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1. Choose carefully (this question 10 is a small question, with 3 points for each small question and 30 points for * * *).
1. If a and -2 are reciprocal, then A is (▲).
A.-2 B- c . d . 2
2. According to statistics, in 2008, the total number of SMS voting for "super boys" was about 327 million. Write this number as a scientific number (▲).
a . 3.27× 106 b . 3.27× 107 c . 3.27× 108d . 3.27× 109
3. The pattern shown in the figure is axisymmetric and the figure is (▲).
4. It is known that α is the inner angle of an equilateral triangle, so cosα is equal to (▲) [Source: Zxxk. Com】。
A.B. C. D。
5. It is known that the side area of the cone is 10πcm2, and the central angle of the side development diagram is 36? The length of the bus of the cone is (▲)
A. 100 cm b. 10 cm C. cm D. cm
6. A tourist climbed 2 kilometers in 1 hour in order to climb to the top of 3 kilometers to watch the sunrise, and climbed to the top of the mountain in 1 hour after resting for 0.5 hour. The functional relationship between the time for tourists to climb the mountain and the height of the mountain is graphically represented as (▲).
A B C D
7. In order to carry forward the spirit of Lei Feng, a middle school is going to build a 2-meter-high human statue of Lei Feng on campus, and collect design plans from all teachers and students. Students in Xiao Bing have consulted relevant materials and learned that the golden section number is often used in the design of human statues. As shown in the figure, the plan of Lei Feng's human figure designed by Xiao Bing students according to the golden section number, in which the design height of the lower part of Lei Feng's human figure (accurate to 0.0 1m, reference data: ≈ 1.4 14, ≈ 1.732, ≈2.236) is (▲).
A.0.62m B.0.76m c.1.24m d.1.62m.
8. If the image of inverse proportional function passes through point (-1, 2), then the image of this function must pass through point (▲).
a 、( 2，- 1) B 、(, 2) C 、(-2，- 1) D 、(, 2)
9. The interactive link of "Treasure Box" in CCTV's "Lucky 52" column is a quiz game. The rules of the game are as follows: among the 20 trademark cards, the back of 5 trademark cards is marked with a certain bonus amount, and the back of other trademark cards is crying. If you become a crying face, you won't get the prize. Spectators who participate in this game have three chances to flop (the turned cards can't be flipped again). An audience has had two before.
A.B. C. D。
10, reading materials: Let two roots of the unary quadratic equation Ax2+BX+C = 0 (A ≠ 0) be x 1, x2, then the relationship between these two roots and the coefficient of the equation is as follows: x 1+X2 =-, X/kloc- X2 =。 Fill in the blanks according to this material: it is known that x 1, X2 is the two real roots of the equation X2+6x++3 = 0, then the value of+is (▲).
A.4 B.6 C.8 D. 10
2. Fill in carefully (there are 6 small questions in this question, each with 4 points and * * 24 points. Pay attention to carefully read the conditions of the question and the contents to be filled in, and fill in the answers as completely as possible. )
1 1. Decomposition factor: x3-4x = _ _ _.
12, and the range of independent variables in the function function is;
13. Draw two circumscribed circles with radii of 4cm and 1cm on a rectangular piece of paper, and the minimum area of the rectangular piece of paper is.
14. As shown in the figure, there is a right-angled trapezoidal part ABCD, AD∨BC, and the length of oblique waist DC is 10cm, and D∞= 120? The length of the other waist AB in this part is m.
15.6, a residential district randomly checks the water consumption (unit: tons) of the district for 6 days, and the results are 30, 34, 32, 37, 28 and 3 1 respectively. So, please estimate that the total water consumption in June (30 days) is about tons.
16. In mathematics, for the sake of simplicity, we will write it as =1+2+3+...+(n-1)+n.1! = 1,2! =2× 1,3! =3×2× 1，…，n！ = n×(n- 1)×(n-2)×…×3×2× 1。 Then-+= _ _.
Answer all the questions (there are 8 small questions in this question, so you should write an answer with a score of ***66, and write the proof process or derivation steps. If you think some questions are a little difficult, you can also write some answers that you can write. )
17 (the perfect score for this small question is 6)
Simplified assessment:, in which:
18 (full score of 6 for this small question)
As shown in the figure, in a square grid, the side length of each small square is 1 unit. It will be translated down by 4 units and then rotated clockwise around the point, so please draw a sum (drawing is needed).
19 (full score of 6 for this small question)
In order to welcome the "City Games", a shooting training team conducted 10 tests on two athletes, A and B, during one month's training. The results are as follows:
(1) Complete the form according to the information provided below.
(2) If you were a coach, which athlete would you choose to take part in the competition?
Please explain the reason.
20 (the perfect score for this little question is 8)
As the picture shows, Xiaoli is observing an AB building.
(1) Please draw the projection of the building in the sun according to the projection of Liang Xiao in the sun.
(2) Given that the height of Xiaoli is 1.65m, and the projection lengths of Xiaoli and AB building are 1.2m and 8m respectively, find the height of AB building.
2 1 (full score for this small question)
Temperature is closely related to our life. Have you observed the thermometer carefully? As shown in figure 12, it is the physical schematic diagram of the thermometer. The scale on the left is Celsius (℃), and the scale on the right is Fahrenheit (F). If the centigrade temperature is x(℃) and the Fahrenheit temperature is Y (F), then Y is a linear function of X. 。
(1) Carefully observe the data in the diagram and try to find the functional expression between y and x;
(2) When the temperature of Celsius is minus 15℃, what is the temperature of Fahrenheit?
22 (the full score of this small question is 10) [Source: Zxxk.Com]
As shown in the figure, △ABC, ∠ ACB = 90 known? , AC=BC, point e,
F is on AB, ∠ECF=45? ,
(1) Verification: △ACF∽△BEC(5 points)
(2) Let the area of △ABC be S, and verify: AF? BE=2S(3)
[Source: Subject Network ZXXK]
[Source: Subject Network ZXXK]
[Source: Zxxk.Com]
23 (the full score of this small question is 10)
As shown in Figure ① ②, Figure ① shows a child playing the game of "rolling the hoop". The iron ring is round. When the iron ring rolls forward, the hook of the iron ring keeps tangent to the iron ring. The game is abstracted as a mathematical problem, as shown in Figure ②. It is known that the radius of the iron ring is 5 units (each unit is 5cm), the center of the iron ring is O, the tangent point between the iron ring hook and the iron ring is M, and the contact point between the iron ring and the ground is A.
(1) Find the height BM AC of point m from the ground (unit: cm);
(2) Let the horizontal distance AC from the standing point C to the point A be equal to 1 1 unit, and find the length MF (unit: cm) of the loop hook.
[Source: Z+xx+k.Com]
24 (the full score of this small question is 12)
As shown in the figure, in the rectangular coordinate system with O as the origin, the coordinate of point A is (0, 1), the straight line x= 1 intersects with the X axis at point B, P is the moving point on line AB, the straight line PC⊥PO, the intersection line x= 1 is at point C, and the straight line passing through point MN intersects with the X axis. ..
(1) When point C is in the first quadrant, it is proved that: △ OPM △ PCN;
(2) When point C is in the first quadrant, let the length of AP be m and the area of quadrilateral POBC be s, find the functional relationship between s and m, and write the range of the independent variable m;
(3) When point P moves on line AB, point C also moves on line x= 1. △ Could △PBC become an isosceles triangle? If possible, find the coordinates of all points P that can make △PBC an isosceles right triangle; If not, please explain why.
20 10 mathematical simulation of Guangzhou senior high school entrance examination
answer sheet
1. Choose carefully (this question 10 is a small question, with 3 points for each small question and 30 points for * * *).
Title 1[ source: z+xx+k. com]234[ source: z # xx # k.com]56789 10
Answer b c d a a d c c d
Fill in carefully (6 questions in this question, 4 points for each question, 24 points for * * *).
1 1 . x(x+2)(x-2). 12。 And; 13.72. 14.5 . 15.960. 16 0.
Three. Comprehensive answer (8 small questions in this question, ***66 points)
17. (Full score for this small question)
Primitive formula
When, the original type
18. (Full score for this small question)
19. (Full score for this small question)
Mode 6 B 7 8 2.2
(2) The answer is not unique.
Reasons for athletes to participate in the competition: on average, their average scores are the same; on variance, A's variance is smaller than B's, and A's scores are more stable than B's; [Source: Zxxk.Com]
Reasons for choosing B athletes to participate in the competition: From the public point of view, B has better performance than A, and from the development trend, B has greater potential than A. ..
20. (The full score for this short question is 8)
(1) as shown in the figure. (2) As shown in the figure, because DE and AF are perpendicular to the ground and the light is DF∨AC, Rt△DEF∽Rt△ABC. So ... So ... So AB = 1 1 (m). That is, the height of building AB is.
2 1. (Full score for this small question)
(1) Let the expression of the linear function be y = kx+b, and get x = 0 and y = 32 from the indicator table of the thermometer. When X = 20, Y = 68. Substitute Y = KX+B, and you can get the solution (choose another two pairs of corresponding values) so Y = X+32. (2) When the centigrade temperature is-15℃, that is, X =- 15, substitute Y = X+32.
[Source: Z.xx.k.Com]
22. (Full score for this small question 10)
Proof: (1) ∵ AC=BC, ∴∠ A = ∠ B.
∫∠ACB = 90？ ，∴∠a =∠b = 45° 0，
∫∠ECF = 45？ ，∴ ∠ECF = ∠B = 45？ ,
∴ ∠ECF+∠ 1 = ∠B+∠ 1
∠∠BCE =∠ECF+∠ 1，∠2 =∠b+∠ 1；
∴ ∠BCE = ∠2, [Source: Zxxk.Com]
∫∠A =∠B，AC=BC，
∴ △ACF∽△BEC .
(2)∫△ACF∽△BEC
∴ AC = BE，BC = AF，
∴△ABC: The ∴△ area? BC = BE？ very
∴AF？ BE=2S。
23. (Full score for this small question 10)
The straight line passing through M is parallel to AC, and intersects OA and FC at H, N.( 1) at Rt△OHM, ∠ ohm = 90, OM = 5, HM = OM× SINα = 3, so OH = 4, MB = HA = 5-4 = 65438. Therefore, the height of hoop hook from the ground is 5cm. (2) Because ∠ Moha +∠ OMH = ∠ OMH+∠ FMN = 90, ∠ FMN = ∠ Moha = α, so = sin α =, that is, FN= FM. That is, FM2 = (FM) 2+82, while FM = 10 (unit), 10× 5 = 50 (cm), so the length FM of the hook is 50cm.
24. (The full score of this short question is 12)
( 1)∫OM∨BN，MN∨OB，∠AOB=900，
The quadrilateral OBNM is a rectangle.
∴MN=OB= 1,∠PMO=∠CNP=900
∫，AO=BO= 1，
∴AM=PM。
∴om=oa-am= 1-am,pn=mn-pm= 1-pm，
∴OM=PN，
∫∠OPC = 900，
∴∠OPM+CPN=900，
∠∠o pm+∠POM = 900 ∴∠cpn=∠pom，
∴△OPM≌△PCN.
(2)∵AM=PM=APsin450=，
∴nc=pm= ,∴bn=om= pn = 1-；
∴BC=BN-NC= 1- - =
(3)△PBC may be an isosceles triangle.
① When P coincides with A, PC=BC= 1, and P (0, 1).
② When point C is in the fourth quadrant and PB=CB,
There is bn = pn = 1-,
∴BC=PB= PN= -m, [Source: subject network ZXXK]
∴nc=bn+bc= 1-+- m,
From 2: NC=PM=，
∴ 1- + -m=，∴m= 1.
∴PM= =，BN= 1- = 1-，
∴P(， 1-)。
∴△PBC is an isosceles triangle, and the coordinates of point P are (0, 1) or (1-).