There are no test questions in the eighth grade math period.

First, multiple-choice questions (30 points)

1, in the formula,,+,9x+, the number of fractions is ().

a、5 B、4 C、3 D、2

2. In the following functions, () decreases with the increase of.

A. () BC

3. As shown in the figure, it is the surface development diagram of an uncovered cubic box. A, B and C are three points on the graph, so the number of times ∠ABC in the cube box is ().

a、 150 B、 120 C、90 D、60

4. Third grade? The number of trees planted by five labor competition groups in a class in one day is 10, 10, 12, x, 8 respectively. If the mode of this set of data is equal to the average, then the median of this set of data is ().

a、 12 B、 10 C、9 D、8

5. The following four propositions;

① Two quadrilaterals with complementary adjacent angles are parallelograms ② Quadrilaterals with equal diagonals are rectangles.

③ A set of quadrangles with parallel opposite sides and another set of quadrangles with equal opposite sides are parallelograms.

(4) The quadrilateral whose diagonal line bisects vertically is a rhombus.

The correct one is ()

a、①④ B、②④ C、②③ D、①③

6, the following calculation is correct ()

① ,② ,③ ,④ ;

a， 1 b，2 c，3 d，4

7. The range of values in the quadratic formula is ()

a，>- 1 b，

8. As shown in the figure, it is known that the extension lines of, and intersect in the parallelogram ABCD, and the following conclusions are drawn: ①; ② ; ③ 。 The correct conclusion is ()

a、①②③B、①②c、②③d、①③

9. In the unary quadratic equation x2+bx+c=0, if the coefficients b and c can be 1, 2, 3, 4, 5, 6, then the number of equations with real number solutions is ().

a， 17 b， 18 c， 19 d，20。

10, a class of students learned that the class won the prize at the award ceremony in the following table:

It is known that 28 students in this class * * * won prizes, of which 13 only won two prizes, so the student who won the most prizes in this class may win the prize ().

A, 5 items B, 4 items C, 3 items D and 2 items

Fill in the blanks (18)

1, calculation: ()-1-(2008) 0+| 1-| = (the result retains the root number).

2. In a trapezoid, if it is the midpoint of each side of the trapezoid,,,, respectively. When a trapezoid meets the conditions, a quadrilateral is a square.

4. The equation 2x2-2x+3m- 1=0 about x has two real roots, x 1, x2 and x1x2 >; X 1+x2-4, and the value range of real number m is.

Biologists have found that the length of a virus is about 0.00000043mm, and the result of this number is expressed by scientific notation.

for

6. The following patterns are made by splicing small squares with side length as a unit according to certain rules. According to this rule, the number of small squares in the fifth pattern is _ _ _ _ _ _ _ _ _.

Three. Problem solving (72 points) (5+6+8+6+8+10+9+12+8 = 72 points)

1, solving the fractional equation:

3. Calculation: (4+4= 8 points)

①、 ②、

5. Manager Wang of a stationery store counted the average monthly sales of A, B and C pens from June 1 to May 2008, and drew 1 (incomplete). The monthly average total profit of selling these three types of pens is 600 yuan, and the profit distribution of each type of pen is shown in Figure 2. It is known that the profits of A, B and C are 0.5 yuan.

(1) Find the monthly average sales volume of Class C pens and complete the chart1; (4 points)

(2) Manager Wang plans to buy 900 models A, B and C in June. Please design a scheme to maximize profits according to the average monthly sales from/kloc-0 to May (regardless of other factors) and explain the reasons (4 points).

6.( 10) When learning Pythagorean theorem, we learn to use figure (I) to verify its correctness; The area of a big square in the figure can be expressed as, or.

From this, Pythagorean theorem A2+B2 = C2 is derived, which is a very simple and intuitive method to infer or verify mathematical laws and formulas according to graphics, and is called "wordless proof" for short.

、

(1) Please use the area expression in Figure (2) to verify the Pythagorean theorem (in which four right triangles are congruent) (the symbol of the 2002 International Conference of Numerologists).

(2) Please combine the figures provided in (III) and verify it with the area expression of the combined figures.

(3) Please design your own graphic combination and verify it with its area expression:

7.(3+6=9 points) A fruit dealer sold a new fruit last month, with an average selling price of 10 yuan/kg and a monthly sales volume of 1000 kg. According to market research, if the price of this fruit is lowered to RMB/kg, the sales volume this month will satisfy a linear function between Y (kg) and X (RMB/kg). When x=5, y = 4000.

(1) Find the functional relationship between y and x;

(2) It is known that the cost price of this fruit was 5 yuan/kg last month and 4 yuan/kg this month. In order to increase the profit of selling this fruit this month by 20% compared with last month and benefit customers, how much should the price of this fruit be reduced to per kilogram?

8.( 12 minutes) As shown in the figure, the straight line Y = KX+2K (k ≠ 0) intersects with the X axis at point B, and the hyperbola Y = (m+5) X2M+ 1 intersects with point A and point C, where point A is in the first quadrant and point C is in the third quadrant.

(1) Find the analytic formula of hyperbola;

(2) Find the coordinates of point B;

(3) If s △ AOB = 2, find the coordinates of point A;

(4) Under the condition of (3), is there a point P on the X axis that makes △AOP an isosceles triangle? If it exists, please write down the coordinates of point P; If not, please explain.

9.(3+5=8 points) Please read the following material questions: As shown in the figure, in the square ABCD and the parallelogram BEFG, three points A, B and E are on the same straight line, and P is the midpoint of the line segment DF, connecting PG and PC. Inquiry: When the angle between PG and PC is how many degrees, is the parallelogram BEFG a square?

Xiao Cong's thinking is as follows: firstly, it can be explained that the quadrilateral BEFG is a rectangle; Then extend the intersection DC of GP to point H, construct congruent triangles, and explore the answer to the question through reasoning.

Please refer to Xiao Cong's ideas to explore and solve this problem.

(1) Verification: quadrilateral BEFG is a rectangle;

(2) 2) What is the included angle between PG and PC? The quadrilateral BEFG is a square, please explain why.

answer

First, multiple choice questions

1、C 2、D 3、D 4、B 5、A

6、A 7、D 8、A 9、C 10、B

Second, fill in the blanks

1, -2, AC=BD or AB = CD 3,4.

4、5/3 & lt； m ≤ 1/2 5、4.3× 10-7 6、4 1

Third, answer questions.

1, no real number solution.