1. Multiple choice questions: (2 points for each small question, * * * 20 points)
1. The following equations are not necessarily quadratic equations ().
A.(a-3)x2=8(a≠0) B.ax2+bx+c=0
C.(x+3)(x-2)=x+5 D。
2. It is known that the unary quadratic equation ax2+c=0(a≠0). If the equation has a solution, there must be C = ().
A.-B.-1C.D. Not sure.
3. If the equation ax2+2(a-b)x+(b-a)=0 about x has two equal real roots, then A: B is equal to ().
A.- 1 or 2b. 1 or c .- or 1 d.-2 or 1.
4. If the unary quadratic equation ky2-4y-3=3y+4 about y has real roots, then the range of k is ().
A.k & gt-b. k ≥- and k ≠ 0 c.k ≥-d.k > and k ≠ 0.
5. If the two roots of the equation are known as a, the root of the equation is ().
A.B. C. D。
6. Equation x2+2(k+2)x+k2=0 Regarding X, if the sum of two real roots is greater than -4, then the value range of K is ().
A.k & gt- 1 b . k & lt； 0 degrees celsius-1< k & lt0d .- 1≤k & lt； 0
7. If the two real roots of the equation x2-kx+6=0 are respectively greater than the two real roots of the equation x2+kx+6=0 by 5, then the value of k is ().
5 BC
8. X that makes the score equal to zero is ()
A.6 b.- 1 or 6 c.- 1 d.-6
9. The solution of equation x2-4│x│+3=0 is ().
A.x = 1 or x = 3b.x = 1 and x = 3c.x =- 1 or x =-3d. There is no real root.
10. If the equations x2-k2- 16=0 and x2-3k+ 12=0 about x have the same real root, then the value of k is ().
A.-7b-7 or 4c-4d. 4
Fill in the blanks: (3 points for each small question, * * * 30 points)
1 1. As we all know, 3- is a root of the equation x2+mx+7=0, so m = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
12. given the equation 3ax2-bx- 1=0, ax2+2bx-5=0, and there are * * * same roots-1, then a = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
13. If the unary quadratic equation ax2+bx+c=0(a≠0) has the root of 1, then A+B A+B+C = _ _ _ _ _ _ _ _ _ _ _ _； If the root of A is-1, the relationship between B and A and C is _ _ _ _ _ _ _ _ _; If a root is zero, then c = _ _ _ _ _ _ _ _ _
14. If two of the equations 2x2-8x+7=0 are exactly the lengths of two right-angled sides of a right-angled triangle, then the length of the hypotenuse of this right-angled triangle is _ _ _ _ _ _ _.
15. The sum of all the real roots of the unary quadratic equation x2-3x- 1=0 and x2-x+3=0 is equal to _ _ _ _ _ _ _ _.
16. After two consecutive price increases 10%, the price of a food is one yuan, so the original price is _ _ _ _ _ _ _ _ _ _.
17. It is known that the product of two numbers is 12, the sum of the squares of these two numbers is 25, and the quadratic equation of one yuan based on these two numbers is _ _ _ _ _ _ _ _.
18. If the equation x2-2( 1-k)+k2=0 about x has real roots α, β, then the value range of α+β is _ _ _ _ _.
19. Let A be the sum of absolute values of all roots of the equation x2- x-520=0, then A2 = _ _ _ _ _ _ _
20. Cut a square with a side length of 5cm on each corner of the rectangular iron sheet, and then fold it into a box without a cover. The length of the iron sheet is twice the width, and the volume of the box is 1.5 cubic decimeter, so the length of the iron sheet is equal to _ _ _ _ _ _ _ _ _ _ _.
Three. Answer: (7 points for each question, ***2 1 point)
2 1. Let x 1, x2 is the two real roots of the equation x2-(k+2)x+2k+ 1=0, and x? 12+x22= 1 1。
(1) Find the value of k; (2) Using the relationship between roots and coefficients, the quadratic equation of one variable is solved, so that one root is the sum of two roots of the original equation and the other root is the square of two differences of the original equation.
22. Let A, B and C be three sides of △ABC, the equation x2+2 x+2c-a=0 about X has two equal real roots, and the root of equation 3cx+2b=2a is 0.
(1) Verification: △ABC is an equilateral triangle;
(2) If A and B are two roots of the equation x2+mx-3m=0, find the value of m. 。
23. As shown in the figure, it is known that in △ABC, ∠ ACB = 90, the point C is CD⊥AB, the vertical foot is D, AD=m, BD= n, AC2: BC2 = 2: 1, and the equation X2-2 of X (n-65438.
Fourth, self-made questions: (9 points)
24. Xiao Li and Xiao Zhang each processed 15 toys, and Xiao Li processed 1 toys more than Xiao Zhang per hour, resulting in fewer hours to complete the task than Xiao Zhang. How many toys can each of them process per hour?
Requirements: First, according to the meaning of the question, set appropriate unknowns to list equations or equations (no need to solve), and then according to your equations or equations, work out an application problem of trip problem, so that the equations or equations listed by you are exactly the equations or equations of your trip application problem, and solve the trip problem.
5. Solving application problems with equations: (65438+ 00 points for each small question, ***20 points)
25. In order to strengthen the macro management of cigarette production and sales, the state implements the policy of additional tax on cigarette sales. Now we know that the market price of a certain brand of cigarettes is 70 yuan. If there is no tax increase, we will produce and sell 1 10,000 cigarettes a year. If the state levies additional tax, it will levy X yuan (called tax rate x%) for every 654.38+000 yuan sold. Then the annual production and sales will be reduced by10x00. If the additional tax levied on this business is 6.5438+0.68 million yuan, and the production and sales of cigarettes are under macro control, and the annual production and sales volume does not exceed 500,000 cigarettes, how to determine the tax rate?
26. It is known that the rated power of a small light bulb is 1.8W, and the rated voltage is less than 8V.. A resistor of 30 is connected in parallel in the circuit, the main circuit current is 0.5A, and the light bulb emits light normally. Find the rated voltage of small light bulb.
Reference answer
1. 1.b dial: ax2+bx+c=0. Only when a≠0 is satisfied is it a quadratic equation.
2.d nudge: If the unary quadratic equation ax2+c=0(a≠0) has a solution, then ax2=-c, x2=, because x2≥0,
There are several solutions, so it is uncertain.
3.b nudge: According to the discriminant of the roots of a quadratic equation, the equation has two equal real roots.
Delta = 0, delta = [2 (a-b)] 2-4× a (b-a) = 4 (a-b) (2a-b), that is, 4(a-b)(2a-b)=0,
∴a=b or a=,
Namely a: b = 1 or a: b = 1: 2.
4.b nudge: k≠0 From the definition of a quadratic equation with one variable, it can be known that the equation has a real root and from the discriminant of the root of the quadratic equation with one variable.
Then △≥0, that is, k≥, so k≥ and k≠0, this problem is easy to miss two conditions: k≠0 and△ = 0.
5.d inching: from, to can be changed to, so its solution is x- 1=a- 1, that is, x=a or x- 1=, that is, X =. This question can easily be misunderstood as x=a or X =.
6. D. Hugging: The equation has two real roots, so △≥0, that is, [2(k+2)]2-4k2≥0, the solution is k≥- 1, and the sum of the two real roots is greater than -4, that is, -2(k+2)>-4, k &
∴- 1≤k<； 0. This problem is easy to ignore that there are two real roots, which need to meet the important condition of △≥0.
7. D. Guidance: Let two of x2-kx+b=0 be x 1, x2, then two of x2+kx+6=0 are x 1+5, x2+5, because x 1+x2=k, (x/.
8. inching: the condition that the score is zero: numerator =0, denominator ≠0, x2-5x-6=0, x=6 or-1, x+ 1, x≦- 1, so x.
9. A cue: ∵x2≥0, │x│0, ∴x2-4│x│+3=0 is the solution of the equation │x│2-4│x│+3=0, (│ x │-65433).
10.d nudge: if two equations have the same real root, then x2+k2-16 = x2-3k+12, and the solution is k=-7 or 4.
When k=- 7, the equation has no real root, ∴ k = 4.
Second,
1 1.m =-6 and the other is 3+.
Pointing: according to the relationship between the root and coefficient of a quadratic equation, let the other root of the equation be x 1,
Then (3- )x 1=7, x 1=3+, (3+ )+(3- )=-m, then m =-6.
12.a= 1，B =-2。 Cuddle:-1 is the root of two equations, then 3A+b=-2. 1 = 0, a-2b-5=0, the solution is A = 1, and B =-.
13.a+b+c=0，b=a+c，c=0。
14.3 inching: let two roots be x 1, x2, and according to the relationship between roots and coefficients, x 1+x2=4, x 1? x2=，
According to Pythagorean Theorem, the square of the hypotenuse length = (x1+x2) 2-2x1x2 =16-2x9, and the hypotenuse length is 3.
15.3 inching: x2-3x-1= 0 △ =13 > δ is 0, x2-x+3 = 0 =-11; 50, does not meet the meaning of the question, was omitted. When x 1=6, 100- 10× 6 = 40.
The tax rate should be set at 6%.
Hugging: This is a practical question about real life knowledge, and it is an important kind of examination questions in recent years. We should really understand and master it.
26. solution: let the rated voltage of the small lamp gun be u, according to the meaning of the question:
, and the solution is U 1=6, U2=9 (left).
The rated voltage is less than 8V, ∴ u = 6.
A: The rated voltage of the small bulb is 6V.
Hugging: This is a comprehensive problem of physics and mathematics. The key to solve this problem is to memorize physical formulas and solve fractional equations that can be transformed into quadratic equations with one variable. Testing is an easily overlooked point in this problem.
Take mine. I don't appreciate it.