Mathematics Test
This paper is divided into two parts: the first volume and the second volume. Volume one is a multiple-choice question, and volume two is a non-multiple choice question.
The full mark of this volume is 120, and the examination time is 120 minutes.
Volume 1 (multiple choice questions, ***20 points)
Note: 1. Candidates must fill in their name, admission ticket number and subjects on the answer sheet before answering the answer sheet 1. After the exam, the invigilator will take back the test paper and the answer sheet together.
2. After choosing the answer for each question, black the answer label of the corresponding question on the answer sheet with 2B pencil. The answer on the test paper is invalid.
First, multiple-choice questions (this big topic * *10 small topic; 2 points for each question, ***20 points. Only one of the four options given in each question meets the requirements of the topic)
The reciprocal of 1 Yes ()
Seventh century BC
2. As shown in figure 1, line A and line B intersect at point O. If ∠ 1 equals 40, ∠2 equals ().
A.50 B.60 C. 140 D. 160
3. According to CCTV's "Wen Chao Tian Xia" reported on May 27, 2007, the current cars in Beijing
The ownership is about 3 100 000. Then 3 100 000 is expressed as () by scientific notation.
a . 0.3 1× 107 b . 3 1× 105
c . 3. 1× 105d . 3. 1× 106
4. As shown in Figure 2, if the image of the inverse proportional function passes through point m (1), then the inverse proportional function
The expression is ()
A.B.
C.D.
In a black box, there is a ball of the same color, among which there are only three red balls. After mixing the balls evenly every time, you can touch a ball at random, write down the color and put it back in the black box. After a lot of repeated touching experiments, it is found that the frequency of touching the red ball is stable at 25%, so it can be inferred that A is about ().
A. 12
6. In Figure 3, EB is the diameter of semicircle O, and point A is on the extension line of EB.
AD tangent semicircle O is at point D, BC⊥AD is at point C, ab = 2, semicircle O.
If the radius of is 2, the length of BC is ()
A.2 B. 1
C. 1.5
7. In the hot summer, Team A installed 66 air conditioners for Community A and Team B installed 60 air conditioners for Community B. Both teams started construction and completed at the same time. Team A installs 2 more air conditioners every day than Team B, and Team B installs X air conditioners every day. According to the meaning of the question, the correct one in the following equation is ().
A.B.
C.D.
8. The ancient "river map" in China consists of 3×3 squares, each of which
There are different numbers of bitmaps, three in each row, column and diagonal.
The sum of the points of a vertex graph is equal.
Fig. 4 shows a partial dot diagram of the "River Map". Please calculate the corresponding point of point p.
The picture shows ()
9. Party A and Party B drive at a constant speed from A to B along the same route, and the distance between A and B ..
It's 20 kilometers ... the distance they travel is between s(km) and t(h) after A leaves.
The functional image of is shown in Figure 5. According to the image information, the following statement is true ()
The speed of A.A is 4 km/h and the speed of b is10 km/h.
C.B leaves A later than A 1 h and arrives at B 3 h later than B.
10.m, n, p and q respectively represent one of four simple geometric figures (line segment, regular triangle, square and circle).
Figure 6- 1- Figure 6-4 is the combination of two graphs in M, N, P and Q (the combination is indicated by "&").
Then, in the combination diagram below, P & amp； Q's is ()
General nuclear division
Entrance Examination for Junior High School Graduates in Hebei Province in 2007
Mathematics Test
Volume 2 (multiple choice questions, *** 100)
Note: 1. Fill in the items on the left side of the sealing line clearly before answering the second volume.
When answering the second question, write the answer directly on the test paper with a blue or black pen or ballpoint pen.
Title 23
19 20 2 1 22 23 24 25 26
score
Scoring reviewer
Second, fill in the blanks (this big question ***8 small questions; 3 points for each small question, 24 points for * * *. Put the answer
Write on the horizontal line of the question)
1 1. Calculation: =.
12. Comparison size: 7. (Fill in ">", "=" or "
13. As shown in Figure 7, if □ABCD and □EBCF are symmetrical about the line where BC is located, ∠ Abe = 90.
Then ∠ f = 0.
14. If is, the value of is.
15. In Figure 8, every square marked with numbers is a reversible wooden sign, and only two wooden signs are marked with winning marks on the back, so the probability of randomly flipping a wooden sign to win the prize is _ _ _ _ _ _ _ _.
16. As shown in Figure 9, in the grid diagram of 10×6 (the side length of each small square is 1 unit), the radius ⊙A is 1 and the radius ⊙ B is 2, so it is necessary to make ⊙A and.
Yao ⊙A needs to be translated to the right by one unit length from the position shown in the figure.
17. It is known that when n= 1, a1= 0; = 0; When n=2, A2 = 2；; When n=3,
a3 = 0； ... then the value of a 1+a2+a3+a4+a5+a6 is.
18. Figure 10- 1 shows three geometric bodies with the same shape standing on a horizontal plane (the bottom surface is a circular surface, unit: cm). When they are combined into a new geometry as shown in figure 10-2, the volume of the new geometry is cm3 ... (the calculation results are retained).
Third, answer questions (this big question ***8 small questions; ***76 points. The solution should be written in words, proving the process or calculation steps)
Scoring reviewer
19. (Full score for this small question)
Given the value of,,.
Scoring reviewer
20. (The full score for this short question is 7)
On the straight-line speed-limited expressway, the maximum speed of cars is not allowed to exceed 60 km/h (that is, m/s). The traffic management department has set up a speed monitoring point A at a distance of 100 m from the expressway. In the coordinate system shown in Figure 1 1, point A is located on the Y axis, velocity measuring section BC is located on the X axis, and point B is located 60 northwest of point A..
(1) Please draw the ray AC representing the direction of 45 northeast in figure 1 1 and mark the position of point C;
(2) The coordinate of point B is, and the coordinate of point C is;
(3) It takes 15 s for the car to travel from point B to point C. Please judge whether the car is speeding on the speed-limited highway through calculation. (In this short question)
Scoring reviewer
2 1. (Full score for this small question 10)
Two basketball teams, Team A and Team B, played five games during the training. After counting the game results, draw a statistical chart, as shown in figure 12- 1 and figure 12-2.
(1) Draw a dotted line in figure 12-2, indicating the changes of team B's performance in five games during training;
(2) It is known that Team A scored an average of 90 points in five games. Please calculate the average score of team B in five games.
(3) For these five games, calculate the difference between the two teams respectively;
(4) If you choose a team from Team A and Team B to participate in the basketball championship, on the basis of the above statistics, try to make a brief analysis from four aspects: average score, disconnection trend, winning times and range. Which team do you think can get better results?
Scoring reviewer
22. (The full score for this short question is 8)
As shown in figure 13, the image of known quadratic function passes through point A and point B. 。
(1) Find the expression of quadratic function;
(2) Write the symmetry axis and vertex coordinates of parabola;
(3) both point P(m, m) and point q are on the function image (where m > 0), and these two points are symmetrical about parabola. Find the value of m and the distance from Q point to X axis.
Scoring reviewer
23. (Full score for this small question 10)
In figure 14- 1- 14-5, the side length of square ABCD is a, the hypotenuse AE of isosceles right triangle FAE is 2b, and the sides AD and AE are on the same straight line.
Operation example
When 2b < a, as shown in figure 14- 1, select point g on BA, make BG = b, connect FG and CG, cut off △FAG and △CGB, and splice them to the positions of △FEH and △CHD respectively to form quadrilateral FGCH. ..
Thinking and discovering
After Xiao Ming's operation, he found that the shear splicing method is to rotate △FAG counterclockwise around point F by 90 to △FEH, so it is easy to know that EH and AD are on the same line. The connection CH, DH=BG can be obtained by shear splicing method, so △CHD △△ CGB can rotate 90 clockwise around point C to △ CHD. For the quadrilateral FGCH obtained by cutting and splicing (as shown in figure 14- 1), the FM⊥AE (abbreviated) whose point F is point M can be judged by SAS axiom, and FH=HC=GC=FG and ∠ FHC = 90 can be easily obtained.
Practical inquiry
The area of (1) square FGCH is; (expressed by a formula containing a and b)
(2) Compared with the cutting and splicing method in figure 14- 1, please draw a schematic diagram of cutting and splicing a new square in three cases: figure 14-2- figure 14-4.
Lenovo development
Xiao Ming found that when b≤a, all these figures can be cut into squares, and the position of the selected point G moves up in the direction of BA with the increase of B.
When b > a, can the figure shown in figure 14-5 be cut into squares? If you can, please draw a schematic diagram of cutting and spelling in the picture; If not, briefly explain the reasons.
Scoring reviewer
24. (Full score for this small question 10)
In △ABC, AB=AC, the extension line of BA intersects at point G. Place an isosceles right-angled triangular ruler as shown in figure 15- 1, with the right-angled vertex of the triangular ruler being f, one right-angled side being in a straight line with the AC side and the other right-angled side passing through point B. 。
(1) In the figure 15- 1, please observe and measure BF and CG.
Length, guess and write the quantitative relationship between BF and CG,
Then prove your guess;
(2) When the triangular ruler translates to the position shown in Figure 15-2 along the AC direction,
One right-angle side is still on the same line as the AC side, and the other
The right-angled edge intersects the BC edge at point D, and the intersection point D is DE⊥BA.
At point e, please observe and measure DE, DF and CG at this time.
The length of, guess and write the satisfaction between DE+DF and CG.
Quantitative relationship, and then prove your guess;
(3) When the triangular ruler continues to be straight along the AC direction on the basis of (2)
Move to the position shown in figure 15-3 (point f is on the AC line,
And point f does not coincide with point c), does the conjecture in (2) hold?
Is it still valid? (No need to explain why)
Scoring reviewer
25. (The full score of this short question is 12)
A mobile phone dealer plans to buy three mobile phones of a certain brand ***60, each with at least 8 sets, and just used up the payment of 6 1 1,000 yuan. Suppose you buy X mobile phones and Y mobile phones. The purchase price and pre-sale price of the three mobile phones are as follows:
Mobile phone models a, b and c
Purchase price (unit: yuan/department) 90012001100.
Pre-sale price (unit: yuan/department)120016001300
(1) Use the formula containing x and y to express the purchase quantity of Class C mobile phones;
(2) Find the functional relationship between y and x;
(3) Assuming that all the purchased mobile phones have been sold, mobile phone dealers need to pay various extra fees in the process of buying and selling these mobile phones *** 1500 yuan.
(1) Find the functional relationship between the expected profit p (yuan) and x (part);
(Note: Estimated profit P = total pre-sale-purchase price-various expenses)
Find out the maximum estimated profit and write down how many mobile phones to buy at this time.
Scoring reviewer
26. (The full score of this short question is 12)
As shown in figure 16, in the isosceles trapezoid ABCD, AD‖BC, AB=DC=50, AD=75, BC = 135. Point P starts from point B and moves at a uniform speed of 5 units per second along the dotted line BA-AD-DC to point C; Point q starts from point c and moves in the direction of CB at a constant speed of 3 units per second. After passing through point Q, the light QK⊥BC goes up, and the intersecting line segment CD-DA-AB starts to move at point E, and points P and Q start to move at the same time. When point P coincides with point C, point Q also stops. Set points p and q move for t seconds (t > 0).
(1) When point P reaches the end point C, find the value of t and point out the length of BQ at this time;
(2) When point P moves to AD, why does the value of t make PQ‖DC?
(3) Let the area of light QK sweeping the trapezoidal ABCD be S, and find out the functional relationship between S and T when point E moves to CD and DA respectively; (Don't write the range of T)
(4) Can △ PQE become a right triangle? If yes, write the range of t; If not, please explain why.