1. Among the following figures, the smallest is ().
A.0.02 b . 0. 1 1 c . 0. 1d . 0. 12
2. The following equation holds ()
A.B.
C.D.
3. In the rectangular coordinate system, the point p (-3,2) is moved to the right by 4 unit lengths, and then moved down by 6 unit lengths, and the obtained point is located at ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
4. A proofreader measured the height of junior three boys 1600, and the results showed that the frequency of the group whose height (unit: m) was 1.58~ 1.65 was 0.4, so the number of people in this group was () A.640, C.400, C.
Qingqing walks from home to the bus stop and waits for the bus to go to school. After getting off the bus, he walked some way to school. The dotted line in the figure shows the functional relationship between the clear journey s (meters) and the time spent t (minutes). The following statement is wrong ().
A, it takes three minutes to wait for the bus. B, the walking speed is 80m/min.
C. the speed of the bus is 500 meters/minute. D. the average speed of the whole journey is 290m/min.
6. As shown in the figure, P is the symmetrical center of the parallelogram ABCD, and a circle is made with P as the center. Any straight line passing through p intersects the circle at m and N points, then the size relationship between line segment BM and d n is ().
A.B.C.D can't determine 2. Fill in the blanks (this topic is entitled ***8 small questions, with 3 points for each small question and 24 points for * * *).
7. In winter, the indoor temperature is 8℃ and the outdoor temperature is -2℃, so the temperature difference between indoor and outdoor is℃.
8. The diameter of an atom is 1.2× 10-2 nm, and the decimal is nanometer.
9. If the figure obtained by the rotation angle of the regular hexagon around the center coincides with the original figure, the minimum value is degrees.
10. Simplified: =
1 1. Please write an unary quadratic equation without real roots.
12. The simplified result is 12.
13. The known cones are placed as shown in the figure. Its front view area is 12, and the circumference of the top view is 6, so the side area of the cone is
14. In the rectangular coordinate system, as shown in the figure, there is △ABC, and now there is a point D that satisfies the congruence between a triangle and vertices A, B and D, so the coordinate of point D is
Three. (This big question is ***2 small questions, each with 5 points, *** 10)
15. Solve the inequality group and express its solution set on the number axis.
16. As shown in the figure, a regular hexagonal turntable is divided into six congruent regular triangles, and the pointer position is fixed. After rotating the turntable, it is allowed to stop freely, and one of the triangles just stops at the position pointed by the pointer, and a number is obtained accordingly (when the pointer points to the common edge of two triangles, it is deemed that the triangle points to the right). At this point, it is said that the turntable has rotated 1 time.
(1) The following statement is incorrect ()
A. the probability of1is equal to the probability of 3; B. Turn the turntable 30 times, and 6 will definitely appear 5 times;
C. The turntable turns three times, and the sum of the three numbers is equal to 19, which is an impossible event.
(2) How many times does the number 2 appear when the turntable rotates 36 times?
Iv. (This big question is ***2 small questions, with 6 points for each small question, *** 12 points)
17. As shown in the figure, the line segment OB is placed in a square grid. Now, please draw the ray OA in Figure 1, Figure 2 and Figure 3 (the tool can only use a ruler) so that the values of tan∠AOB are 1, 2 and 3 respectively.
18. We know that 32+42=52, which is an equation composed of three consecutive positive integers, and the sum of the squares of the first two numbers is equal to the square of the third number. Is there another equation that consists of three consecutive positive integers, and the sum of the squares of the first two numbers is equal to the square of the third number? Try to give your reasons.
Verb (abbreviation of verb) (this big question is ***2 small questions, each with 8 points, *** 16 points)
19. In a safety knowledge test, all students' scores are integers, with a full score of 10 and a score of 9, which is excellent. In this test, the number of people in Group A and Group B is the same, and the scores are as follows: (1) In the score chart of Group B, the central angle of the sector where 8 points are located is degrees;
(2) Please complete the following statistical analysis table:
Average variance model median excellent rate
Group A 7 27 7 20
Group b 10%
(3) Students in Group A say that their excellent rate is higher than that in Group B, so their grades are better than that in Group B, but students in Group B think that their grades are better than that in Group A. Please give two reasons to support their views.
20. As shown in the figure, the quadrilateral AFCD is a diamond, the circle O with the diameter of AB passes through the point D, e is the point above ⊙O, and ∠ AED = 45.
(1) Judge the positional relationship between CD and ⊙O, and explain the reasons; 2) If the diameter ⊙O is 10cm, find the length of AE. (Sin 67.5 = 0.92, Tan 67.5 = 2.4 1, accurate to 0. 1)
Six, (this big topic ***2 small questions, 9 points for each small question, *** 18 points.
2 1. A store bought the first batch of some kind of stationery boxes for 1050 yuan, and they sold out quickly. It also bought the second batch of such pencil boxes at 1440 yuan, but the purchase price of each pencil box in the second batch was 1.2 times that of the first batch, and the quantity was more than that of the first batch 10.
(1) What is the purchase price of each pencil box in the first batch?
(2) The first batch is sold out, and the second batch is sold at the price of 24 yuan/piece. Just when half of them were sold out, according to the market situation, the store decided to sell all the remaining pencil boxes at a discount at one time according to the same standard, but the profit of these pencil boxes should not be less than 288 yuan. What's the lowest discount?
22. It is known that in △ABC, AB=AC, point O is within △ABC, ∠ BOC = 90, OB=OC, D, E, F and G are the midpoint of AB, OB, OC and AC respectively.
(1) Verification: the quadrilateral DEFG is a rectangle;
(2) If DE=2 and EF=3, find the area of △ABC.
Seven, (this big topic * * 1 small topic, *** 10 points)
23. As shown in the figure, in the plane rectangular coordinate system, the straight line AD intersects the parabola at a (- 1, 0) and.
D (2 2,3), and points C and F are the intersection and vertex of parabola and Y axis respectively. (1) Try to find the values of b and c and the coordinates of the vertex f of the parabola;
(2) Find the area of △ADC;
(3) The known point Q is the moving point on the parabola above the straight line AD (the point Q does not coincide with A and D). During the movement of point Q, some people say that the area of △AQD is the largest when point Q and point F coincide. Do you think this statement is correct? If you think the required area of △AQD is correct at this time, if you think it is incorrect, please explain the reasons and find the maximum area of △AQD.
Eight. (The topic is *** 1, and the score is *** 12).
24. As shown in the figure, there is a rectangular piece of paper ABCD, which is known as AB=2 and BC=4. If point E is a moving point on AD (not coincident with point A) and 0 < AE ≤ 2, then point A falls to point P and is connected to PC after △ABE is folded in half along BE.
(1) The correct serial number in the following statement is ()
①. △ Abe and △Pbe are symmetrical about the straight line BE.
② Draw an arc with B as the center and the length of BA as the radius. If BC is at H, then point P is on AH (except point A).
③ The length of line segment PC may be less than 2.
④ Quadrilateral ABPE can be square.
(2) Try to find the length of line segment PC under the following conditions (you can use a calculator, accurate to 0. 1).
① A triangle with P, C and D as its vertices is an isosceles triangle; ② The straight line CP is perpendicular to BE.
Mathematical simulation volume reference answer
First, multiple-choice questions (this topic is entitled ***6 small questions, with 3 points for each small question and * *18 points)
1.A. 2。 b，3。 d，4。 Answer 5. d，6。 C
Fill in the blanks (this topic is entitled ***8 small questions, with 3 points for each small question and 24 points for * * *).
7.10, 8.0.0 12, 9.6010,1.For example, -x+3 = 0,12. A+B 13。
14.(-2,-3)、(4,3)、(4,-3)
Three. (This big question is ***2 small questions, each with 5 points, *** 10)
15. solution: the inequality group is deformed into two points.
That's three points.
So the solution set of the inequality group is: .4 points.
Express the solution set of inequality group on the number axis as shown in figure: 5 points.
16. Solution: (1) b; .............................., two points.
(2) Because the probability of 2 appearing is 0, the number of 2 appearing 36 times by rotating the turntable is about 36×6 times.
Five points.
Four. (This big question is ***2 small questions, each with 6 points, *** 12 17. Solution: (2 points for each drawing of 1).
18. solution: suppose there are three numbers, in which the middle number is n,
Yes, ....................................... got three points.
Finishing, ∴n=0, or n=4, and n≥2, ∴n=4..................5 points.
In addition, there is no other such equation .......................... 6 points.
Verb (abbreviation of verb) (this big question is ***2 small questions, each with 8 points, *** 16 points)
19. Solution: (1)144 ..............................., 2 points.
(2) The mean, variance, mode and median of group B were 7, 2.6, 8 and 7.5 respectively; .......................... scored six points.
(3) The mode of group B is higher than that of group A; The median of group B was 8 points higher than that of group A..
20. Solution: (1) The reasons for tangency are as follows:
Connect DO, aed = 45, ∴∠ AOD = 90.
The quadrilateral ABCD is a diamond,
DC∨AB
∴∠ Cod
∴CD is the tangent of ⊙ o.4.
(2) connecting EB,
∫∠DAF = 45, AB is the diameter,
∴∠ AEB = 90 points and 5 points.
Also, the quadrilateral ABCD is a diamond.
AD=AF，
ADF =∣ADF
∴ SIN 67.5 =，∴ AE = 0.92× 10 = 9.2 ..............................................................................................................................
Six, (this big topic ***2 small questions, 9 points for each small question, *** 18 points)
2 1. Solution: (1) Let the purchase price of each pencil box in the first batch be X yuan.
According to the meaning of the question: 2 points.
The solution is X = 15.
After testing, X = 15 is the root of the equation. ........................................................................................................................................................
A: The purchase price of the first batch of pencil boxes is 15 yuan/piece. ...................................................................................................................................................
(2) set the minimum discount as m.
(24- 15 × 1.2) × 12 ×+(24 ×- 15 × 1.2) × 12 × ≥ 288 ......................................................................
m≥8
Answer: The minimum discount is 20% and 9 points for .......................................
22. solution: (1) connect AO and extend BC to h,
∵AB=AC, OB=OC, ∴AH is the vertical line of BC, that is, AH⊥BC is at h...2 points.
∫D, E, F and G are the midpoint of AB, OB, OC and AC respectively, DG∨EF∨BC, DE∨AH∨GF,
∴ quadrilateral DEFG is a parallelogram with four points.
∵EF∥BC,AH⊥BC,∴AH⊥EF,DE∥AH，
∴EF⊥DE，
∴ parallelogram is defined as rectangular ............................................................... with 5 points.
(2)∫△BOC is an isosceles right triangle,
∴BC=2EF=2OH=2×3=6，
AH=OA+OH=2DE+EF=2×2+3=7，
∴ = × 6× 7 = 21............................. 9 points.
Seven, (this big topic * * 1 small topic, *** 10 points)
23. solution: (1)∵ parabola passes through point a and point d,
∴∴, c (0 0,3) ............................... 2 points.
∴ The analytical formula of parabola is
∴ ,
∴ Vertex f (1, 4); Three points
(2) As shown in figure 1, the ∫ straight line AD also passes through point A and point D,
∴ , ,
∴ The analytical formula of linear AD is y=x+ 1, and the intersection e of linear AD and Y axis is (0, 1).
CE=3- 1=2, and the distances from point A and point D to Y axis are 1, 2 respectively.
∴ ; Seven points
As shown in the answer of fig. 2, if the straight line AD where QP∨y axis intersects Q is at p, then Q (,), P (,+1).
∴ pq =-1=++2, and the sum of the distances from point A and point D to line PQ is 3.
∴=×pq×3 =×(+2)×3 =，
, ... 8 points.
∫f( 1, 4), when x= 1, =3, ............................................ scores 9 points.
When x=, = > 3,
This statement is not correct. When x=, the area of △AQD is the largest, and the maximum value is ...................... 10.
Eight. (The topic is *** 1, and the score is *** 12).
24. Solution: (1)1244 ... 3 points.
(2) There are two kinds of isosceles triangles with P, C and D as vertices.
Case 1: as shown in figure 1, when point p coincides with the midpoint h of BC: CH=CD.
That is PC = ch = 2；; Four points.
In the second case, when point P is on the middle vertical line of CD, PD=PC, let the midpoint of DC be k, and if P is over, let PF⊥BC be f.
The quadrilateral PFCK is a rectangle, PF=CK= 1, PB=2. ∴BF=，∴FC=4-，
∴ PC material 2.5 ..................................... 7 points.
(2) As shown in Figure 2, let CP⊥BE be g, ∵BP⊥EP.∴△PGB∽△BPE.
∴BG？ BE = 4……①
∠∠aeb =∠ebc，∠ EAB =∠ BGC = 90，△EAB∽△BGC ∴，
Is it? BG=4？ …………②
From ① and ②, AE = 1 9.
∴be= ∴pe=ae= 1, BG=, ................... 10.
And ∵PG×BE× =PE? PB×
∴PG=，∴CG= …
∴ PC = CG-PG =-= Material 2.7 ........................12 points.