First, choose carefully.
1. Of the following operations, the correct one is ().
a、x3？ x3=x6B、3x2÷2x=xC 、( x2)3=x5D 、( x+y2)2=x2+y4
2. In the following patterns, the axis symmetry is ().
3. Among the following variations from left to right, factorization is ().
a、a(x+y)=ax+ay B、x2-4x+4=x(x-4)+4
c、 10x2-5x=5x(2x- 1) D、x2- 16+3x=(x-4)(x+4)+3x
4. The following statement is true ()
A, 0.25 is the square root of 0.5, and negative numbers have square roots.
The square roots of c and 72 are 7D, and positive numbers have two square roots, and the sum of these two square roots is equal to 0.
5. In the following curve, it is () that cannot indicate that y is a function of x.
6. As shown in the figure, if four points are on a straight line, adding another condition still cannot prove that ⊿ABC≌⊿DEF is ().
A.AB=DE B..DF∑AC
C.∠E =∠ABC D . AB∨DE
7. As we all know, then the value is ().
a、9 B、C、 12 D、
8. It is known that the function value y of the proportional function (k≠0) decreases with the increase of x, so the image of the linear function y = x+k is roughly ().
9. Turn on the switch of the washing machine. When washing clothes (there is no water in the washing machine), the washing machine goes through four continuous processes: water intake, washing, drainage and dehydration, in which the water volume y (liter) in the washing machine and time x (minute) satisfy a certain functional relationship, and the functional image is roughly ().
10. One side of a given isosceles triangle is 4, the other side is 10, and the circumference of the isosceles triangle is ().
A, 14B, 18C, 24D, 18 or 24.
1 1. In real numbers, the number of irrational numbers is ().
A. 1
12. It is known that the image of a linear function is parallel to the straight line y=-x+ 1 and passes through the point (8,2), then the analytical formula of this linear function is ().
a . y =-x-2 b . y =-x-6 c . y =-x+ 10d . y =-x- 1
13. If the monomial and x3ya+b are similar terms, then the product of these two monomials is ().
A.x6y4 B.-x3y2 C.- x3y2 D.-x6y4
14. The result of calculating (-3a3)2÷a2 is ().
a . 9 a4 B- 9 a4 c . 6 a4 d . 9 a3
15. If m+n=7 and mn= 12, the value of m2-mn+n2 is ().
a . 1 1 b . 13 c . 37d . 6 1
16. The following types are completely flat ()
a . x2-x+b . 1+x2 c . x+xy+l d . x2+2a-l
17. The image of linear function y=mx-n is shown in the figure, so the following conclusion is correct ().
Morning & lt0, n & lt0b.m0c.m > 0，n & gt0d . m & gt； 0，n & lt0
18. The personal monthly income of a company's marketing department has a functional relationship with its monthly sales. The image is as shown in the figure. As can be seen from the information given in the figure, the income of marketers is () when there is no sales.
3 10 yuan B. 300 yuan
C. 280 yuan, 290 yuan
19. Given that the factorization factor of polynomial 2x2+bx+c is 2(x-3)(x+ 1), the values of b and c are ().
A.b=3，c=- 1 B.b=-6，c=2
C.b=-6，c=-4 D.b=-4，c=-6
20. The value range of the independent variable x in the function y= is ().
a . x≥2 b . x≠ 1 c . x & gt； -2 and x≠ 1 D. X ≥-2 and x≠ 1.
2 1. The straight line y=-2x+a passes through (3, y 1,) and (-2, y2), then the relationship between y 1 and y2 is ().
a . y 1 & gt； y2 b . y 1 & lt； Y2d。 Not sure. 2. Fill it in carefully and try it.
1. What about a4? Ay=a 19, then y = _ _ _ _ _ _ _ _ _
2. Calculation: () 2008× (-) 2009× (-1) 2007 = _ _ _ _ _ _.
3. If the polynomial x2+mx+9 happens to be the square of another polynomial, then m = _ _ _ _ _ _ _ _ _
4. If: known, the arithmetic square root of x+y is _ _ _ _ _ _ _ _.
5. If the point A (-2,4) is known, the coordinates of the point symmetrical about the Y axis of the point A are _ _ _ _ _ _ _ _.
6. For an isosceles triangle with a perimeter of 10cm, the functional relationship between the waist length Y(cm) and the base length x(cm) is _ _ _ _ _ _ _ _.
7. Translate the image of the straight line y=4x+ 1 down by 3 unit lengths to get the straight line _ _ _ _ _ _ _ _.
8. If a+ =3, the value of a2+ is _ _ _ _ _ _ _.
9. It is known that the images of linear functions y=-x+a and y=x+b intersect at point (m, 8), then a+b = _ _ _ _ _ _ _ _ _.
10. Given that the imaginary points of straight lines y=x-3 and y=2x+2 are (-5, -8), the solution of the equation is _ _ _ _ _ _ _.
1 1. If the triangle area enclosed by the straight line y=-2x+k and the two coordinate axes is 9, then the value of k is _ _ _ _ _ _ _ _ _.
12. Observe the following monomials:
x，-2x2，4x3，-8x4， 16x5，…
Write the 10 item as _ _ _ _ _ _, and the nth item as _ _ _ _ _ _.
13. The three sides of a triangle are 3cm, 5cm and xcm respectively, so the functional relationship between the perimeter y(cm) and x(cm) of this triangle is.
14. If both x and y are real numbers, the cube root of x+3y is.
Third, answer seriously. Be careful!
1. Calculation:
( 1)(2)[(-3x2y 4)2x 3-2x(3x2y 2)3 y2]÷9x7y 8
(3)[(x+2y)2-(x+y)(x-y)-4y2]÷2y
2. Break down the following types.
( 1)3x- 12x 3(2)(x2+y2)2-4x2y 2
3. Simplify first, then evaluate: known: a2+b2+2a-4b+5=0, and find the value of: 3a2+4b-3.
4. Simplify first, then evaluate.
5. As shown in the figure, in △ABC, AB=AC, DE is a straight line passing through point A, BD⊥DE is at point D, and CE⊥DE is at point E;
6. It is known that y=y 1+y2, y 1 is proportional to x- 1, y2 is proportional to x, when x=2, y=4, when x=- 1, y=-5, find the resolution function of y and x.
(1) If B and C are on the same side of de (as shown in figure 1) and AD=CE, then the verification is: AB⊥AC.
(2) If B and C are on both sides of DE (as shown in Figure 2), are AB and AC still vertical, and other conditions remain unchanged? If yes, please give proof; If not, please explain why.
7. A school is going to make a batch of New Year's commemorative books for students. Company A proposed that each book should be charged a material fee of 5 yuan and a design fee of 1200 yuan. Proposed by company b; 8 yuan is charged for each roll of materials, with a 10% discount, and no design fee is charged.
(1) Please write down the functional relationship between the charge y 1 of Company A and the number X of commemorative books produced;
(2) Please write down the functional relationship between the charge y2 of Company B and the number X of commemorative books produced;
(3) If there are 580 students in this school, which company do you think is cheaper?
8. the straight line y=kx+b passes through point a (-1, 5) and is parallel to the straight line y =-x.
(1) Find the analytical formula of this straight line; (2) Find the area of △AOB.
(3) If point B (m, -5) is on a straight line and O is the coordinate origin, find the value of m;
9. Drawing questions (don't write drawing steps, keep drawing traces).
As shown in the figure, OM and ON are two expressways, and A and B are two factories. Now we need to build a warehouse P, so that the distance to the two roads is equal and the distance to the two factories is equal. Please confirm the location of warehouse P. ..
10, as shown in the figure, the function expression y=2x+3 when a straight line intersects with point p, and the abscissa of point p is-1.
The y axis is at point a (0, 1). Find the functional expression of a straight line.
1 1. As shown in the figure, oc is the bisector of ∠AOB, and p is a point on oc. PD ⊥ OA passes through OA in D, PE⊥OB passes through OB in E, and F is another point on OC, connecting d F and EF. Verification: DF = ef.
12. Before answering, please read the following answering process:
Simplifying the form, as long as we find two numbers A, B, make, make, then there will be:
For example, simplification
Solution: first, change it to, here, because 4+3=7,
That is to say,
∴ = =
Simplify by imitating the above example:
13. The price of each brush in Xinhua Stationery is 2.5 yuan, and the price of each calligraphy exercise book is 0.5 yuan. Stationery stores have formulated two preferential measures for promotion: a) buying a writing brush to send calligraphy exercise books; B: 10% off the purchase amount.
Experimental middle school wants to buy 10 brush and x(x≥ 10) calligraphy exercise books for the school's calligraphy interest group.
(1) Please use the preferential method A to write the functional relationship between the actual payment amount Y A (yuan) and X (capital);
(2) Please write down the functional relationship between the actual payment amount Y, B (Yuan) and X (Ben) by the second preferential method;
(3) Please analyze which preferential payment method is more economical.
14, exploration question:
..... (1) Try to evaluate.
② What is the single digit of the judgment value?
20 10-20 1 1 eighth grade mathematics first semester final examination paper (2)
Choose one first to see who is careful.
1. The result of calculation is ()
A.2B. 2C-2D.4
2. The result of calculation is ()
A.B. C. D。
3. If the formula is meaningful in the real number range, the value range of x is ().
A.x>5 B.x≥5 C.x≠5 D.x≥0
4. As shown in the figure, among the following conditions, the condition that △ Abd△ BAC cannot be judged is ().
A.∠D=∠C，∠BAD=∠ABC
B.∠BAD=∠ABC，∠ABD=∠BAC
C.BD=AC，∠BAD=∠ABC
D.AD=BC，BD=AC
5. As shown in the figure, the hexagonal ABCDEF is an axisymmetric figure, and the straight line where CF is located is its axis of symmetry. If ∠ AFE+∠ BCD = 280, the size of ∠AFC+∠BCF is ().
140
C. 160
6. In the figure below, the image composed of points with the solution of the equation as coordinates is ().
7. Any given non-zero real number is calculated according to the following procedure, and the final output result is ().
A.B. C. D。
8. The image of the known linear function is as shown in the figure, so the value range is ().
A.B.
C.D.
9. As shown in the figure, it is known that in △ABC, ∠ ABC = 45, AC = 4°, and H is the intersection of high AD and BE, then the length of straight line BH is ().
A. The 4th day of 5th BC
10. The picture shows the relationship between the length (meters) and the time (days) of a highway built by an engineering team in the "Village to Village" project. According to the information provided by the image, we can know that the length of the expressway is () meters.
A.504B.432C.324D.720
12. If the straight line y=kx+2 passes through (1, -2), then the value of k is ().
A.4B to 4C. -8D.8
1 1. The following calculation is correct ().
a、a2？ a3=a6B、y3÷y3=yC、3m+3n=6mnD 、( x3)2=x6
12. In the following figures, the one that is not axisymmetric is ().
13. The image of the known linear function is shown in the figure, so the range of values is ().
A.B. C. D。
14 As shown in the figure, connect the midpoint O of two steel bars AA' and BB' together, so that AA' and BB' can freely rotate around the point O to make a measuring workpiece, and the length of A'B' is equal to the width of the inner groove AB, so the reason for judging △ OAB △ OAB is ().
(a) corner edge (b) corner edge
(c) side edge (d) corner edge
15. As shown in the figure, in the rectangle, the midpoint is connected and merged.
If the extension line of the intersection line extends to this point, then the congruent right triangle in the figure has ().
A.3 to B.4 to C.5 to D.6.
16. In 2007, the China Railway increased its speed for the sixth time. A train travels from City A to City B at a constant speed of 200 km/h, and the functional relationship between the distance (unit: km) of the train from City B and the traveling time (unit: hour) is graphically represented as correct ().
Second, fill in and see who is careful.
1. Calculation: (π-3. 14) o =.
2. As shown in the figure, △ABC and △ A ′ B ′ C ′ are symmetrical about a straight line, then the degree of ∠B is.
3. The range of independent variables of the function is.
4. If the single sum is similar, the value of is.
5. Factorization:
6. Given the ratio of the degrees of two internal angles of an isosceles triangle 1∶4, the degree of the vertex of this isosceles triangle is.
7. As shown in the figure, AC and BD intersect at point O, ∠ A = ∠ D, please add another condition to make △ AOB △ Doc, and your supplementary condition is.
8. As shown in the figure, in the middle ∠ C = 90, ∠ABC = 60, BD divides ∠ABC equally, if AD=6, CD=.
9. As shown in the figure, △ABC is an equilateral triangle with a side length of 3, △BDC is an isosceles triangle, △ BDC =120. Make a 60-degree angle with D as the vertex, make its two sides intersect at point M, AC at point N, and connect MN, then the circumference of △AMN is.
10. As shown in the figure, the images of given functions y = 3x+b and y = ax-3 intersect at point p (-2, -5), and the solution set of inequality 3x+b > ax-3 is _ _ _ _ _ _ _.
1 1. If the base angle of an isosceles triangle is 40 degrees, then the degree of its vertex angle is.
12. Please note the following:
; ……
According to the previous rules, it can be concluded that.
13. Calculation: -28X4Y2÷7x3Y = 17. What about a4? Ay=a 19, then y = _ _ _ _ _ _ _ _ _
14. As shown in the figure, follow the rules and fill in the blanks.
15. Calculation: () 2008× (-) 2009× (-1) 2007 = _ _ _ _ _ _.
16. If the point A (-2,4) is known, the coordinates of the point A that is symmetrical about the Y axis are _ _ _ _ _ _ _ _ _.
Third, figure out who is better.
17. Calculation:. 18. Factorization:.
19. Known: As shown in the figure, AB=AD, AC=AE, ∠BAC=∠DAE. Verification: BC=DE.
20.(4) Simplify first and then evaluate, where x=-2 and y=.
2 1. From June 20081,China implemented the "plastic restriction order" and began to use reusable shopping bags for compensation. In order to meet the market demand, a manufacturer produces two kinds of reusable shopping bags made of cloth, with a daily output of 4500. The cost and price of two kinds of shopping bags are shown in the following table. Suppose a shopping bag is produced every day, and the daily profit is RMB.
Cost (RMB/unit) and selling price (RMB/unit)
2 2.3
3 3.5
(1) Find the functional relationship of and; (2) If the maximum daily input cost of the factory is 10000 yuan, what is the maximum daily profit?
23. As shown in the figure, in the plane rectangular coordinate system, the image of the function is the bisector of the first quadrant and the third quadrant.
Experimental exploration: By observing the chart, it is easy to know that the coordinate of A (0 0,2) about the symmetrical point of a straight line is (2,0). Please mark the positions of the symmetrical points of B (5,3) and C (-2,5) about a straight line in the figure, and write down their coordinates:,;
Induction and discovery: by observing the coordinates of the above three groups of points graphically, we will find that the coordinates of any point P(m, n) on the coordinate plane about the symmetrical point of the bisector of the first and third quadrants are:
22. Xiaoli's family used New Year's Day to drive to a scenic spot for three days. There were 36 liters of oil in the tank before the car left. After driving for several hours, I added a few liters of oil at the gas station on the way. The relationship between the remaining fuel quantity Q(L) in the fuel tank and the driving time t(h) is shown in the figure. Answer the following questions according to the pictures:
(1) refuel after driving for _ _ _ _ _ _ h, and refuel in the middle of _ _ _ _ _ _ _ l;
(2) Find the functional relationship between the remaining oil quantity Q of the fuel tank before refueling and the driving time t;
(3) If the gas station is 200km away from the scenic spot and the speed is 80km/h, will the oil in the fuel tank reach the destination?
Please explain the reason.
On Sunday, Xiaoming and Xiaogang traveled 50 kilometers away from home by bike. When they were driving at a constant speed of 1.5 hours, one of their bicycles broke down, so they repaired it in the bicycle repair shop for half an hour, and then continued to drive at the original speed for 1 hour to reach their destination. Please draw the distance s (km) matching their driving in the right plane rectangular coordinate system.
25. The position in the plane rectangular coordinate system is as shown.
(1) is about axis symmetry;
(2) Translate down by 3 unit lengths and draw the translated.
Fourth, answer questions.
1. Simplify before evaluating:
, among them.
2. As shown in the figure, in Rt△ABC, ∠ c = 90, AC = 4, BC = 3. Draw an isosceles triangle with one side of △ABC as its edge, so that its third vertex is on the other side of △ABC. Please draw a qualified isosceles triangle in Figure ①, Figure ② and Figure ③ respectively. The isosceles triangles in the three figures are different.
3. Place two identical right-angled triangles with an angle of 30 degrees as shown in the figure, so that the two straight lines AC, c1a1* *.
(1) How many pairs of congruent triangles are there in the picture? And write them out;
(2) Choose a pair of congruent triangles to prove it. (except △ ABC△ a1b1c1)
4. As shown in the figure, the analytical expression of a straight line is that it intersects the axis at a point, the straight line passes through the point, and the straight line intersects the point. (1) Find the analytical expression of a straight line; (2) the area to be discovered;
5. In May 2007, the xx China Yichang Three Gorges International Dragon Boat Rally kicked off in Huangling Temple. At 9: 00 am on the 20th, the dragon boat race started from Huangling Temple at the same time. During the competition, the functional relationship between the distance y (km) of Team A and the time x (hours) is shown in the figure. Team A arrived at the destination of Huangbaihe Port at 1 1: 30 in the morning.
(1) Which team reached the finish line first? When can Team B catch up with Team A?
(2) When is the biggest gap between Team A and Team B in the competition?
26. As we all know, as shown in the figure, points B, F, C and E are on the same straight line, AC and DF intersect at points G, AB⊥BE, the vertical foot is B, DE⊥BE, the vertical foot is E, and AB = DE, BF = CE.
Verification: (1) △ ABC △ def;
(2)GF=GC .
27. As shown in the figure, the center, center, center and intersection point are the midpoint of the edge, and the connecting line and intersection point.
(1) Verification:; (2) Verification:
(3) What does it have to do with? Try to prove your conclusion.