Junior one mathematics midterm examination paper volume 2
1. Multiple choice questions: 3 points for each question, * * 30 points.
1. The result of simplifying a23 is
a8 D.a9
2. Among the following decomposition factors, the result is correct.
a.x2﹣ 1=x﹣ 12 b.x2+2x﹣ 1=x+ 12
c.2x2﹣2=2x+ 1x﹣ 1 d.x2﹣6x+9=xx﹣6+9
3. As shown in the figure, point E is on the extension line of AC. Which of the following conditions can judge AB∑CD?
A.∠3 =∠4b∠D =∠DCE c∠ 1 =∠2d∠B =∠2
4. As shown in the figure, it is known that AB∨CD and straight line EF intersect AB and CD at points E and F respectively, and EG bisects ∠BEF. If ∠ 1 = 50, the number of times of ∠2 is
A.50 B.60 C.65 D.70
5. As shown in the figure, ∠ 1, ∠2, ∠3 and ∠4 are the external angles of pentagonal ABCDE, ∠1= ∠ 2 = ∠ 3 = ∠ 4 = 773.
a . 80 b . 100 c . 108d . 1 10
6. The teacher gave:, and the value you can calculate is.
A, B, C, D,
7. If,, then the size of three numbers is
A.B. C. D。
8. As shown in the figure, two right-angled triangles overlap, and one of them is translated to the position of △DEF along the BC side, ∠ B = 90, AB= 10, DH=2, and the translation distance is 3, then the area of the shadow part is
A.20 B.24 C.27 D.36
9. There is a two-digit number, and the sum of its ten digits and one digit is 6, so the qualified two digits are
A.5 B.6 C.7 D.8
10. The cubic power of a positive integer m greater than 1 can be "split" into the sum of several consecutive odd numbers, such as 23 = 3+5, 33 = 7+9+ 1 1, 43 =13+/kloc.
43 B.44 C.45 D.4
Two. Fill in the blanks: 3 points for each question, * * 30 points.
1 1. The common factor of polynomial 2a2b3+6ab2 is.
12. The diameter of human red blood cells is about 0.0000077m, which is expressed by scientific notation.
13. If the lengths of two sides of a triangle are 1 and 4 respectively, then the third side A is acceptable. Fill in the qualified numbers.
14. As shown in the figure, in △ABC, the point where point A falls on the triangle plane is A 1. If ∠ A = 30 and ∠ BDA 1 = 80, then ∠CEA 1.
15. As shown in the figure, the straight line 1∑2, AB⊥ 1, the vertical foot is O, BC and 2 intersect at point E, if ∠ 1 = 43, then ∠2=.
16. As shown in the figure, after a rectangular piece of paper is folded along EF, points D and C fall at D' and C' respectively, and the extension line of ED' intersects BC at point G, if ∠ EFG = 55, ∠ 1 = 0.
17. If every outer angle of a polygon is 60, then the polygon is a polygon, and the sum of its inner angles is 0.
18. It is known that the solution of the binary linear equation kx-2y = 4 about x and y is, then k=.
19. Draw with an isosceles right triangle, translate the triangle along the dotted line in the figure and then rotate counterclockwise around point m, then the included angle between the hypotenuse of the triangle and the ray is.
Iii. Answer 7 questions in this question, with ***60 points.
20. Calculation: 25 points for this question.
1 ﹣2÷﹣ 0+﹣23; 22a﹣3b2﹣4aa﹣3b.
Decomposition factor: M4 ~ 2m2+ 1.4 solving equations.
5 Simplify first and then evaluate: 4xx-1-2x+12x-1,where x =- 1.
2 1. Fill in the blanks by drawing: 6 points for this question.
As shown in the figure, the vertices of △ABC are all on the grid points of the grid paper. Translate △ABC down twice, and then translate 3 squares to the right.
1 Please draw the translated △ a ′ b ′ c ′ in the picture;
2. Draw the height C'D' of A'B'C' in the drawing, and mark the position of point d';
If the side length of each small square is 1, then the area of △ a ′ b ′ c ′ =. The answer is written directly on the horizontal line in the question.
22. This question scores 6 points. The distance between Party A and Party B is10km. Both set out at the same time and marched in the same direction. Party A can catch up with Party B within 2.5 hours. Go in the opposite direction, meet in 1 hour, and find the speed of both.
23. This question is divided into six points, as shown in the figure. In △ABC, AD⊥BC and AE share ∠BAC, ∠ B = 40, ∠ C = 60, and find the degree of ∠DAE.
24. This question is divided into eight parts as shown in the figure, CD⊥AB, EF⊥AB, and the vertical feet are D, F, ∠ 1=∠2 respectively.
1 Try to judge the positional relationship between DG and BC and explain the reasons.
If ∠ A = 70 and ∠ BCG = 40, find the degree of ∠AGD.
25. Figure ① shows a rectangle with a length of 2m and a width of 2n. Cut the big rectangle into four identical small rectangles along the dotted line in the figure with scissors, and then make a square according to the shape in Figure ②.
1 Please look at Figure ②, and write the equivalent relationship among three algebraic expressions m+n2, m-n2 and mn with the area of the figure; ______________.
According to the conclusion in 2, if x+y=-6 and xy=2.75, then x-y=.
There are many algebraic identities that can be expressed by the area of a graph, as shown in Figure ③, which means 2m+nm+n=2m2+3mn+n2. Try to draw a geometric figure so that its area can represent the algebraic identity m+nm3 = m2+4mn+3N2.
The reference answer of the mid-term examination paper in the second volume of the first day of junior high school
1. Multiple choice questions: 3 points for each question, * * 30 points.
The title is 1 23455 6789 10.
Answer BCCC CC CC CC CC CC CC CC CC CC CC
Fill in the blanks: 2 points for each blank, 33 points for * * *.
1 1.2ab2 12。 7.7× 10﹣6 13.4 14.20 15. 1 10 16.70
17.6,72018. -5 19.22.
Three, answer this question ***8 questions, ***60 points.
20. Calculation: 25 points for this question.
1 original formula = 9 ÷1+-8 = 9-8 =1;
2 Original formula = 4a2-12ab+9b2-4a2+12ab = 9b2.
3 The original formula = m2-12 = m+12m-12.
4 solution:,
①×2+②: 5x=0, that is, x=0,
Substitute x=0 into ① to get y=2,
Then the solution of the equation is.
5 solution: the original formula = 4x2-4x-4x2+1=-4x+1,
When x =- 1, the original formula =4+ 1=5.
2 1. Fill in the blanks by drawing: 6 points for this question.
Solution: 12 omitted
The area of 3 △ a ′ b ′ c ′ = ×3×3=.
22. This question is 6 points.
Solution: let the speed of a be X km/h and the speed of b be Y km/h,
Judging from the meaning of the question,
Solution:.
A: The speed of A is 7 km/h, and the degree of B is 3 km/h. 。
23. This question is 6 points.
Solution: ∫∠B = 40, ∠ C = 60,
∴∠BAC= 180 ﹣∠B﹣∠C=80，
∫AE sharing∠ ∠BAC,
∴∠BAE= ∠BAC=40，
∴∠AEC=∠B+∠BAE=80，
∵AD⊥BC，
∴∠ADE=90，
∴∠dae= 180 ﹣∠ade﹣∠aed= 10。
Answer: The degree of ∠DAE is 10.
24. This question is 8 points.
Solution: 1DG is parallel to BC. The reason for this is the following：
∵CD⊥AB,EF⊥AB，
∴CD∥EF，
∴∠ 1=∠BCD，
∵∠ 1=∠2,
∴∠2=∠BCD，
∴dg∥bc；
2∶DG∨BC，
∴∠AGD=∠BCG=40。
25. 9 points for this question.
1m+N2 = m-N2+4mn2 53