(Detection time:120min, full mark:120min)
Class: _ _ _ _ _ _ Name: _ _ _ _ _ Score: _ _ _ _ _ _ _
First, multiple-choice questions (3 points × 10=30 points)
1. The following equation is an unary quadratic equation ().
①3x2+x=20，②2x2-3xy+4=0，③x2- =4，④x2=0，⑤x2- +3=0
A.①② B.①②④⑤ C.①③④ D.①④⑤
2. If, the value range of x is ()
A.x & lt3 b . x≤3 c . 0≤x & lt； 3 D.x≥0
3. If =7-x, the value range of x is ()
a . x≥7 b . x≤7 c . x & gt； 7d . x & lt； seven
4. When x takes a real number range, the value of algebra+is a constant, which is ().
B. 16 C. 13 D.3
5. The root of the equation (x-3)2=(x-3) is ().
A.3b.4c.4 or 3d. -4 or 3
6. If the value of algebraic expression x2+4x+4 is 16, then the value of x must be ().
A.-2 B.2，-2 C.2，-6 D.30，-34
7. If c(c≠0) is the root of quadratic equation x2+bx+c=0, then the value of c+b is ().
A. 1 B.- 1 C.2 D.-2
8. Cut a rectangle with a width of 2cm from the square iron sheet, and the area of the remaining rectangle is 80cm2, so the area of the original square is ().
a . 100 cm2 b . 12 1 cm2 c . 144 cm2 d . 169 cm2
9. The product of all the roots of the equations x2+3x-6=0 and x2-6x+3=0 is equal to ().
A.- 18
10. The two sides of the triangle are 8 and 6 respectively, and the third side is the real root of the unary quadratic equation x2- 16x+60=0, so the area of the triangle is ().
A.24b.48c.24 or 8d.8
Two. Fill in the blanks (3 points × 10=30 points)
1 1. If =3, =2, and AB
12. Simplification = _ _ _ _ _.
The integer part of 13. It is _ _ _ _ _.
14. between two consecutive integers a and b, a
15 . x2- 10x+_ _ _ _ _ _ _ _ =(x-_ _ _ _ _ _ _ _)2。
16. If the unary quadratic equation of X (m+3)x2+5x+m2+2m-3=0 has a root of 0, then m = _ _ _ _ _ _ _ _ _ _ _ _
17. Equation x2-3x- 10=0, and the ratio of two roots is _ _ _ _ _.
18. It is known that two of the equations x2-7x+ 12=0 are exactly the lengths of two sides of Rt△ABC, so the length of the third side of RT △ ABC is _ _ _ _ _.
19. A two-digit number is three times larger than the ten-digit number, and the square of one digit is just equal to this two-digit number, so this two-digit number is _ _ _ _ _.
20. A supermarket bought two kinds of sweets from a city in the west of China, one is A kg, with X yuan per kg, and the other is B kg, with Y yuan per kg. If these two kinds of sweets are sold together, the break-even price will be _ _ _ _ _ _ _ _ _ _ yuan/kg.
Iii. Answering questions (***60 points)
2 1. Calculation (3 points for each small question, ***6 points)
( 1) ( + )- ( - ) (2)( + )÷
22. Solve the following equations with appropriate methods (3 points for each small question, *** 12 points).
( 1)(3x- 1)2 =(x+ 1)2(2)2 x2+x-= 0
(3) Solving the equation by collocation method: x2-4x+1= 0; p
(4) Solve the equation with method of substitution: (x2+x)2+(x2+x)=6.
23.(6 points) Given Equation 2(m+ 1)x2+4mx+3m=2, find the value of m according to one of the following conditions.
The (1) equation has two equal real roots; (2) The equation has two opposite real roots;
(3) One root of the equation is 0.
24.(5 points) It is known that x 1 and x2 are two real roots of quadratic equation 2x2-2x+m+ 1=0.
(1) the value range of real number m;
(2) If x 1, x2 satisfies the inequality 7+4x1x2 >; X 12+x22, and m is an integer, find the value of m 。
25.(5 points) Given x=, find the value of the algebraic formula x3+2x2- 1.
26.(6 points) The area of a circle with radius r is just the difference between the areas of two circles with radius 5 and radius 2. Find the value of R.
27.(6 points) At a commodity fair, all participating merchants signed contracts, and * * * signed 36 contracts. How many businessmen attended the fair?
28.(7 points) Fence material length 100 meter. If you want to enclose a rectangular open-air warehouse, the required area is not less than 600 square meters. There is an ancient wall 50 meters long to the north of the site. Someone used this fence to enclose a rectangular warehouse with a length of 40 meters and a width of 10 meters, but the area was only 400 square meters, which did not meet the requirements. Now please design the length of the rectangular warehouse.
29.(7 points) The figure "The rise and fall of national luck depends on education" shows the annual investment in education in China from 1998 to 2002.
(1) As can be seen from the figure, during the five years from 1998 to 2002, China's education expenditure showed a trend of _ _ _ _ _ _;
(2) According to the data given in the figure, find the annual average of China's education funds from/kloc-0 to 2002;
(3) If China's education expenditure increases from 548 billion yuan in 2002 to 789,654.38 billion yuan in 2004, what is the average annual growth rate of education expenditure in these two years? (The result is accurate to 0.0 1, = 1.200).
Answer:
1.D 2。 C 3。 B 4。 D 5。 C 6。 C 7。 B 8。 A nine. A 10。 C
1 1.-7 12.2- 13.4 14 . a = 3，b=4 15.25，5 16. 1，-
17.- or-18.5 or 19.25 or 36 20.
2 1.( 1) - ; (2) +
22.( 1)x 1=0，x2 = 1； (2)x =-；
(3)(x-2)2=3，x 1=2+，x2 = 2-；
(4) let x2+x=y, then y2+y=6, y 1 =-3, y2=2, then x2+x=-3 has no solution, x2+x=2, x 1=-2, x2 = 1.
23.△= 16 m2-8(m+ 1)(3m-2)=-8 m2-8m+ 16，
The (1) equation has two equal real roots,
∴△=0, that is, -8m2-8m+ 16=0, and m 1=-2, m2 =1;
(2) Because the equation has two equal real roots,
So the sum of the two roots is 0 and △≥0, then -=0, and m = 0； is obtained;
(3) The equation has a m = 0, ∴3m-2=0.
24.( 1)△=-8m-4≥0,∴m≤-； (2)m=-2，- 1
25.0 26.27.9
28. Option 1: The design is rectangular (both length and width are used: the length and width of the equation can be calculated by 30m and 20m);
Scheme 2: The design is square. Under the condition of equal circumference, the area of square is larger than that of rectangle, and its side length is 25 meters;
Scheme 3: Use part of the old wall: If the old wall in the north of the site is used, the length of the rectangle is parallel to the old wall, one side of the rectangle perpendicular to the wall is x meters, and the other side is (100-2x) meters, then one side is (25+5) meters (about 43 meters) and the other side is 14 meters.
Scheme 4: Make full use of the old wall in the north, with an area of1250m2.
29.( 1) As can be seen from the figure, during the five years from 1998 to 2002, China's investment in education showed an increasing trend year by year; (2) From 1998 to 2002, the average education expenditure in China was:
=4053 (100 million yuan);
(3) Let the average annual growth rate of education funds in 2002-2004 be X,
Then from the meaning of the question, we get 5480( 1+x2)=789 1, and the solution is x ≈ 20%.