Fill in the blanks (4 points for each question, 40 points)

1, an isosceles triangle with a base angle of 30 and a base height of 9cm, and a waist length of _ _ _18 cm _ _.

2, 3 meters

5m

The picture shows a staircase. If you want to lay a red carpet on the stairs, it is known that the price of this carpet is 30 yuan per square meter, and the width of the stairs is 2m, so it will cost at least _ _ _ _ _ _ _ yuan to buy this carpet.

3、 9

Calculation = _ _ _ _ _

4. If the algebraic expression is meaningful in the real number range, the value range of X is _ _ _ _ _ _ _ _ _ _ _ _ _.

5. The root of the unary quadratic equation is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

6. If the two roots of the equation x 1 and x2 are known, then = _ _ _ 3 _ _ _ _

7. In a right triangle, if the lengths of the two median lines drawn from the vertex of the acute angle are 5 and 5 respectively, then the length of the hypotenuse of this right triangle is _ _ _ _ _ _.

8. Last year, a school invested 20,000 yuan in experimental equipment, and it is expected to invest 80,000 yuan this year and next. If the average growth rate of experimental equipment investment in this campus in recent two years is X, the equation can be _ _ _ _ _ _ _ _ _ _ _.

9. If the sum of the outer angles of a polygon is the sum of the inner angles, then the number of sides of the polygon is _ _ _ _ _ _.

10. Divide the sample with capacity of 64 into 8 groups. The frequencies from 1 group to the fourth group are 5, 7,1,13 respectively, and the frequencies from the fifth group to the seventh group are 0. 125, so the frequency of the eighth group is _ _

Second, the choice (4 points for each question, 40 points)

1, the following statement is incorrect ()

A a triangle with the ratio of three angles of 3: 4: 5 is a right triangle.

B A triangle with a ratio of 3: 4: 5 is a right triangle.

C A triangle whose ratio of three angles is 1: 2: 3 is a right triangle.

D A triangle whose ratio of three sides is 1: 2 is a right triangle.

2, equilateral triangle side length is a, then the area of the triangle is ()

A, B, C, D,

3. For any real numbers A and B, the following equation always holds ().

A, B,

C, D,

4. If the value of the algebraic expression is ()

a、0 B、 1 C 、- 1 D、

5. If is, the value of is ()

A, 1 B, -4 c, 1 or -4 d,-1 or 3.

6, the equation into the form of, then the value of m and n is ().

A, B, C, D,

three

Number of students

15 20 25 30 35

frequency

10

12

five

7, under given conditions, can draw a parallelogram is ().

A, with 60cm as diagonal, 20cm and 34cm as two adjacent sides.

five

B, 6cm, 10cm are two diagonal lines, and 8cm is one side.

C, 20cm and 36cm are two diagonal lines, and 22cm is one side.

D, 6cm is diagonal, 3cm, 10cm is two adjacent sides.

8, square and diamond don't necessarily have the property of ().

A, diagonal bisection; B, diagonal lines are equal.

Question 10 frequency distribution map

C, the diagonal bisects a set of diagonal lines D, and the diagonal lines are perpendicular to each other.

9, with two identical right triangle, can't spell into the following figure is ()

A, parallelogram b, rectangle c, isosceles triangle d, trapezoid

10. In order to know the physical condition of the eighth-grade students in our school, 30 students were randomly selected, and the number of sit-ups at 1 minute was tested, and the frequency distribution histogram as shown in the upper right figure was made. Please calculate the number of 25 ~ 30 sit-ups according to the information () in the picture.

a、0.4 B、0.3 C、0.2 D、0. 1

Three. Calculation (8 points for each question, 16 points)

( 1)

(2) When, the calculated value

Four, solve the equation (10 points)

V. Application problems (12 points)

A shopping mall originally sold a commodity with the purchase price of 80 yuan at 100 yuan per piece, and it can sell 100 pieces a day. Later, after market research, it was found that the sales volume of this commodity could increase by 1 0 for every decrease in unit price.

(1) How much profit can a shopping mall make from this commodity?

(2) How much should the price of each commodity be reduced in order to get a profit of 2 160 yuan a day from the operation of this commodity?

VI. Operational problems (10 score)

A square can be spliced into a triangle by cutting as follows:

①

②

①

②

Imitate the graphic method, answer the following questions and operate the design.

(1) For the right triangle, design a scheme, divide it into several fast, and then make it into a rectangle with the same area as the original triangle;

(2) For any triangle, design a scheme, divide it into several blocks, and then make a rectangle with the same area as the original triangle.

7.( 10) As shown in the figure, in □ABCD, BE and CE divide equally ∠ABC and ∠BCD, and on AD, e, BE = 12 cm and CE = 5 cm. Find the perimeter and area of □ABCD.

A

E

D

C

B

(12) In order to understand the physical condition of middle school students, a school selected 50 eighth-grade students to take a one-minute skipping test. After sorting out the obtained data, the frequency distribution histogram as shown in the following figure is drawn. It is known that the frequencies of the first, second, third and fifth groups from left to right are 0.04, 0. 12, 0.4 and O, respectively.

(1) What is the frequency of the fourth group? How did you get it?

(2) What are the frequencies of these five groups?

(3) In this skipping, which group does the median number of skipping belong to?

(4) Complete the histogram of frequency distribution, write out each group of frequencies, and draw a line chart of frequency distribution.

frequency

Number of students

/kloc-below 0/60

160~ 170 times

170~ 180 times

180~ 190 times

Over 190 times

Reference answer:

fill (up) a vacancy

1,18cm2,420 3,4,5 has two unequal real roots.

6、3 7、 8、 9、9 10、20

Second, choose

1、A 2、C 3、C4、C 5、C 6、B 7、C 8、B 9、D 10、A

Third, calculation

( 1) (2)

Fourth, solve the equation

Verb (abbreviation of verb) application problem

(1)2000 yuan

(2) Assuming that each commodity should be reduced by X yuan, then

solve

That is, every commodity must be reduced in price in 2 yuan or 8 yuan.

Six,

①

②

①

②

①

②

③

midpoint

①

②

③

Seven, circumference of 39cm, area of 60cm2.

Eight solutions: (1) Subtract the sum of the frequencies of four known groups with 1, and the frequency of the fifth group is1-(0.04+0.12+O.4+O.28) = 0./kloc-0.

(2) Given the frequency =, and knowing that the frequency of each group is 0.04, 0. 12, 0.4, 0. 16, O.28 and the total number of people is 50, there are 50× o.04 = 2,50× o./kloc-0.

(3) The median should be half of the sum of the truancy times of the 25th and 26th students. Judging from the histogram of frequency distribution, the skipping times of students No.25 and No.26 are in the third group. So it can be seen that in this test, the median number of skipping falls in the third group;

(4) Because the frequency of the fourth group is 8 and the frequency of the first group is 2, the height of the fourth group of small rectangles should be four times that of the first group. (Figure omitted)