Question and answer of the first volume of the ninth grade mathematics practice test on the quadratic equation of one variable.

1, given that the equation x2-6x+q=0 can be expressed as (x-p)2=7, then x2-6x+q=2 can be expressed as follows ().

a 、( x-p)2=5 B 、( x-p)2=9

c 、( x-p+2)2=9 D 、( x-p+2)2=5

2. It is known that m is a root of the equation x2-x- 1=0, then the value of the algebraic expression m2-m is equal to ().

a 、- 1 B、0 C、 1 D、2

3. If α and β are two real roots of the equation x2+2x-2005=0, the value of α2+3α+β is ().

A, 2005b, 203c, 205d, 40 10

4. The equation kx2+3x- 1=0 about x has real roots, so the range of k is ().

A, k≤- B, k≥- and k≠0

C, k≥- D, k >- and k≠0

5. If the two roots of the quadratic equation of x are x 1= 1 and x2=2, then this equation is ().

a、x2+3x-2=0 B、x2-3x+2=0

c、x2-2x+3=0 D、x2+3x+2=0

6. It is known that the equation x2-(2k- 1)x+k2=0 about x has two unequal real roots, so the maximum integer value of k is ().

a 、-2 B 、- 1 C、0 D、 1

At the end of 2004, the green area of a city was 300 hectares. After two years of greening, the green area has increased year by year, reaching 363 hectares by the end of 2006. Let the average annual growth rate of green area be x, and the equation listed in the question is correct ().

a、300( 1+x)=363 B、300( 1+x)2=363

c、300( 1+2x)=363 D、363( 1-x)2=300

8. Two students, A and B, solved the quadratic equation of one variable respectively. Because A misread the coefficient of the first term, two of the equations are -3 and 5, while B misread the constant term, and two are 2+ and 2-, so the original equation is ().

a、x2+4x- 15=0 B、x2-4x+ 15=0

c、x2+4x+ 15=0 D、x2-4x- 15=0

9. If the equation x2+mx+ 1=0 and the equation x2-x-m=0 have the same real root, then the value of m is ().

a、2 B、0 C 、- 1 D、

10. Given that the lengths of both sides of right triangle X and Y satisfy |x2-4|+ =0, the length of the third side is ().

A, 2 or b, or 2

C, or 2 D,, 2 or

Fill in the blanks (3 points for each small question, 30 points for * * *)

1 1. If one root of equation 2x2-3x+c=0 is 1, the other root is.

12 and the solution of the unary quadratic equation x2-3x-2=0 is.

13, if (2a+2b+1) (2a+2b-1) = 63, then the value of a+b is.

In 14 and isosceles △ABC, BC=8, and the lengths of AB and AC are two of the equations x2- 10x+m=0 about X, then the value of m is.

15, the per capita GDP of a city in 2005 is about 1.2 times that of 2003. If the annual per capita GDP growth rate of the city remains unchanged, then the growth rate is.

16. Scientific research shows that when the ratio of the length to the height of a person's lower limbs is 0.6 18, it looks the most beautiful. Adult female height 153cm, lower limb length 92cm. The best height of the high heels worn by this lady is about cm. (accurate to 0. 1cm).

17. The diameter of a well is 2m. Straight into the bottom of the well with a bamboo pole, which is 0.5m higher than the wellhead. If the bamboo pole enters the wellhead obliquely, the depth of the well is m and the length of the bamboo pole is m.

18, the perimeter of a right triangle is 2+, and the median line on the hypotenuse is 1, so the area of this right triangle is.

19. If the equation 3x2-ax+a-3=0 has only one positive root, the value of is.

20. Assuming that the two roots of the equation x2+3x+ 1=0 are α and β, the value of+is.

Iii. Answering questions (***60 points)

2 1, solve the equation (3 points for each small question, *** 12 points)

( 1)(x-5)2 = 16(2)x2-4x+ 1 = 0

(3)x3-2x2-3x=0 (4)x2+5x+3=0

22.(8 points) It is known that x 1 and x2 are two real roots of equation x2+(2a- 1)x+a2=0, and (x1+2) (x2+2) =1.

23.(8 points) Equation X2-2 is known about X (m+ 1) X+M2 = 0.

What is the value of (1) equation?

(2) Choose an appropriate integer for m, so that the equation has two unequal real roots, and find these two roots.

24.(8 points) It is known that the quadratic equation x2-4x+k=0 has two unequal real roots.

(1) Find the range of k.

(2) If k is the largest integer satisfying the condition, and the unary quadratic equation x2-4x+k=0 and x2+mx- 1=0 have the same root, find the value of m at this time.

25.(8 points) It is known that A, B and C are opposite sides of ∠A, ∠B and ∠C in △ABC, and the equation (c-b)x2+2(b-a)x+(a-b)=0 about X has two equal real roots. Just try it.

26.(8 points) An engineering team contracted a demolition project during the renovation of shanty towns in our city. It was originally planned to demolish 1250m2 every day. Due to insufficient preparation, the amount of demolition on the first day was reduced by 20%. From the second day, the construction team accelerated the demolition, and on the third day, 1440m2 was demolished.

Q: (1) The daily demolition area of the construction team on the second and third days is the same as that of the previous day. Find this percentage.

27. (points) A fruit wholesale mall sells a high-grade fruit. Profit per kilogram 10 yuan, you can sell 500 kilograms every day. According to market research, if the price per kilogram increases by 1 yuan, the daily sales will be reduced by 20 kilograms.

(1) At present, shopping malls should ensure a profit of 6,000 yuan per day, and at the same time, let customers get benefits, so how much is the price increase per kilogram?

(2) From a purely economic point of view, how much price increase per kilogram of this fruit will maximize the profit of shopping malls?

Reference answer to unit test questions of quadratic equation in one variable

First, multiple choice questions

1~5 BCBCB 6~ 10 CBDAD

Tip: 3. ∫ α is the root of the equation x2+2x-2005=0, ∴α2+2α=2005.

α+β=-2 ∴α2+3α+β=2005-2=2003.

Second, fill in the blanks

1 1 ~ 15 4 25 or 16 10%

16~20 6.7 , 4 3

Tip: the lengths of 14, ∫AB and AC are two of the equations x2- 10x+m=0 about x.

∴

Isosceles triangle △ABC