Junior high school mathematics competition test questions

1. Multiple-choice questions (8 questions in this question, 6 points for each question, out of 48 points): Only one of the options given in the following questions is correct. Please fill in the code of the correct option in the brackets after the question.

1. It is known that the function y = x2+1–x, and the point P(x, y) is on the image of this function. Then, the point P(x, y) should be on the rectangular coordinate plane ().

(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

2. There are m red balls, 10 white balls and n black balls in a box, and each ball is the same except the color. If you choose a ball from them, the probability of getting a white ball is the same as the probability of not getting a white ball, then the relationship between m and n is ().

(A)m+n = 10(B)m+n = 5(C)m = n = 10(D)m = 2，n = 3

3. Our province stipulates that a junior high school math contest will be held on the last Sunday of June every year 1 1, and the date of next year's junior high school math contest is ().

(a)165438+1October 26th (b)165438+/October 27th (c)165438+1October 29th.

4. There are two points A (–2,2), B (3 3,2) and C in the plane rectangular coordinate system. If △ABC is a right triangle, then the point C that meets the conditions is ().

1 (B)2 (C)4 (D)6。

5. As shown in the figure, there are points E and F on the sides BC and CA of the regular triangle ABC, which satisfy the following requirements.

BE = CF = a，EC = FA = b(a & gt； b)。 When BF divides AE equally, the value of ab is ().

(A)5– 12(B)5–22(C)5+ 12(D)5+22

6. A company ordered 22 lunches in a fast food restaurant, which cost 140 yuan. There are three kinds of lunches: A, B and C, and the unit prices are 8 yuan, 5 yuan and 3 yuan respectively. Then the possible different sorting schemes are ().

1 (B)2 (C)3 (D)4。

7. As we all know, a > 0, b>0 and a (a+4b) = 3b (a+2b). Then the value of a+6ab–8b2a–3ab+2b is ().

(A) 1(B)2(C) 19 1 1(D)2

8. As shown in the figure, in trapezoidal ABCD, ∠ d = 90, and m is the midpoint of AB, if

CM = 6.5, BC+CD+DA = 17, then the area of trapezoidal ABCD is ().

20 (B)30 (C)40 (D)50

Fill in the blanks (4 small questions in this question, 8 points for each small question, out of 32 points): Answer the question.

Fill in directly on the horizontal line of the corresponding topic.

9. As shown in the figure, in the rhombic ABCD, ∠ A = 100, m and n are AB and BC respectively.

If MP⊥CD is at p, then the degree of ∠NPC is.

10. if the real number a satisfies a3+a2–3a+2 = 3a–1a2–1a3,

Then a+ 1A =

1 1. As shown in the figure, in △ABC, ∠ BAC = 45, AD⊥BC in D, if BD = 3, CD.

= 2, then S⊿ABC =

12. The linear function y =–33x+1intersects the X axis and the Y axis respectively.

Points A and B form a square ABCD (e.g.

Figure). There is a point P(a, 12) in the second quadrant, which satisfies the square ABCD of s △ ABP = S.

Then a =

Third, answer the question (this question ***3 small questions, 20 points for each small question, out of 60 points)

13, as shown in the figure, points Al, Bl, C 1 are respectively on the sides of AB, BC and CA of △ABC.

And aa1ab = bb1BC = cc1ca = k (k

The perimeter of is p 1. Verification: p 1

14. There are several students living in a dormitory of a school, one of whom is the head of the dormitory. On New Year's Day, each student in the dormitory gave each other a card, and each dormitory administrator also gave the person in charge of the dormitory a card, so * * * used 5 1 card. Ask how many students live in this dormitory.

15. if a 1, a2, …, an are all positive integers, and A 1

Reference answer:

I baddc cbb ii . 9.50 10.2 or–3 1 1. 15 12.32–8。

Three. 13. Omit 14. 6 students 15. Omit.