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One,
Multiple choice
1.
The following groups are the lengths of three sides of a triangle, and the groups that can form a right triangle are (
)
A.
3,4,5
B.
7, 12, 15
C.
13, 16,20
D.
8,24,25
2.
The following statement is true (
)
A.
Irrational numbers include positive irrational numbers and negative irrational numbers
B.
Real numbers only include rational numbers and irrational numbers
C.
Irrational numbers are infinite decimals.
D.
A number without a root sign is a rational number.
3.
The following figures, which are both axisymmetric and centrosymmetric, are (
)
A.
Diamond, square, circle
B.
Parallelogram, rhombus, square
C.
Isosceles trapezoid, rectangle, square
D.
Regular triangle, rectangle, circle
4.
Among the following properties, what diamonds have but rectangles don't have is (
)
A.
The sum of internal angles is equal to 3600.
B.
Diagonal lines bisect a set of diagonal lines.
C.
Diagonal equality
D.
Adjacent angle complementation
5.
The following graphics with exactly the same shape and size cannot be densely covered (
)
A.
Regular hexagon
B.
regular polygon
C.
parallelogram
D.
isosceles triangle
6.
The following propositions: ① diagonal bisection of parallelogram.
(2) A quadrilateral whose diagonal is bisected is a parallelogram; (3) The diagonals of squares are perpendicular to each other.
(4) The quadrilateral whose diagonals are perpendicular to each other is a square, in which the correct one is (
)
A.
four
B.
three
C.
two
D.
1
7.
In the following categories, the correct one is (
)
A.
B.
C.
D.
8.
In the rotation of graphics, the following statement is wrong (
)
A.
Every point on the graph moves at the same angle.
The edges of any two points on a graph are equal to the edges of these two points.
C.
The distance between the centers of rotation of each point on the graph is equal.
D.
There may be fixed points on the diagram.
9. The quadrant of point P (-4, 1) in the plane rectangular coordinate system is (
)
A.
four
B.
three
C.
two
D.
one
10.
A tourist climbed 2.4 kilometers with 1 hour, rested with 1 hour, and then climbed to the top with 1 hour. The functional relationship between tourists' climbing time t (hours) and mountain height h (kilometers) is shown in Figure (
)
A
B
C
D
Second,
fill-in-the-blank question
1.
The square root of 4 is
The cube root of 8 is
The arithmetic square root of is
2.
The right side of a right triangle is 3 cm long and the hypotenuse is 5 cm long, so the height of the hypotenuse is
3.
The sum of the internal angles of a Pentagon is
The sum of the outer angles of the decagon is
4.
As shown in the quadrangle ABCD, the diagonal lines AC and BD intersect at
Point o, when the condition is met.
When,
It is a parallelogram. (Just fill in one condition that you think is correct)
5.
If a straight line is in
, when x = 1, y = 2；; When x = 0 and y = 3, the expression of the straight line is
6.
For functions
, y with x
And reduce.
7.
The coordinates of point A(3, 2) relative to point B of X axis symmetry are
8.
The circumference of a diamond is 40 cm, and the diagonal length is 12 cm, so the area of this diamond is
9.
It is known that the intersection angle of two diagonals of a rectangle is 600, and the short side of the rectangle is 4cm, so its diagonals are long.
Cm, the long side is
Centimeter.
Third,
calculate
1.
2.
Fourth,
As shown in the figure, the quadrilateral ABCD is a rectangle, and the diagonal lines AC and BD intersect at the extension line E of O, CE‖DB and AB, which proves that AC = CE.
Five,
As shown in the figure, it is known that in △ABC, AD divides ∠BAC, DE‖AC and DF‖AB equally.
(1) Try to prove the shape of quadrilateral AEDF.
⑵ When △ABC meets any conditions, the quadrilateral AEDF is a square. Why?
Six,
When a food factory sells cookies to A city, it costs 0.58 yuan per kilogram for railway consignment and 0.28 yuan per kilogram for road transportation, and it also needs to subsidize 600 yuan on business trip.
(1) The factory sells X kilograms of biscuits to City A, and the freight is y 1 yuan for railway and y2 yuan for highway. Write the relationship between the costs y and x of the two transportation schemes respectively.
(2) How many kilograms of biscuits are sold to City A, and are the costs of the two distribution schemes the same?
⑶ Assuming that the weight of biscuits sold is 2500 kg, discuss which distribution scheme is more cost-effective.
Seven,
It is known that A is 3km south of B, and A and B are moving in a straight line at a constant speed. The relationship between their distance S(km) from A and their travel time t(h) is shown in the figure, where l 1 represents the movement process of A and l2 represents the movement process of B. According to the image, answer:
( 1)
Which is at A and which is at B?
(2)
How long did it take A to catch up with B?
(3)
Find the functional expression of l 1, l2?
(4)
When the two people are 3km apart again, explain by calculation.