Mathematics final examination paper of the ninth grade last semester

A, multiple-choice questions (this big question * * has 10 small questions, each small question 4 points, * * * 40 points. There is only one correct option for each small question. Please fill in the letter code of the correct option in brackets after the question.

2. If the square root is meaningful in the range of real numbers, the value range of is ().

(A) (B) (C) (D)

3. The following statement is true ()

A.？ Turn on the TV, the news broadcast is playing? Is an inevitable event;

B. The probability of winning the lottery is, that is to say, every time you buy 100 lottery tickets, you will win a prize;

C. If you want to know the per capita annual income level of urban residents in Taizhou, you should take a sample survey.

D. It will definitely snow in our city in the next three days;

4. If is, the value of is equal to ()

ABC or 2d 0 or

5. As shown in the figure, put the triangular ruler ABC (where? ABC=60？ ,? C=90？ ) around point B.

Rotate an angle clockwise to the position of A 1BC 1, so that points a, b and C 1 are in the position of.

On the same straight line, then this angle is equal to ().

A. 120？ B.90？

C.60？ D.30？

6. Change the equation into the form of, then the values are () respectively.

(a) and (b) and (c) and (d) and

As shown in the figure, in ⊙O, ABDC is a quadrilateral inscribed with a circle. BOC= 1 10？ And then what? The degree of BDC is ()

A. 1 10？ B.70？ C.55？ D. 125？

8. As shown in the figure, if a sector of the circumference is cut off from a circular paper with a radius of 9cm, and the remaining sectors form a cone (joints do not overlap), then the height of this cone is ().

A. 6 cm b.cm c. 8 cm d.cm

9. At the same time, two cubic dice with uniform texture are thrown, and the six sides of the dice are engraved with points, so the probability of the sum of the points on the upward side of the two dice is ()

(A) (B)

(C) (D)

10. As shown in the figure, * * has 12 small squares with the same size, among which the five small squares in the shaded part are

Part of the surface development diagram of a cube is now drawn from any other small square.

On the shadow, the probability of forming the plane expansion diagram of this cube is

A.B. C. D。

Scoring reviewer

Fill in the blanks (there are 8 small questions in this big question, with 4 points for each small question and * * 32 points. Please fill in the answer on the horizontal line of the question. )

1 1. Then, the equation about has two equal real roots.

12. When a _ _ _ _ _ _ the quadratic radical is meaningful in the real number range.

14. As shown in the figure, in the concentric circle ⊙O, AB is the diameter of the big circle, AC is the chord of the big circle, and AC is tangent to the small circle at point D. If the radius of the small circle is 3cm, BC= cm.

15. In the unary quadratic equation, if, and satisfy the relationship, the equation must have a root value.

16. There are 1 red balls, 2 white balls and 3 black balls in the bag. They are exactly the same except for the color. The probability that a ball is white when it is taken out of the bag is.

17. If two circles are tangent, the center distance is, the radius of one circle is, and the radius of the other circle is _ _ _ _.

18. Suppose A, B and C are three sides of a triangle, then

= 。

Third, the solution: this big question ***8 small questions, out of 78 points, should write the necessary calculation process, reasoning steps or text instructions when answering the question.

Scoring reviewer

19, 6 points for each small question, out of 12 points.

(1) Solve the equation:

20, this question is full of 8 points.

Known: the equation about x

⑴ Verification: The equation has two unequal real roots;

(2) If one root of the equation is-1, find the other root and k value.

Scoring reviewer

2 1, this little question is 8 points.

As shown in the figure, the inscribed circle ⊙O of △ABC is tangent to points D, E, F, AB=9cm, BC= 14cm, CA= 13 cm, and the lengths of AF, BD and CE are found.

23. (This little question is 10)

With people's pursuit of material life, coupled with the shortage of resources and rising prices of raw materials, house prices are rising. After two consecutive price increases, the price of a house in a certain place changed from per square meter 1600 yuan to 3,600 yuan per square meter. What is the average percentage of each price increase?

Scoring reviewer

24. This small problem is 10.

In order to study the image of inverse proportional function, Xiaoming takes any number in -2,-1 and 1 as the abscissa and any number in -2,-1 and 2 as the ordinate to form the coordinates of point P.

(1) Find the number of all possible results of the point P coordinate. (Solve with a list or draw a tree diagram)

(2) Find the probability of the upper P point. Inverse proportional function image.

25, this small problem 10 points.

As shown in the figure, it is known as diameter ⊙, midpoint ⊙, and.

Proof: it is the tangent of ⊙.

26. This little problem is 12.

According to the regulations of a school, the electricity consumption of each teacher in the school can't exceed A degrees per month, so only 10 yuan is required this month. If it exceeds a degree, you still need to pay 10 yuan this month, and the excess will be paid in kWh.

(1) Mr. Hu 65438+90 degrees of electricity consumption in February, exceeding the prescribed A degree. How much should he pay for the excess? (represented by algebraic expression with a)

(2) The following are the electricity consumption and payment of teachers in 10 and 1 1 two months:

Monthly electricity consumption (kWh) Total electricity charge (Yuan)

65438+ October 45th 10

165438+1October 80, 25

According to the data in the above table, find a value and calculate how much electricity the teacher should pay in June+February of 5438.

Grade 9 (1) Reference Answers to Mathematics Test Questions

First, multiple-choice questions (40 points) DACDA CDBBA( 1? 10 question)

Two. Fill in the blanks (32 points)

Third, answer questions.

19, 6 points for each small question, out of 12 points.

Solution: (1) Factorization: 2 points.

So: 4 points

So: 6 points

(2) Solution: the original formula = 3 points.

6 points

20. solution: (1) 2x2+KX- 1 = 0,

, 1 min

No matter what the value of k is, k2? 0, so, that is,

? This equation has two unequal real roots. Three points

(2) Yes, the root,

? 5 points

Solving equation 7 points

? The other root of is that the value of k is 1. Eight points.

22.(8 points)

Solution: (1) A (0,4), C(3, 1) 2 points.

(2) 4 points

(3) 6 points

Route length from point a to point A':

Arc for 8 minutes

23, (10)

Solution: let the average percentage of each price reduction be x 2 points.

According to the meaning of the question: 5 points

Solve this equation and you will get: (it doesn't meet the meaning of the question, so it is removed), 8 points.

A: The average percentage rate of each price increase is 50% 10 point.

24, (10)

Solution: (1)

6 points

The number of all possible outcomes is 9.7.

(2)P (on the image) = 10.

25, (10)

Prove:

Connecting outside diameter, 2 points

∫ is the diameter of ⊙.

? O is the midpoint of point AB 4.

D is the midpoint of BC

? OD∑AC 6 point

∵ Germany? Alternating current

? OD？ De 8 fen

∵OD is the radius of⊙ o.

? DE is the tangent of point ⊙O 10.

26, (12 points)

(1) 3 points

(2), finishing A2-80a+ 1500 = 0.5.

The solution is A 1=50, A2=30, 7 minutes.

From the electricity bill paid in June of 10, we can know that a? 45, 8 points

? A=50, 9 points

65438+electricity payable in February 1 1.

Answer: 30 yuan should pay the electricity bill in February. 12 point

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