Mathematics Weekly Cup "2009 National Junior Middle School Mathematics Competition Examination Questions"
1. Multiple-choice questions (* * 2009 junior high school physics competition 5 questions, 7 points for each question, ***35 points. Each of the following questions is given four options, code-named A, B, C and D, of which one and only one option is correct. Please fill in the code of the correct option in the brackets after the question, and get 0 point)
, which is equal to ().
(A)- 1 (B)0 (C) 1 (D)2
2. As shown in the figure, if the side length of diamond ABCD is a, point O is a point on diagonal AC, OA = A, Ob = OC = OD = 1, then A is equal to ().
1 (D)2
3. If a cube dice with hexagon number 16 is thrown for the second time, the probability that the equations about X and Y have only positive solutions is ().
(A) (B) (C) (D)
4. As shown in figure 1, in the right-angled trapezoidal ABCD, AB‖DC, The moving point P starts from point B and moves from B→C→D→A along the side of the trapezoid. Let point P move as X, and the area of △ABP is Y. If Y is regarded as a function of X, and the image of the function is shown in Figure 2, the area of △ABC is ().
(A) 10(B) 16(C) 18(D)32
5. The integer solution of the equation about x, y (x, Mathematics Weekly Y) has the group number of ().
(A)2 groups (B)3 groups (C)4 groups (d) infinite groups
Fill in the blanks (
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"Mathematics Weekly Cup" 2009 National Junior High School Mathematics Competition Examination Questions (including answers)
..... Professional Committee of Middle School Mathematics Teaching of National Education Association
"Mathematics Weekly Cup" 2009 National Junior Middle School Mathematics Competition Examination Questions
1. Multiple-choice questions (* * 2009 junior high school physics competition 5 questions, 7 points for each question, ***35 points. Each of the following questions is given four options, code-named A, B, C and D, of which one and only one option is correct. Please fill in the code of the correct option in the brackets after the question, and get 0 point)
, which is equal to ().
(A)- 1 (B)0 (C) 1 (D)2
2. As shown in the figure, if the side length of diamond ABCD is a, point O is a point on diagonal AC, OA = A, Ob = OC = OD = 1, then A is equal to ().
1 (D)2
3. If a cube dice with hexagon number 16 is thrown for the second time, the probability that the equations about X and Y have only positive solutions is ().
(A) (B) (C) (D)
4. As shown in figure 1, in the right-angled trapezoidal ABCD, AB‖DC, The moving point P starts from point B and moves from B→C→D→A along the side of the trapezoid. Let point P move as X, and the area of △ABP is Y. If Y is regarded as a function of X, and the image of the function is shown in Figure 2, the area of △ABC is ().
(A) 10(B) 16(C) 18(D)32
5. The integer solution of the equation about x, y (x, Mathematics Weekly Y) has the group number of ().
(A)2 groups (B)3 groups (C)4 groups (d) infinite groups
Fill in the blanks (
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Mathematics Weekly Cup 2009 National Junior High School Mathematics Competition Test Questions and Answers
...... 1 (D)2
Answer a.
Solution: Because of the △ BOC ∽△ ABC junior high school physics competition in 2009, that is,
So ...
Leave, leave.
3. If a cube dice with hexagon number 16 is thrown for the second time, the probability that the equations about X and Y have only positive solutions is ().
(A) (B) (C) (D)
Answer D.
Solution: At that time, the equations had no solution.
At that time, the solution of the equation was
From the known situation, it is possible to obtain or.
Your actual meaning is 1, 2, 3, 4, 5, 6, available.
* * * There are 5× 2 = 10 cases; Or ***3 cases.
The basic events of two dice rolls * * * 6 × 6 = 36 situations, which is required by the English competition in 2009.
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Reference Answer of "Mathematics Weekly Cup" 2008 National Junior Middle School Mathematics Competition
.......... 3. Don't hand in the draft paper.
A, multiple-choice questions (***5 weeks math small report, each small 6 points, out of 30 points. Each of the following questions gives four options, code A, B, C and D, of which one and only one option is correct. Please fill in the code of the correct option in the brackets after the question. Don't fill in, fill in too much or fill in the wrong, 0 points).
If is satisfied, the value of is ().
Article 7 (2) (3) (iv) 5
Answer (a)
Solution: Because ≥0 is derived from known conditions.
, ,
So seven.
Another solution: from the known:, obviously, the root of the quadratic equation is, so
Therefore =
2. Throw a cube dice with six sides numbered 16 respectively, and the probability that the numbered quadratic function with the front facing upwards has two different intersections with the X axis is ().
(a) (b) (c) (d) 6× 6 = 36, meaning 36 = > 0, meaning > 4.
According to the enumeration, there are 17 pairs that meet the requirements.
3. There are two concentric circles, four different points on the big circle and two different points on the small circle. The answer of Mathematics Weekly is that these six points can at least determine different straight lines ().
Article 6
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