Math test
Note: 1, the whole volume is divided into two parts, the first part is multiple-choice questions, and the second part is non-multiple-choice questions, with 4 pages. The examination time is 90 minutes, and the full mark is 100.
2. In this volume, candidates must answer according to the regulations on the answer sheet; Any answer on the test paper or draft paper will be invalid. The answer sheet must be kept clean and cannot be folded.
3. Before answering the question, please write your name, candidate number, examination room number, examination room number and seat number on the answer sheet with the prescribed pen, and stick a barcode on it.
4. The multiple-choice question in this volume is 1- 10. After choosing the answer for each question, use 2B pencil to black the answer label of the corresponding question in the multiple-choice answer area of the answer sheet. Wipe it clean with an eraser if necessary, and then choose another answer. Non-multiple-choice questions 1 1-22. The answers (including auxiliary lines) must be written in the non-multiple-choice answer area of the answer sheet with the specified pen according to the answer number.
At the end of the exam, please return the test paper and answer sheet together.
The first part of multiple choice questions
(There are *** 10 questions in this section, with 3 points for each question and 30 points for * * *. Each question is given four options, only one of which is correct. )
The arithmetic square root of 1.4 is
A.-4 B.4 C.-2 D.2
2. The following operation is correct
A. BC
3. In the 2008 Beijing Olympic Games, 2 1880 torchbearers were selected worldwide, setting a historical record. Make this data accurate to thousands.
Represented by scientific symbols as
A.B. C. D。
4. As shown in figure 1, the left view of the cylinder is
Figure 1 A B C D
5. In the following figures, which are both axisymmetric and central symmetric are
A B C D
6. Six students in a class participated in the physical fitness test, and the results were as follows: 80, 90, 75, 75, 80, 80. The following statement is incorrect.
A. mode 80 b, median 75 c, average 80 d, interval 15.
7. This year, the Ministry of Finance adjusted the stamp duty rate of securities transactions from 3‰ to 1‰( 1‰ means one thousandth). If someone buys the adjusted stock of 100000 yuan, how much less will he pay the stamp duty on securities transactions than before the adjustment?
A.200 yuan B.2000 yuan C. 100 yuan D. 1000 yuan.
8. What is wrong in the following proposition is
A. the opposite sides of a parallelogram are equal. Two groups of parallelograms with equal opposite sides are parallelograms.
C. The diagonals of the rectangles are equal. A quadrilateral with equal diagonal lines is a rectangle.
9. Shift the image of quadratic function to the right by 1 unit, and then shift it up by 2 units to get the function table of the image.
Dashi islands
A.B.
C.D.
10. As shown in Figure 2, the rhombic ABCD with the side length of 1 rotates around point A, when there are two points B and C ..
When it falls on the arc EF of the sector AEF, the length of the arc BC is equal to
A.B. C. D。
Part II Non-multiple choice questions
Fill in the blanks (there are ***5 small questions in this question, each with 3 points, *** 15 points)
1 1. Five cards with the same texture have the same back, and five different Fuwa images are printed on the front, which are Beibei, Jingjing, Huanhuan, Yingying and Nini. Now that their backs are facing up, the probability of drawing any card is "Huanhuan".
12. Decomposition factor:
13. As shown in Figure 3, the image of the straight line OA and the inverse proportional function intersect at point A in the first quadrant, and the axis AB⊥x is at.
If the area of point B and delta delta △△OAB is 2, then k =
14. to build a milk station on the street to provide milk to residential areas a and b, where should the milk station be built to make it from a,
The sum of the distances from it is the shortest? Xiao Cong established the plane as shown in Figure 4 with the street edge as the X axis according to the actual situation.
In the rectangular coordinate system, the coordinates of point A are (0,3), and the coordinates of point B are (6,5), so you can reach the milk station from point A and point B.
The minimum value of the sum of distances is
15. Observe table 1 to find the rules. Tables 2 and 3 are selected from table 1 respectively, so the value of a+b is
0 1 2 3 …
1 3 5 7 …
2 5 8 1 1 …
3 7 1 1 15 …
… … … … …
1 1
14
a
1 1 13
17 b
Tables 1, 2 and 3
Answer (this topic is entitled ***7, in which 6 points are in 16, 7 points in 17, 7 points in 18, 8 points in 19, 8 points in 20 questions and 9 points in 2 1 questions.
16. Calculation:
17. First simplify the algebraic expression \, and then select an appropriate value of a and substitute it for evaluation.
18. As shown in Figure 5, in the trapezoidal ABCD, AB‖DC and DB divide ∠ADC equally, and point A is AE‖BD, which intersects with CD.
The extension line is at point e, and ∠ c = 2 ∠ e.
(1) Verification: The trapezoidal ABCD is an isosceles trapezoid.
(2) If ∠ BDC = 30 and AD = 5, find the length of the CD.
19. A shopping mall has made statistics on the sales of three brands of Zongzi, A, B and C, at this year's Dragon Boat Festival, as shown in Figure 6 and.
The statistical chart is shown in Figure 7. Answer the following questions according to the information in the chart:
(1) Which brand of zongzi sells the most?
(2) Complete the bar chart in Figure 6.
(3) Write the degree of the central angle of a brand of zongzi in Figure 7.
(4) According to the above statistical information, how will the stores purchase three brands of Zongzi, A, B and C, during the Dragon Boat Festival next year?
Please make reasonable suggestions.
20.
2 1. "The earthquake disaster is merciless." The Civil Affairs Bureau packed the materials donated by the whole city to the Sichuan disaster area, including tents and food.
There are 320 items, and tents are 80 more than food.
(1) How many tents and food do you want to pack?
(2) It is planned to rent 8 trucks A and B to transport all tents and food to the disaster area at one time. It is known that A's truck can hold up to 40 tents and 10 food, and B's truck can hold up to 20 tents and food. How many schemes does the Civil Affairs Bureau have when arranging the trucks of A and B? Please help design it.
(3) Under the condition of (2), if Class A freight car needs to pay 4000 yuan and Class B freight car needs to pay 3600 yuan, which scheme should the Civil Affairs Bureau choose to minimize the freight? How much is the minimum transportation fee?
22. As shown in Figure 9, in the plane rectangular coordinate system, the vertex of the quadratic function image is point d,
It intersects with Y axis at point C, and intersects with X axis at points A and B. Point A is on the left side of the origin, and the coordinate of point B is (3,0).
OB=OC，tan∠ACO=。
(1) Find the expression of this quadratic function.
(2) The straight line passing through points C and D intersects the X axis at point E. Is there such a point F on this parabola, and the quadrilateral with points A, C, E and F as its vertices is a parallelogram? If it exists, request the coordinates of point f; If it does not exist, please explain why.
(3) If a straight line parallel to the X axis intersects with a parabola at two points, m and n, and a circle with a diameter of MN is tangent to the X axis, find the length of the radius of the circle.
(4) As shown in figure 10, if point G(2, y) is a point on the parabola and point P is a moving point on the parabola below the straight line AG, when point P moves to what position, what is the maximum area of △APG? Find the coordinates of point P and the maximum area of △APG at this time.
Academic Examination of Shenzhen Junior High School Graduates in 2008
Math test
Reference answers and grading opinions
The first part of the multiple-choice question (this question * * 10 small question, each small question 3 points, ***30 points)
The title is 1 23455 6789 10.
Answer: DBC, DBC, BBA, DBA, DBC.
Part II Non-multiple choice questions
Fill in the blanks (there are ***5 small questions in this question, each with 3 points, *** 15 points)
The title is112131415.
answer
4 10 37
Answer (this topic is entitled ***7, in which 6 points are in 16, 7 points in 17, 7 points in 18, 8 points in 19, 8 points in 20 questions and 9 points in 2 1 questions.
16. solution: original formula = original formula of ............
= ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
= 1 ...6 points.
(Note: Only the last two steps give full marks. )
17. Solution: Method 1: Original formula =
=
= ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
(Note: Give points step by step, and simplify to 5 points. )
Method 2: Original formula =
=
= ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
Take a = 1 and get 6 points.
Original formula = 5: 07.
(Note: The answer is not unique. If you evaluate this step with A = 2 or -2, you won't get any points. )
18.( 1) Proof: ∫AE‖BD, ∴∠ E = ∠ BDC.
DB division ∠ ADC ∴ ADC = 2 ∠ BDC
∫∠C = 2∠E
∴∠ADC=∠BCD
∴ Trapezoidal ABCD is an isosceles trapezoidal ............................................. with 3 points.
(2) solution: from the problem (1), we get ∠ c = 2 ∠ e = 2 ∠ BDC = 60, BC = ad = 5.
∫In△BCD，∠ C = 60，∠ BDC = 30。
∴∠DBC=90
∴ SAR = 2bc =10 ................................. 7 points.
19. Solution: (1)C card. (No points will be deducted if the unit is not taken) ..............................................................................................................................
(2) ellipsis. (The sales volume of brand B is 800, and no points will be deducted if there are no figures marked on the bar chart) ... 4 points.
(3) 60. (No unit will not be deducted) 6 points.
(4) ellipsis. (All reasonable explanations are given points) 8 points.
20.
2 1. solution: (1) suppose there are x tents packed into blocks, then
(or) .................................. 2 points.
Solution, 3 points.
A: The packaged tents and food are 200 pieces and 120 pieces respectively. ..................................................................................................................................................
Method 2: suppose there are x tents and y pieces of food are packed into pieces, then
..............................., two points.
The solution is ... 3 o'clock.
A: The packaged tents and food are 200 pieces and 120 pieces respectively. ..................................................................................................................................................
(Note: Full marks are also given in arithmetic. )
(2) If X Class A trucks are rented, then
..............................., 4 points.
The solution is ... 5 o'clock.
∴ x = 2 or 3 or 4, the Civil Affairs Bureau has three schemes when arranging A and B trucks.
The design scheme is as follows: ① there are 2 cars a and 6 cars b;
(2) There are 3 vehicles in Car A and 5 vehicles in Car B;
(3) A car has 4 cars, and B car has 4 cars. ......................... scored 6 points.
(3) The freight rates of the three schemes are as follows:
①2×4000+6×3600=29600;
②3×4000+5×3600=30000;
③ 4× 4000+4× 3600 = 30400 ................................, 8 points.
∴ Scheme ① has the least freight, with the lowest freight of 29,600 yuan. .....................................................................................................................................................
(Note: The nature of the linear function indicates that Scheme ① will not be deducted at least. )
22.( 1) Method 1: From the known: C(0, -3), a (- 1, 0) ..............................................1min.
Substitute the coordinates of a, b and c.
Solution: 3 points.
So the expression of this quadratic function is
Method 2: From the known: C(0, -3), a (- 1, 0) ...............................1min.
Let this expression be
Substitute the coordinates of point C.
So the expression of this quadratic function is
(Note: The final result of the expression will not be deducted in any of the three forms)
(2) Method 1: exists, and the coordinates of point F are (2, -3)4 points.
Because: D( 1, -4) is easy to get, the analytical formula of linear CD is:
∴ The coordinate of point E is (-3,0) ............................ 4 points.
From the coordinates of a, c, e and f, AE = cf = 2, AE ‖ cf.
A quadrilateral with vertices a, c, e and f is a parallelogram.
∴ There is point F, and the coordinates are (2, -3). ...................................................................................................................................................
Method 2: D( 1, -4) is easy to obtain, so the analytical formula of linear CD is:
∴ The coordinate of point E is (-3,0) ............................ 4 points.
A quadrilateral with vertices A, C, E and F is a parallelogram.
∴ The coordinates of point F are (2, -3) or (-2, -3) or (-4, 3).
Only (2, -3) satisfies the parabolic expression test.
∴ There is point F, and the coordinates are (2, -3). ...................................................................................................................................................
(3) As shown in the figure, ① When the straight line MN is above the X axis, let the radius of the circle be r (r >; 0), then N(R+ 1, r),
Substituting into the expression of parabola, the solution is
② When the straight line MN is below the X axis, let the radius of the circle be r (r >; 0),
Then N(r+ 1, -r),
Substitute the parabola expression and you get ... 7 points.
The radius of a circle is 7 points or ........................
(4) When the Y axis intersects AG at point Q, the parallel line passing through point P,
G(2, -3) is easily obtained, and the straight line AG is ........................................................................................................................................................
Let P(x,), then Q(x, -x- 1), pq.
Nine points
When △APG has the largest area.
At this point, the coordinates of point p are, ...................................................................................................................................................................