，
∴∠ DCB =∠ CDE =∠ DEA = 120, ................... 1 min.
DE = CD
∴∠DEC=∠DCE=30，
∴.∠CEA=∠ECB=90，
∴ Quadrilateral EABC is a rectangle with 2 points.
∴de=x·m，
∴AE=6-x, DF= x, EC = ........................... 3 points.
s =(0 & lt； x & lt6) ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
When x=4m, the maximum value of S =12m2, and ....................................................... scored 8 points.
26. Solution: (1) 3500× 3.06 %× 80% = 85.68 (yuan),
At maturity, his actual interest income is 85.68 yuan. .........................................................................................................................................................
(2) Assuming that his deposit principal is X yuan,
Then x (1+2.79% × 80%) = 2555.8, ...
The solution is x=2500,
The principal of this deposit is 2500 yuan. ..............................................................................................................................................................
(3) Suppose Xiaoming's father's deposit has been deposited for X days before the transfer.
l 0000××0.72%+ 10000××3.06% & gt； 10000× 2.79%, ... 8 points.
Get x
When his deposit has been deposited no more than 4 1 day before the transfer; He should transfer it; Otherwise, there is no need to transfer .......................... 10.
27. Solution: (1) As shown in Figure 2, point P is the drawn point ............................................................................................................................... (the answer is not unique ... point P is drawn in the middle of AC, and no points are given).
(2) As shown in Figure 3, point P is the point ...................... 3 points (the answer is not unique. Correct drawings, no penalty points without written explanation; No trace or unclear trace.
(3) linking the database,
In △DCF and △BCE,
∠DCF=∠BCE，
∠CDF=∠CBE，
∠ CF=CE。
∴△DCF≌△BCE(AAS), ............................... scored 5 points.
∴CD=CB，
∴∠ CDB = ∠ CBD ........................................... 6 points.
Port Development Board
∴PD=PB，
∵PA≠PC
∴ Point P is the quasi-equidistant point of quadrilateral ABCD ................................................................... 8 points.
(4) (1) When the diagonals of a quadrilateral are perpendicular to each other and none of them bisects the other, or the diagonals bisect each other and are not perpendicular, the number of quasi-equidistant points is zero; Nine points
(2) When the diagonals of a quadrilateral are not perpendicular to each other and are not equally divided, and the median perpendicular of one diagonal passes through the midpoint of the other diagonal, the number of quasi-equidistant points is1; ............................ 10.
(3) When the diagonals of the quadrilateral are neither vertical nor bisected, and the median perpendicular of any diagonal does not pass through the midpoint of the other diagonal, the number of quasi-equidistant points is two; .......................... 1 1 min.
(4) When the diagonals of a quadrilateral are perpendicular to each other and at least one diagonal bisects the other diagonal, there are countless quasi-equidistant points. 1 point (the answer is not unique. If the drawings are correct, no penalty will be deducted if there is no written explanation; Point p is drawn in the middle of a C. .............................................................................................................................................................
(Item (4) only talks about the number of equidistant points, and can't give full marks)