Eighth grade mathematics final examination paper examination questions
Multiple choice questions (3 points for each question, ***2 1 point). Answer in the answer area of the corresponding question on the answer sheet.
1. In the plane rectangular coordinate system, the coordinate of the point (,) about the axisymmetric point is ().
A.(，)b .(，)c .(，)d .(，)
2. In the function, the value range of the independent variable is ()
A.& gt BC? D.
3. To judge whether the heights of the two dance teams A and B are neat, it is usually necessary to compare the heights of the two dance teams ().
A. variance B. median C. mode D. average
4. The following statement is wrong ()
A. The quadrilateral bisected by two diagonal lines is a parallelogram; B. Two quadrangles with equal diagonals are rectangles;
C A rectangle with two diagonal lines perpendicular to each other is a square; Two diamonds with equal diagonal lines are squares.
5. Known inverse proportional function, the following conclusion is incorrect ().
A. the image must pass through the point (1, 2) b. It decreases with the increase of.
C. the image is located in the first and third quadrants d. If >: 1
6. As shown in the figure, in the diamond ABCD,? A=60？ , the perimeter is 16, and the area of the diamond is ()
a 16 b 16 c 16d . 8
7. As shown in the figure, the edge of the rectangle is on the positive semi-axis of the axis in the plane rectangular coordinate system, the point is on the left side of the point, and the straight line passes through the point (3, 3) and the point, and the straight line is translated downward along the axis to get the straight line. If the point falls within a rectangle, the value range is ().
A.B. C. D。
Fill in the blanks (4 points for each small question, ***40 points) and answer in the answer area of the corresponding topic on the answer sheet.
8. Simplify:
9.0.000000 123 is expressed as scientific notation.
10. In □ABCD,? A:? So B = 3: 2? D = degrees.
The image of 1 1. linear function is shown in the figure. When is, the value range of is.
12. In order to develop campus football, a school football team was established. The age distribution of the players is shown at the top right, so the age pattern of these players is.
13. Simplification: =.
14. If point M(m, 1) is on the image of inverse proportional function, then m =.
15. The coordinates of the intersection of a straight line and an axis are.
16. In the plane rectangular coordinate system, the coordinates of the vertex and the square are (-1, 1) respectively.
(-1,-1), (1,-1), then the coordinates of the vertices are.
17. As shown in the figure, in △ABC, BC = 10, AB = 6, AC = 8, and P is
Move over BC, PE? AB, PF in E? AC in f and m in EF.
Midpoint, then (1) degrees; (2) The minimum value of 2)AM is.
Third, answer the questions in the answer area corresponding to the questions on the answer sheet (9 questions, ***89 points).
18.(9 points) Calculation:
19.(9 points) Simplify first and then evaluate:, in which
20.(9 points) As shown in the figure, in a rectangle, the diagonal line intersects with points,, and finds the length.
2 1.(9 points) As shown in the figure, the image of the linear function and the image of the inverse proportional function intersect at point A and point C, the Y axis intersects at point B, and the X axis intersects at point D. 。
(1) Find the expressions of inverse proportional function and linear function;
(2) connect OA and OC. Find the area of △AOC.
22.(9 points) When the school establishes student scholarships, it is stipulated that the person with the highest comprehensive score will win the first prize. The comprehensive achievement includes three items: physical education achievement, moral education achievement and academic achievement, which are respectively included in the comprehensive achievement according to the ratio of 1︰3︰6. Xiao Ming and Liang Xiao were shortlisted for evaluation. See the table below for their sports, moral and academic achievements. Please calculate their comprehensive scores.
Physical education achievements, moral education achievements, academic achievements.
Xiaoming 96 94 90
Liang Xiao
23.(9 points) Senior two students in a school take a bus to a social practice base 40 kilometers away from the school to carry out social practice. Some students take long-distance buses, while others take buses. They started at the same time. As a result, the students who took the bus were 8 minutes late. It is known that the speed of long-distance bus is 0.2 times that of 65438+ bus, so we can find out the speed of bus.
24.(9 points) As shown in the figure, in the right-angle ABCD, AB =4cm, BC =8cm, the middle vertical line EF of AC intersects with AD and BC at points E and F respectively, and the vertical foot is point O. 。
(1) Connect AF and CE, and verify that the quadrilateral AFCE is a diamond;
(2) Find the length of AF.
25.( 13) Party A and Party B started from school and ran to the gymnasium along the same route. After Party A ran a distance, Party B started. When Party B exceeds Party A150m, Party B stops here and waits for Party A. After they meet, Party B and Party A run to the gymnasium at the original speed of Party A, as shown in the figure.
(1) During the whole running, A * * * ran meters, and A's speed was meters per second;
(2) Find the running speed of B and the time for B to wait for A on the way;
How long did it take for Begun B to meet A for the first time?
26.( 13 point) As shown in the figure, in the plane rectangular coordinate system, the straight line: intersects with the axis at the point, and intersects with the straight line: at the point.
The coordinates of the point (1) are: the coordinates of the point are: the coordinates of the point are:
(2) If it is a point on a line segment with an area of 12, find the function expression of a straight line;
(3) Under the condition of (2), if it is a point on the ray, is there a point on the plane that makes the quadrilateral with the vertices of,, and a rhombus? If it exists, directly write out the coordinates of the point; If it does not exist, please explain why.
Reference answer to the final examination paper of eighth grade mathematics
First, multiple-choice questions (3 points for each small question, ***2 1 point)
1.d； 2.b； 3.a； 4.b； 5.b； 6.d； 7.c；
Fill in the blanks (4 points for each small question, 40 points for * * *)
8.； 9.； 10.72; 1 1.； 12. 14 years old (no points will be deducted if there is no unit); 13.； 14.；
15.(0,2); 16.( 1, 1); 17.( 1)90; (2) 2.4
Iii. Answering questions (***89 points)
18.(9 points) Solution:
= 8 points
=6? 9 points
19.(9 points) Solution:
= 3 points
= 5 points
= ? 6 points
When, the original formula =? 7 points
=2? 9 points
20.(9 points) Solution: In a rectangle.
, 2 points
? 3 points
∵
? This is an equilateral triangle. 5 points
6 points
In Rt,
9 points
2 1.(9 points) Solution: (1)∵ The image of the inverse proportional function passes through points A-2, -5,
? m=(-2)？ ( -5)= 10.
? The expression of the inverse proportional function is .2 points.
∵ point c 5, n on the inverse proportional function image
? .
? The coordinates of c are-5,2-.3 minutes.
∵ The image of a linear function passes through point A and point C, and is substituted into the coordinates of these two points.
Solve? 5 points
? The expression for finding a linear function is y=x-3. 6 points
(2) an image with a linear function y=x-3 intersects the y axis at point b,
? The coordinates of point B are -0, -3-.7 minutes.
? OB=3。
∵ The abscissa of point A is -2, and the abscissa of point C is 5.
? S△AOC= S△AOB+ S△BOC=。 Nine points
22.(9 points) Solution: Xiao Ming's comprehensive score = (4 points)
Xiao Liang's comprehensive score =? (8 points)
∫92. 1 & gt； 9 1.8 , ? Xiao Liang can win the first prize. (9 points)
23.(9 points)
Solution: If the bus speed is km/h, then the bus speed is km/h? 1 point
According to the meaning of the question? 5 points
Solve? 7 points
Is the solution of the original equation, does it meet the meaning of the question? 8 points
A: The speed of the bus is 50 kilometers per hour. 9 points
24.(9 points) (1) Proof:
∵ quadrilateral ABCD is a rectangle,
? In ∨ BC,
AEO =？ Chief financial officer,
∵ the middle vertical line EF of AC,
? AO = OC，AC？ EF, 2 points
In delta △AEO and delta △CFO
∵
? △ AEO△ Chief Financial Officer (AAS), 3 points
? OE = OF，
∫O A = OC，
? Quadrilateral AECF is a parallelogram with four points.
∵AC？ EF，
? The parallelogram AECF is a diamond; 5 points
(2) Solution: Let AF=acm,
∫ The quadrilateral AECF is a diamond,
? AF=CF=acm, 6 points.
BC = 8cm，
? BF=(8-a)cm，
In Rt△ABF, we get 42+(8-a) 2 = A2,8 points from Pythagorean theorem.
A=5, that is, AF=5cm. 9 points
25.( 13) solution: (1)900, 1.5.4.
(2) pass b as it is? The x axis is on the e axis.
A runs for 500 seconds, which is 500? 1.5 = 750m, 5 points.
How long does it take for A to run 600 meters (750- 150)? 1.5=400 seconds and 6 minutes.
What is the running speed of B? (400 ~ 100) = 2.5m/s，？ 7 points
The time for B to wait for A on the way is 500-400 = 100 seconds. Eight minutes.
(3)∫D(600，900)，A( 100，0)，B(400，750)，
? The functional relationship of OD is 9 points.
What is the functional relationship of AB? 1 1 min
According to the meaning of the question
Solution, 12 points
? B meets A for the first time in 150 seconds. 13.
26.( 13 points) Solution: (1) (6,3); ( 12,0); (0,6); 3 points
(2) Let D(x, x),
The area of △COD is 12,
? ,
Solution:
? D (4 4,2), 5 points
Let the function expression of straight line CD be,
Substituting c (0 0,6) and d (4 4,2) gives:
Solution:
Then the analytical formula of straight CD is; 7 points
(3) There is a point Q, so that the quadrilateral with the vertices of O, C, P and Q is a diamond.
As shown in the figure, it is considered in three situations:
(i) When the quadrilateral is a diamond, the quadrilateral is a square, that is, (6, 6); 9 points
(2) When the quadrilateral is a diamond, the coordinate is (0,6) and the ordinate is 3.
Substituting into the linear analytical formula, we get:, which is (-3,3); 1 1 min
(iii) When the quadrilateral is a diamond, then,
At this time (3, -3), 13 o'clock.
To sum up, the coordinates of a point are (6,6) or (-3,3) or (3,3).
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