Eighth grade math test questions

First, multiple-choice questions (3 points for each small question, ***24 points)

1. In the following function, the value range of the independent variable x is

A.B. C. D。

2. The average diameter of mature red blood cells in human body is 0.0000077m, which is expressed as.

A.B. C. D。

3. If the graphic angle of the linear function of x passes through the first, third and fourth quadrants, then the range of the value of k.

A.k > 0 b . k < 0 c . 0 < k < 1d . k > 1

4. After Xiao Ming learned to use Pythagorean theorem to do irrational numbers on the number axis, he found a point D at the position of two unit lengths on the number axis, and then this point D made a line segment CD perpendicular to the number axis. CD is three unit lengths, taking the origin as the center and the distance from point C as the radius to make an arc, which intersects with the number axis at a point, so the position of this point is roughly on the number axis. ..................

Between a.2 and 3, B.3 and 4, and c.d. between 4 and 5. Between five and six o'clock.

Question 4

Question 5

The picture shows a beautiful Pythagorean tree, in which all quadrangles are squares and all triangles are right triangles. If the side lengths of squares A, B, C and D are 3, 5, 2 and 3 respectively, then the area of the largest square E is ..............

A. 13

6. Give the following propositions: ① In data 3, 4, 4 and 5, 4 and 5 are all modes; ② The median of data 5, 4, 4 and 6 is 4.5; (3) If the average value of data 3, 4, 5, 6 and A is 4, then a= 1, where the correct number of people is ............

A.0.b. 1.c.2.d.3

7. The image of the linear function passing through point A intersects the image of the proportional function y=2x at point B, and the analytical formula of the linear function is

A.B. C. D。

8. The images of functions y=2x and y=ax+4 intersect at point A(m, 3), then the solution set of inequality 2x < ax+4 is ...

A.x> B.x3

Fill in the blanks (3 points for each small question, 24 points for * * *)

9. If the square root is meaningful, the value range of X is _ _ _ _ _ _ _ _ _

10. Calculation: = _ _ _ _ _ _ _ _ _ _ _

11.-1-2 3,5 The variance of the data is _ _ _ _ _ _ _ _ _

12. If two squares with areas of 64 and 49 are placed as shown in the figure, the length of the line segment AC between the two vertices A and C selected on these two squares is _ _ _ _ _ _ _ _ _.

13. As shown in the figure, the diagonal of a square ABCD with a length of 2 intersects with point O, and the straight line EF passing through point O intersects with point E and point F respectively, so the area of the shaded part in the figure is _ _ _ _ _ _ _ _ _ _ _.

14. The average and variance of the shooting scores of the four players 10 are as follows:

Contestants; candidates

first

second

The third/third in ten days' work

man

Average (circular)

9.2

9.2

9.2

9.2

Difference (second ring)

0.035

0.0 15

0.025

0.027

Then the most stable performance of these four people is _ _ _ _ _ _ _

15. As shown in the figure, point E is the midpoint of the side AD of a square ABCD with a side length of 2, point P is a moving point on the diagonal BD, and the minimum value of point P PA+PE in the moving process is _ _ _ _ _ _ _ _ _ _ _ _.

16. As shown in the figure, fold the rectangular ABCD in half, so that point D and point B coincide, and the crease is EF. If AD=9 and AB=3, the perimeter of the quadrilateral BFDE is _ _ _ _ _ _ _ _ _.

Three answering questions

17.(8 points) Calculation:

18.( 10 minute) In the square grid with unit length of 1 as shown in the figure, points A, B, C and D are all on the grid.

(1) Find the area of quadrilateral ABCD;

(2) Point out the degree of ∠ABC and explain the reasons.

19.( 10 minute) As shown in the figure, in □ABCD, point O is the intersection of AC and BD, and the straight line passing through point O intersects with the extension lines of BA and DC at point E and point F respectively.

(1) Verification: △ AOE △ COF; 、

(2) Please connect EC and AF, so if EF and AC meet any conditions, the quadrilateral AECF is a rectangle, and explain the reasons.

20.( 10) A school actively carried out sunshine sports activities, organized eighth-grade students to shoot at fixed points, and required each student to shoot three times. Now count the shooting times of each student in Class 8 (1) and draw the following two statistical charts. According to the information provided in the chart, answer the following questions.

(1) Find the number of students in Grade 8 (1);

(2) Complete two statistical charts;

(3) calculating the degree of the third central angle in the fan-shaped statistical chart;

(4) There are 200 eighth-grade students, and the number of clicks is expected to be more than 2 times (including 2 times).

2 1.( 10 minute) As shown in the figure, in the rectangular AOCB, point O is at the origin of the plane rectangular coordinate system, OC and OA are on the X axis and Y axis respectively, OC=8, OA= 10. Find a D point on the AB line and fold it along the OD. The A point falls right on the E point on the BC.

22.( 10) Xiao Cong and Xiao Ming set off from school at the same time to go to Tianyi Pavilion in Ningbo to check the information. The distance from the school to Tianyi Pavilion is 4 kilometers. Xiao Cong rides a bike and Xiao Ming walks. When Xiao Cong returned to school by the original road, Xiao Ming just arrived at Tianyi Pavilion. The dotted line O-A-B-C and the line segment OD in the figure represent the distance (kilometers) from the school and the distance they have passed.

(1) Xiao Cong spends _ _ _ _ _ minutes in Tianyige, and the speed of Xiao Cong's return to school is _ _ _ _ _ km/minute.

(2) Please find out the functional relationship between Xiao Ming's distance from school (kilometers) and the elapsed time (minutes);

(3) How many kilometers were Xiao Cong and Xiao Ming from school when they met head-on?

23.( 12) The drought disaster in our province is serious this year. Area A is in urgent need of drought-resistant water150,000 tons, and Area B130,000 tons. At present, two reservoirs A and B have transferred water140,000 tons to support drought-resistant areas A and B, and Area A is away from Area B. It's 60 kilometers from B to A and 45 kilometers from B to A. 。

(1) Assume that the amount of water transferred from reservoir A to land A is x million tons, and complete the following table.

Transfer location

Transfer to position

first

second

be equal to

A

x

14

B

14

be equal to

15

13

28

(2) Please design a transportation scheme to make the water transportation as small as possible. (Transport volume = transport water weight × transport distance, unit: 10,000 tons? Kilometers)