(Time120min, total120min)
The total score of the first, second and third questions
19 20 2 1 22 23 24 25
score
First, multiple-choice questions (3 points for each small question, 36 points for * * *)
The title is123455678911112.
answer
1. The following calculation is correct.
A.a2？ a3 = a6 b . y3÷y3 = y c . 3m+3n = 6mn d .(x3)2 = X6
2. In real numbers, the number of irrational numbers is
A. 1
3. The following statement is correct.
A.-4 is the square root of-16, and b.4 is the square root of (-4) 2.
The square root of C.(-6) 2 is-6 d. The square root is 4.
4. In the following changes from left to right, factorization is
a . a(x+y)= ax+ay b . 10x 2-5x = 5x(2x- 1)
C.x2-4x+4 = x(x-4)+4d . x2- 16+3x =(x-4)(x+4)+3x
5. The image of the known linear function is as shown in the figure, so the range of values is
A.B. C. D。
6. When one of the following conditions is met, it can be determined that △ABC and △DEF are congruent.
A.∠A=∠E，AB=EF，∠B =∠D； B.AB=DE，BC=EF，∠A =∠E；
C.∠A=∠D，AB=DE，∠B =∠E； D.AB=DE，BC=EF，∠C=∠F。
7. If m+n=7 and mn= 12, the value of m2-mn+n2 is
a . 1 1 b . 13 c . 37d . 6 1
8. It is known that the image of a linear function is parallel to the straight line y=-x+ 1 and crosses the point (8,2), then the analytical formula of this linear function is
a . y = x-6 b . y =-x+6 c . y =-x+ 10d . y = 2x- 18
9. Given,, the value of is
A. 12
10. As shown in the figure, it is known that at △ABC, ∠ ABC = 45, AC=4, and H is the intersection of high AD and BE, the length of straight line BH is
A. The 4th day of 5th BC
1 1. As shown in the figure, it is an image of a function, so the following conclusion is correct.
A. when the value of x is
B. when the approximate value of x is 0,2.
C. at that time, the function value was the largest.
D. when, it increases with the increase of x.
12. The straight line Y = X- 1 intersects the two coordinate axes at point A and point B respectively, and point C is on the coordinate axis. If △ABC is an isosceles triangle, there are at most () points C that meet the conditions.
A.4 B.5 C.7 D.8
Fill in the blanks (3 points for each small question, *** 18 points)
13. The range of function independent variable x is.
14. Given the ratio of degrees of two internal angles of an isosceles triangle 1∶4, the degree of the vertex of this isosceles triangle is.
15. If known, then =
16. If the straight line y=-2x+k and the area of the triangle surrounded by two coordinate axes is 9, then the value of k is _ _ _ _ _ _ _ _ _.
17. as shown in the figure, given that the images of functions y = 3x+b and y = ax-3 intersect at point p (-2, -5), the solution set of inequality 3x+b > ax-3 is _ _ _ _ _ _.
18. Polynomial can become the complete square of algebraic expression after adding a monomial, so the added monomial can be. Just fill in what you think is correct.
Iii. Answering questions (***66 points)
19. (4 points for each small question, *** 12 points)
(1) Solve the equation:
(2) Decomposition factor:
(3) Calculation:
20. (6 points for this question)
The following table is a part of Yang Hui's triangle coefficient table, which is used to guide readers to write the coefficient in the form of (a+b)n(n is a positive integer) according to the law. Please carefully observe the rules in the table below and fill in the missing coefficients in the (a+b)4 expansion.
+ + +
2 1. (8 points for this question)
As shown in the figure, in the plane rectangular coordinate system, …
The area of (1) is.
(2) Make a symmetrical figure about the axis in the figure.
(3) Write the coordinates of the points.
22. (8 points for this question)
As the picture shows, a city has a rectangular plot, which is meters long and meters wide. The planning department plans to green the shadow part and build a statue in the middle. How many square meters is the green area? And calculate when the green area is.
23. (This question 10)
Two sporting goods stores, A and B, sell the same table tennis bat and table tennis. Each ping-pong bat costs 20 yuan, and each box of ping-pong balls costs 5 yuan. Now both stores are engaged in promotional activities. Shopkeeper A: Every time you buy a racket, you get a box of table tennis. Store B: 10% discount on the price. A class needs to buy 4 rackets and several boxes of table tennis (no less than 4 boxes).
(1) Let the number of ping-pong boxes purchased be X (boxes), the number of payments purchased in store A be (yuan), and the number of payments purchased in store B be (yuan). Write the functional relationship between the number of payments made in two stores and the number of ping-pong boxes X.
(2) On the number of table tennis boxes, which store is good enough to buy?
(3) If the class needs to buy 4 rackets and 12 boxes of table tennis, please help design the most economical purchase plan.
24. (This question 10)
In Figure 1 and Figure 2, point C is a point on the AB line, and △ACM and △CBN are equilateral triangles.
(1) As shown in figure 1, are the line segments AN and BM equal? Prove your conclusion;
(2) As shown in Figure 2, AN and MC meet at point E, BM and CN meet at point F. Explore the shape of △CEF and prove your conclusion.
25. (This is entitled 12 points)
In trapezoidal ABCO OC∑AB, a plane rectangular coordinate system is established with O as the origin, and the coordinates of points A, B and C are A (8 8,0), B (8 8,0/0) and C (0 0,4) respectively. Point D (4,7) is the midpoint of BC line, and moving point P starts from point O..
(1) Find the analytical formula of straight line BC;
(2) Let the area of △OPD be S, find the functional relationship between S and T, and point out the range of independent variable T;
(3) When t is what value, the area of △OPD is the area of trapezoidal OABC.
Eighth grade math reference answer
First, multiple-choice questions: DCBBAC BCADBC
Second, fill in the blanks:
13.x ≤ 3 14.20 or 120 15.7 16. 6.
17.x >-2 18。 -1 or -4a2 or 4a or -4a (only fill in one).
Third, answer questions:
19.( 1) 7 or-1; (2) ; (3)-3
20.4,6,4
2 1.( 1) 7.5 (3 points); (2) The drawings are correct (2 points); (3) (3 points)
22.(6 points) 63 square meters. (2 points)
23. (1) = 60+5x (x ≥ 4) = 4.5x+72 (x ≥ 4) (4 points)
(2) =, x=24, and the prices of the two stores are the same;
>, x > 24, it is cost-effective to go to store B;
while
(3) Because we need to buy four rackets and 12 boxes of table tennis,
Purchase scheme 1: preferential method ① purchase, which costs RMB; ( 1)
Procurement Scheme 2: Two procurement methods are adopted,
Buying 4 sets of rackets in Shop A requires 80 yuan, and you can get 4 boxes of table tennis at the same time;
It costs RMB to buy 8 boxes of table tennis in store B.
* * * Cost 80+36= 1 16 yuan. Obviously, 1 16 < 120.
The best purchase plan is:
Buy 4 rackets in Shop A and get 4 boxes of table tennis. Buy 8 boxes of table tennis in Store B (2 points)
24. Omit. (5 points for each small question, *** 10)
25.( 1) (3 points)
(2) (6 points)
(3) seconds or seconds (3 minutes)