First, multiple-choice questions (each question has only one correct answer, with 4 points for each question and 40 points for * * *)
1, as shown in the figure, two straight lines a∨b, the number of angles equal to ∠ 1 is ().
a， 1 b，2 c，3 d，4
2. The solution set of inequality group is ()
A, b, c, d, no solution
3. If, then the correct one of the following items is ()
A, B, C, D,
4. As shown in the figure, △ Abd △ BAC is derived from ∠ d = ∠ c and ∠ bad = ∠ ABC, and the abbreviation of the decision theorem used is ().
a、AAS B、ASA C、SAS D、SSS
5. A set of data is known as 1, 7, 10, 8, x, 6, 0, 3. If =5, then x should be equal to ().
a、6 B、5 C、4 D、2
6, the following statement is wrong ()
A, cuboids and cubes are prisms; B, the side of a triangle is a triangle;
C, six sides are covered by six sides, and the sides are rectangular; D, the three views of the sphere are all graphics with the same size;
7. The three sides of △ ABC are A, B and C, and then ()
A, △ABC is an acute triangle; The diagonal lines of side B and side C are right angles;
C and △ABC are obtuse triangles; The diagonal of side d and side a is a right angle;
8. In order to prepare for the class's junior high school graduation party, the monitor asked the students what kinds of fruits they like to eat, so what kind of fruit to buy, the most noteworthy of the following survey data is ().
A, median; B, general; C. mode; D, weighted average;
9. As shown on the right, there are three cubes with the same size. The six numbers 1, 2, 3, 4, 5 and 6 are marked on the six faces of each cube in the same order, and all the faces marked with "6" are placed on the left, so the sum of the three numbers marked on their bottom faces is equal to ().
a、8 B、9 C、 10 D、 1 1
10. In order to encourage residents to save water, Beijing has introduced a new standard for charging water for residents: (1) If the monthly water consumption of each household does not exceed 4 cubic meters, it will be calculated as 2 meters per cubic meter; (2) If the monthly water consumption of each household exceeds 4 cubic meters, the excess is calculated at 4.5 meters per cubic meter (the excess is still calculated at 2 yuan per cubic meter). Now suppose that a resident in this city uses X cubic meters of water a month, and the water fee is Y yuan, then the functional relationship between Y and X is correct by image ().
Fill in the blanks (4 points for each small question, 32 points for * * *)
1 1, and the solution set of inequality is _ _ _ _ _ _ _ _ _ _ _;
12, it is known that point A is in the fourth quadrant, and the distances to the X axis and Y axis are 3 and 5 respectively, so the coordinates of point A are _ _ _ _ _ _ _ _ _ _ _;
13. In order to know the weight of 400 students in the third grade of a school, 50 students were randomly selected for statistical analysis. In this question, it generally refers to _ _ _ _ _ _ _;
14, one PE exam in a class, 4 students 100,190 students,1/80 students, 8 students 70, 5 students 60 and the remaining 8 students * *
15. As shown in the figure, it is known that ∠B=∠DEF and AB=DE. Please add a condition to make △ ABC△ def, and the condition to be added is _ _ _ _ _ _ _ _;
16, as shown in the figure, AD and BC intersect at point O, OA=OD, OB=OC, if ∠ B = 40, ∠ AOB = 1 10, ∠ D = _ _ _ _ _ _
17, the relationship between the length y(cm) of the spring and the mass x (kg) of the suspended object is a linear function.
The image is as shown on the right, and the length of the spring-free object is _ _ _ _ _ _ _ _ cm.
/DrawingNo. KLOC-0/5/DrawingNo. KLOC-0/6/DrawingNo. KLOC-0/7
18, as shown in the figure below, which is a three-dimensional diagram. Please name the 3D graphics according to the view:
The corresponding three-dimensional graphics are three views of _ _ _ _ _ _ _ _ _ _ _ _.
Iii. Answering questions (***78 points)
19, (8 points) solution inequality, indicating that the solution set is on the number axis.
20.(8 points) Fill in the blanks (complete the following proofs and the reasoning basis in brackets):
As shown in the figure, it is known that AD⊥BC is in D, EF⊥BC is in F, ∠ 1=∠3,
Proof: AD divides equally ∠BAC.
Answer:
First, multiple choice questions
1 C 2 A 3D 4 A 5B 6 B 7D 8 C 9 A 10 C
Second, fill in the blanks
1 1, x > 2 12, (5, -3) 13, the weight of all 400 students in grade three in a school 14, 80 points 15, BC=EF.
16,8017,918, rhombic or pentahedral
Third, answer questions.
19, solution:
)
20. Proof: ∵AD⊥BC, EF⊥BC in F (known)
∴AD∥EF (at the same angle, two straight lines are equal or in the same plane, and two straight lines perpendicular to the same trunk line are parallel)
∴∠∠ 1 =∠ E (two straight lines are parallel and have the same angle)
∠2=∠3 (two straight lines are parallel with equal internal angles)
∫∠3 =∠ 1 (known)
∴∠ 1=∠2 (equivalent substitution)
∴AD bisects ∠BAC(AD bisects ∠BAC ∠ 1 = ∠ 2, AD is ∠BAC bisector)