Mid-term math test questions in eighth grade
(Examination time 100, full score 120)
First of all, choose one carefully and fill in the only correct answer in the brackets before the question! (2 points for each small question, ***26 points)
The square roots of 1 and () 4 are
a、2 B、2 C、D、
2. () The following writing is wrong.
A, B,
c、D 、=-4
3, () calculation-the result is
A, B, C, D and VII
4. () The result of the factorization factor x3-x is
a、x(x2- 1) B、x(x- 1)2 C、x(x+ 1)2 D、x(x+ 1)(x- 1)
5, () the result of calculating x is
A, B, C, D,
6, () and the number of points on the axis one-to-one correspondence is
A, fraction b, rational number c, irrational number d, real number
7. () In real numbers, 0,, 0.101001001…,, the irrational number is
a，0 b， 1 c，2 d，3。
8. () We know it is irrational, so which two integers are-1?
A, 1 and 2 B, 2 and 3 C, 3 and 4 D, 4 and 5
The result of 9, () (2+x) (x-2) is
a、2 - x2 B、2+x2 C、4 + x2 D、x2-4
10, () If x is not included in, then m and n satisfy.
1 1, () The calculation result is as follows
A, B, C, D,
12, () as shown in figure 1: Find the area of the black part (rectangle) as follows
a、24 B、30 C、48 D、 18
13, () Let three sides of a triangle be the following groups, then a group that is not a right triangle is.
a、3、4、5； b、6，8， 10； c、5 12， 13； d、5、6、8；
Second, fill in carefully and write the answer on the horizontal line. I believe you can fill it out correctly! (2 points for each small question, ***26 points)
14, calculation: _.
15. If A, B and C are three sides of △ABC, and a = 3cm, B = 4cm and C = 5cm, then the height of the largest side of △ABC is _ _ _ _ _ _ _ _.
16, the common factor of polynomial is.
17, if (x-1) (x+1) = x2+px-1,then P.
The value of is _ _ _ _.
18, as shown in Figure 2, there are two trees, one is 6 meters high, the other is 2 meters high, and the two trees are 3 meters apart.
A bird flies from the treetop of one tree to the treetop of another, at least several meters away.
Calculate 19 and (1+x) (x-1) (x+1).
20. Using a simple method to calculate 2008-40 16× 2007+2007, the result is _ _ _.
2 1, knowing that x2+x- 1 = 0, the value of algebraic formula x3+2x2+2008 is.
22. As shown in Figure 3, a big tree was 3 meters above the ground when a strong typhoon interrupted it.
The top of the fallen tree is 4 meters away from the root, and the big tree is breaking.
The height of the front is _ _ _ _ _ _ _ meters.
23. If the sum of two square roots of a positive number is A-2, this positive number is Figure 3.
24. Fill in the appropriate numbers in the horizontal line to make the equation hold:
25. As shown in Figure 4, in order to measure the width of the lake, Xiaoming sets piles at point A, point B and point C respectively.
And measured AC = 52, BC = 48, please calculate the width of the lake should be _ _ _ _ _ _ _ meters.
26, _ _ _ _ _ _ _ _. Figure 4
Three, careful calculation, simplification or solution, the solution should write out the necessary calculation process, write out the steps, grade step by step.
Note: (6 points for 27 questions; 28 to 33 questions, 3 points for each small question, 18 points; 4 points for 34 small questions; 35 to 38 questions, 5 points for each small question, 20 points, ***48 points)
27, factorization:
①②x2(x-y)-(x-y)④3a-6a+3
28. Calculation: 29. Calculation: x3. (2x3) 2 degrees.
30. Simplify (x2-x) 3+(3x4-2x3) ÷ (-x) 3 1. Calculation:
32. Calculation: (x-1) (x-3)-(x-1) 2 33. Solve the equation:
34. Simplify before evaluating:-,where.
As shown in the figure, each small square is a square with a side length of 1. Find the perimeter of △ABC (the result is indicated by the root sign).
36. It is known that there is a quadrangular open space ABCD in a development zone, as shown in the figure. Now it is planned to plant turf in this clearing. According to the measurement, ∠ A = 60, AB = AD = 8m, CD = 10m, BC = 6m. If you need 200 yuan per square meter of turf, how much will it cost? ( ≈ 1.73)
37. As shown in the figure, there are two points A and B 50km apart on a straight highway, C and D are two villages, DA⊥AB is at point A and CB⊥AB is at point B. It is known that DA=30km and CB=20km. Now a local product purchasing station E will be built in the AB section of highway, so that the distance from village C and village D to purchasing station E will be equal.
38. As shown in the figure, the residential building is parallel to the road, with a distance of 9m, and the distance of 4 1m from the truck can be affected by noise. How long will the truck traveling at the speed of 4m/s bring noise impact to the residents on the first floor? If the time exceeds 25 seconds, this road is forbidden to pass. Do you think trucks can pass on this road? (6 points for this question)
See if there are any mistakes or omissions in the above questions, and don't leave regrets! If you have time and spare capacity, you can complete the following additional questions: (65438+ 00 points for each small question, * * * 20 points).
1, as shown in figure, in quadrilateral,,, and.
Try to find: (1) degrees;
(2) The area of quadrilateral (the root sign is retained as a result).
2. One day, Teacher Zhang wrote three formulas on the blackboard: 5-3 = 8×2, 9-7 = 8× 4, 15-3 = 8× 27.
Wang Hua then wrote two formulas with the same law: 1 1 5 = 8× 12, 15-7 = 8× 22. ...
(1) Please use the above rules to write two more formulas (different from the above formulas);
(2) Write the law reflecting the above formula in words;
(3) Try to prove that this rule is correct.