Math test questions
The first volume (multiple choice questions, ***36 points)
First, multiple-choice questions: this big question * *12 small question, only one of the four options given in each small question is correct.
Please select the correct option. 3 points for each small choice; Choose wrong, don't choose or choose multiple answers, zero.
1. equals
a、2 B、2 C、D、
2. The following operation is correct
a、x？ x3=x3 B、x2+x2=x4
c 、(-4xy2)2=-8x2y4 D 、(-2x2)(-4x3)=8x5
3. The value range of the independent variable X in the function is
A, x≥2 B, x≤2 C, x≤2 and x≠ 2 D, x < 2.
4. As shown in the figure, four people, A, B, C and D, sit in four different directions of a square table and see the pattern on the table in the shape of "A".
A，A B，B C，C D，D
In this year's "two sessions", Premier Wen Jiabao proposed in the government work report that the agricultural tax should be phased out throughout the country within five years to reduce the burden on farmers. At present, the annual agricultural tax paid by farmers in China is about 30 billion yuan, which is expressed by scientific notation (the results retain three significant figures).
A, 3.00× 10 10 yuan b, 3×1kloc-0/0 yuan c, 3×10/yuan d, 3.00×1060.
6. Put a triangle on the table with 9 matchsticks of equal length on it (don't break the matchsticks, use them all). How many triangles can be spelled into different shapes?
a、 1 B、2 C、3 D、4
7. In the formula, when the voltage U is constant, the functional relationship between the current I and the resistance R can be graphically expressed as
8.△ABC is an isosceles triangle inscribed with ⊙O with a diameter of 10cm. If the base BC of this isosceles triangle is 8 cm, then the area of △ABC is
A, 8cm2 B, 12cm2 C, 12cm2 or 32cm2 D, 8cm2 or 32cm2.
9. It is known that the equation K2X2-(2k- 1) x+ 1 = 0 about X has two unequal real roots, so the k value that makes the two real roots of the equation opposite to each other is
A, no b, 1 C,-1 d,
10. As shown in the figure, it is a rectangular ABCD venue with length AB = 102m and width ad = 51m.. The width of the middle road from the two entrances A and B is 1m, and the width of the road where the two paths intersect is 2m. The rest is planted with lawns.
A, 5050 square meters b, 4900 square meters c, 5000 square meters d, 4998 square meters
1 1. If a commodity is sold after 20% price reduction, the percentage that should be increased on the basis of the selling price after a period of time is
a、20% B、30% C、35% D、25%
12. As shown in the figure, the side length of the cube box is 2, the midpoint of BC is m, and an ant climbs from point m to point D 1 along the surface of the cube. What is the shortest distance for ants to crawl?
a、B、3 C、5 D、
Volume 2 (multiple choice questions, ***84 points)
Second, fill in the blanks: this big question is ***5 small questions, *** 15 points; Only the final result is needed, and each item is given 3 points.
13. If the value of algebraic expression x2+3x-5 is 2, then the value of algebraic expression 2x2+6x-3 is _ _ _ _.
14. As shown in the figure, AB and CD intersect at point O, and AB = CD. Please add a condition to make △ aod △ cob. Your supplementary condition is _ _ _ _.
15. If the image of a linear function passes through two points (1, m) and (n, 2) on the inverse proportional function image, the analytical expression of this linear function is _ _ _ _.
16. As shown in the figure, the length of rectangular ABCD is AB = 4cm, and the width of ABCD is AD = 2cm. O is the midpoint OP⊥AB, and the diameters of the two semicircles are AO and OB respectively. The vertex of the parabola is O, which is symmetrical about OP and passes through C and D, so the area of the shaded part in the figure is _ _ _ cm2.
17. Scientific discovery: The number of petals, sepals, fruits and other characteristics of plants is very consistent with a strange series-the famous Peibonahi series: 1, 1, 2, 3, 5, 8, 13, 265438+.
Third, the solution: this big question is ***8 small questions, with ***69 points. The solution should be written in words, proof process or calculus steps.
18. (The full mark of this small problem is 8) Solve the equation.
19. (Full score for this small question)
Xiaoming went to a glass shop and bought a rectangular glass with a length of 40 cm and a width of 30 cm. After the owner drew it, Xiao Ming thought of using the existing tools in the glass shop to verify whether the glass drawn by the owner meets the requirements. Please help Xiao Ming design a verification scheme (the tools available in the glass shop are meter ruler and ruler).
20. (The full score for this short question is 8)
Two car sales companies, A and B in City A, have been selling the same brand of cars every month from last year 1 month to1month, as shown in the figure below:
(1) Please fill in the following table according to the above figure:
Median model of average variance of sales companies
Jia 9
B 9 17.0 8
(2) Please analyze the sales of two automobile sales companies in last year 1- 10 from the following two different aspects:
① From the combination of mean and variance;
(2) According to the sales trends of A and B car sales companies on the line chart (analyze which car sales company has more potential).
2 1. (Full score for this small question)
In a math activity class, a classmate asked, "Who can help me find the line segment AB with an uncalibrated triangle?"
The midpoint of? Xiaohua said, "I can do it. My way is to treat this group of triangles as a straight line Mn ‖ AB; Zaizhi
Take any point P on the same side of AB line and MN line, connect PA and PB, and intersect with straight line MN at C and D respectively; Reconnect the advertisement,
BC, intersecting at point e; Draw the intersection line AB of ray PE at point O, and point O is the midpoint of line AB. "What do you think of point O?
Is it the midpoint of line AB? And explain why.
22. (The full score for this short question is 8)
A county in our city is known as "Garlic Capital of China". A transportation company plans to use 65,438+000 vehicles to transport 65,438+000 tons of A, B and C kind of garlic to other places. According to the regulations, each car can only carry the same kind of garlic, and it must be fully loaded, and each kind of garlic is not less than one car.
(1) suppose that train x is used to transport a kind of garlic and train y is used to transport a kind of garlic. Find y and x according to the information provided in the table below.
Find the range of the independent variable x according to the functional relationship between them;
⑵ Let this transportation profit be M (100 yuan), find the functional relationship between m and x and the maximum transportation profit, and arrange them.
At this time, the corresponding vehicle allocation scheme.
Garlic varieties a, b and c
Each vehicle is fully loaded (ton) with 8 10 1 1
Profit per ton of garlic transportation (100 yuan) 2.2 2. 1.2
23. (The full score for this short question is 9)
As shown in the figure, AD is the bisector of △ABC external angle ∠EAC, the extension line of intersection BC is at point D, and the circumscribed circle of DA intersection △ABC extends at point F. 。
(1) Verification: FB = fc
⑵ If, find the length of FB.
24. (The full score of this short question is 12)
Read the following materials:
When calculating1+4+7+10+13+16+19+22+25+28, we find that the difference between each subsequent number and its preceding number is the same constant.
Then s =1+4+7+10+13+16+19+22+25+28.
= = 145.
Use the above knowledge to solve the following problems:
A town in our city has the reputation of "the hometown of trees in the north of China". By the end of 2000, there were 20,000 mu of seedlings in this town. In order to increase farmers' income, this town has implemented the strategy of "revitalizing the town with seedlings" and plans to expand seedlings year by year. Since 200 1, more seedlings of the same area have been planted every year. From 200 1, the seedlings are sold every year, and then the seedlings of the same area are sold every year compared with the previous year. The table below shows the statistical data of seedling area planted and sold in 200 1, 2002 and 2003.
Year 200 1 2002 2003
The area (mu) for planting seedlings every year is 4000 5000 6000.
The annual sales area of seedlings (mu) is 2000-2500-3000.
Assuming that the survival rate of all seedlings is 100%, at the end of which year, the seedling area of this town will reach 50,000 mu.
25. (Full score for this small question 10)
The parabola y = x2-(2m- 1) x+4m-6 is known.
(1) Try to explain that for every real number m, the parabola passes through a fixed point on the X axis;
⑵ Let the two intersections of parabola and X axis A (X 1 0) and B (X2, 0) (X 1 < X2) be on both sides of the origin, and the distance between the two points A and B is less than 6, so as to find the range of m;
(3) The axis of symmetry of parabola intersects with X axis at point C. Under the condition of (2), try to judge whether there is a value of m, so that the positive semi-axis of ⊙M is tangent to point D through point C and an intersection of parabola and X axis, and the sum of the bad arcs cut by X axis is equal. If yes, find out all the values of m that meet the conditions; If it does not exist, explain why.
/shit is xxh/2004/shuxue/2004 shuxue1-jining.rar.