It's a few good questions, and this set of papers is not bad either. I hope it will help you, and I wish you better study!
In 2004, the first group of examination papers in the competition of mathematical thinking training class in Shangcheng District (seven years)
test paper
(Full score: 120, time: 120 minutes)
1. Please choose the only correct result set in each question: (There are 6 small questions in this question, with 5 points for each small question and ***30 points)
1. Calculation: (-4) 2003 (-0.25) 2004 =
2. When both X and Y are prime numbers, the solution of equation 2x+y =2004 is as follows.
(a) No solution (b) Only one set of solutions (c) Only three sets of solutions (d) At least five sets of solutions.
3. As shown in the figure, the lengths of line segments AD, AB, BC and EF are 1, 3,2, 1 respectively. If the area of the closed polyline AEBCFD is s, which of the following four is (A) S ≈ 7.5? (B) S ≈ 5。 2 (C) 5。 4 & ltS & lt6 .4 ? 6.4 & ltS & lt7 .2
As shown in the picture, this is an ornament consisting of three cubes with different sizes.
Now draw its surface. Suppose the side lengths of three cubes are different.
Is a, b, c, where a
When the decoration is placed horizontally on the table, it is invisible from the appearance.
Any nudity of decorative texture) is
(A) 5(a2+b2+c2) (B) 5a2+4b2+5c2
(C) 5a2+4b2+4c2。 4a2+4b2+5c2
As shown in the figure, ABCD is a rectangle with vertices.
And draw a rectangle AHIJ through d, so that h falls on BC; and
Draw a square BEFG, make EF pass by, and G is above if = 10.8㎝= 10㎝━.
2. Fill in the required contents: (This question has 6 small questions, with 5 points for each small question and ***30 points)
7. If the sum of a and its absolute value is zero, then = ▲;
8. Cut the surface of the cube along some edges and spread it into a plane figure (no piece falls off), then the edge to be cut should be ▲.
At 9.2: 20, the included angle (acute angle) between the hour hand and the minute hand is ▲ degrees.
10. As shown in the figure, we call a triangle whose vertex is at the vertex of such a small square a triangle.
Grid triangle. (1) Please draw two examples on the far right and the far left.
Checked triangles with different shapes; (2) Can you sum up how many digits a * * * can draw in this picture?
Can I set different (same shape) lattice triangles? A: There is always * * ▲.
1 1. At 0 o'clock.
12. A factory implements hourly wage system, and every worker works 1 hour to reward 6 yuan, working 8 hours a day. However, the clock used for timing is not allowed: the minute hand and the hour hand coincide only once every 69 minutes, so the factory pays less to each worker every day.
3. Express your answer to the question in written language: (There are 5 small questions in this question, each with 12 score ***60 score)
13. Write a multiple of 3 at will, cube and add the numbers separately, and then cube and add each of the newly obtained numbers separately to get a new number, which is repeated all the time ... You find that "24 points" is calculated by four numbers "-6, -0.5, 2, 3".
Terms:
(1) Every number must be used;
(2) Each number can only be used once (including exponential use, for example, 2 and 3 are used for 23);
(3) The absolute value is considered infinite;
(4) Two formulas that conform to "exchange law" and "combination law" are considered as the same formula;
(5) If you still know "negative exponent" and "square root", then you can use it;
(6) In order to cooperate with the teacher in marking papers, you should carefully write calculus steps;
(7) Every time you write a formula correctly, you get 3 points, and the score of this question can exceed 12, but the total score of the whole volume does not exceed 120.
In 2004, the first group of examination papers in the competition of mathematical thinking training class in Shangcheng District.
answer sheet
(Full score: 120, time: 120 minutes)
First, multiple-choice questions (this question has 6 small questions, each with 5 points and ***30 points)
Fill in the blanks (6 small questions in this question, 5 points for each small question, 30 points for * * *)
7.； 8.； 9.；
10.
( 1)
(2) ;
1 1. 12.
Third, answer the question (this question is 5 small questions, ***60 points)
13.( 12 points)
14.( 12 points)
15.( 12 points)
16.( 12 points)
17.( 12 points)
In 2004, the first group of examination papers in the competition of mathematical thinking training class in Shangcheng District.
Reference solution and grading standard
First, multiple-choice questions (5 points for each small question, 30 points for * * *)
1 .C
2.A
Only y=2, then x+ 1 = 1002, that is, x =1001=1,but this is not a prime number.
3.C
S is less than 2, and the area with a length of 3 .6 is larger than the area with a width of 1. 5. The area with a length of 3 .6 is wider than the area with a length of 3 .6.
Two small squares (2a2), two middle squares (2b2) and 1 large squares (c2) can be subtracted from the square surface of three cubes.
5.B
S quadrilateral AHIJ= S quadrilateral ABCD =S square BEFG= 102= 100, that is AJ IJ (10.8) = 100, AJ=9.26cm.
6.B
Fill in the blanks (5 points for each small question, 30 points for * * *)
7.3a
Article 8.7;
9.50 (
Minute hand: walk for 20 minutes120 (;
Clockhand: rotation angle is minute hand, that is, rotation10 (;
Then, ∠ DOC=20 (,and ∠B OC= 3 0 (.
10.( 1), draw a right one for 1 minute, (**2 points).
(2).76 (3 points)
1 1. 1
At that time, 2≤a≤3 scored the highest. So, the workers earned a day.
International working hours are (hours), exceeding (hours).
Pay less.
Iii. Answering questions (***60 points)
1 3( 12 points).
(1) take number 3: cube and add each number separately, then cube and add each new number, and then cube and add each new number. Take one year 12 months as 12 drawer, (3 points)
Think of 25 students as 25 apples, (3 points)
Students with birthdays in the same month can be regarded as apples in the same drawer, because 25 = 12× 2+ 1, (3 points).
According to pigeonhole principle II, there are three apples in at least one drawer, which means there must be three people whose birthdays are in the same month. (3 points)
15.( 12 points)
( 1) 16
(2)3n+ 1 (4 points)
(3) If 2004 sheets are divisible, 3n+ 1=2004, 3n=2003, and n has no integer solution, so it is impossible to get 2004 sheets by divisibility several times. (4 points)
16.( 12 points)
( 1)Draw( 1)(-6+2)×3÷(-0.5)；
(2) 23 × ( - 6) × ( - 0.5) ;
(3) 2( - 6) × ( - 0.5) × 3 ;
(4)│ - 6│ × (│ - 0.5│ × 2+3) ;
(5)│( - 6)2 ÷ 3 ÷ ( - 0.5)│ ;
(6)│( - 6) +3 ÷ ( - 0.5)│ × 2 ;
(7) ( - 6) ÷ ( - 0.5)3 ÷ 2 ;
(8)│32 ÷ ( - 0.5)│ - ( - 6) ;
(9) ,
Give 3 points for each correct article, the score of this question can exceed 12, but the total score of the whole article does not exceed 120.
Page 7 (***3) of the examination paper of junior one competition.
(Question 6)
(Question 3)
F
E
D
C
B
A
A
Question 9
B
B
A
Question 9
C
A
(Question 4)
Scoring reviewer
QuestionNo. 1 234 56 Answer
Total score of question 1231~ 67 ~121314151617.
C
Question 20
C
D
B
A
F
E
Map number 13
D
C
B
A
A
C
D
B
O
six
three
nine
12
Question 16
C
D
J
I
H
(Question 5)
G
F
E
D
C
B
A
(A) -4 (B) -2004 (C) -0.25 (D)
B
Scoring reviewer
A
B
D
C
Question 16
As shown in the figure, ABCD is a rectangle with vertices.
And draw a rectangle AHIJ through d, so that h falls on BC; and
Draw a square BEFG, make EF pass by, and G is above if = 10.8㎝= 10㎝━.
2. Fill in the required contents: (This question has 6 small questions, with 5 points for each small question and ***30 points)
7. If the sum of a and its absolute value is zero, then = ▲;
8. Cut the surface of the cube along some edges and spread it into a plane figure (no piece falls off), then the edge to be cut should be ▲.
At 9.2: 20, the included angle (acute angle) between the hour hand and the minute hand is ▲ degrees.
10. As shown in the figure, we call a triangle whose vertex is at the vertex of such a small square a triangle.
Grid triangle. (1) Please draw two examples on the far right and the far left.
Checked triangles with different shapes; (2) Can you sum up how many digits a * * * can draw in this picture?
Can I set different (same shape) lattice triangles? A: There is always * * ▲.
1 1. At 0 o'clock.
12. A factory implements hourly wage system, and every worker works 1 hour to reward 6 yuan, working 8 hours a day. However, the clock used for timing is not allowed: the minute hand and the hour hand coincide only once every 69 minutes, so the factory pays less to each worker every day.
3. Express your answer to the question in written language: (There are 5 small questions in this question, each with 12 score ***60 score)
13. Write a multiple of 3 at will, cube and add the numbers separately, and then cube and add each of the newly obtained numbers separately to get a new number, which is repeated all the time ... You find that "24 points" is calculated by four numbers "-6, -0.5, 2, 3".
Terms:
(1) Every number must be used;
(2) Each number can only be used once (including exponential use, for example, 2 and 3 are used for 23);
(3) The absolute value is considered infinite;
(4) Two formulas that conform to "exchange law" and "combination law" are considered as the same formula;
(5) If you still know "negative exponent" and "square root", then you can use it;
(6) In order to cooperate with the teacher in marking papers, you should carefully write calculus steps;
(7) Every time you write a formula correctly, you get 3 points, and the score of this question can exceed 12, but the total score of the whole volume does not exceed 120.
In 2004, the first group of examination papers in the competition of mathematical thinking training class in Shangcheng District.
answer sheet
(Full score: 120, time: 120 minutes)
First, multiple-choice questions (this question has 6 small questions, each with 5 points and ***30 points)
Fill in the blanks (6 small questions in this question, 5 points for each small question, 30 points for * * *)
7.； 8.； 9.；
10.
( 1)
(2) ;
1 1. 12.
Third, answer the question (this question is 5 small questions, ***60 points)
13.( 12 points)
14.( 12 points)
15.( 12 points)
16.( 12 points)
17.( 12 points)
In 2004, the first group of examination papers in the competition of mathematical thinking training class in Shangcheng District.
Reference solution and grading standard
First, multiple-choice questions (5 points for each small question, 30 points for * * *)
1 .C
2.A
Only y=2, then x+ 1 = 1002, that is, x =1001=1,but this is not a prime number.
3.C
If s is less than 2, the area with the length of 3 .6 is larger than the area with the width of 1. 5. The area with a length of 3 .6 is 3 .6.
Two small squares (2a2), two middle squares (2b2) and 1 large squares (c2) can be subtracted from the square surface of three cubes.
5.B
S quadrilateral AHIJ= S quadrilateral ABCD =S square BEFG= 102= 100, that is AJ IJ (10.8) = 100, AJ=9.26cm.
6.B
Fill in the blanks (5 points for each small question, 30 points for * * *)
7.3a
Article 8.7;
9.50 (
Minute hand: walk for 20 minutes120 (;
Clockhand: rotation angle is minute hand, that is, rotation10 (;
Then, ∠ DOC=20 (,and ∠B OC= 3 0 (.
10.( 1), draw a right one for 1 minute, (**2 points).
(2).76 (3 points)
1 1. 1
At that time, 2≤a≤3 scored the highest. So, the workers earned a day.
International working hours are (hours), exceeding (hours).
Pay less.
Iii. Answering questions (***60 points)
1 3( 12 points).
(1) take number 3: cube and add each number separately, then cube and add each new number, and then cube and add each new number. Take one year 12 months as 12 drawer, (3 points)
Think of 25 students as 25 apples, (3 points)
Students with birthdays in the same month can be regarded as apples in the same drawer, because 25 = 12× 2+ 1, (3 points).
According to pigeonhole principle II, there are three apples in at least one drawer, which means there must be three people whose birthdays are in the same month. (3 points)
15.( 12 points)
(1) 16 (4 points)
(2)3n+ 1 (4 points)
(3) If 2004 sheets are divisible, 3n+ 1=2004, 3n=2003, and n has no integer solution, so it is impossible to get 2004 sheets by divisibility several times. (4 points)
16.( 12 points)
( 1)Draw( 1)(-6+2)×3÷(-0.5)；
(2) 23 × ( - 6) × ( - 0.5) ;
(3) 2( - 6) × ( - 0.5) × 3 ;
(4)│ - 6│ × (│ - 0.5│ × 2+3) ;
(5)│( - 6)2 ÷ 3 ÷ ( - 0.5)│ ;
(6)│( - 6) +3 ÷ ( - 0.5)│ × 2 ;
(7) ( - 6) ÷ ( - 0.5)3 ÷ 2 ;
(8)│32 ÷ ( - 0.5)│ - ( - 6) ;
(9) ,
Give 3 points for each correct article, the score of this question can exceed 12, but the total score of the whole article does not exceed 120.
Page 7 (***3) of the examination paper of junior one competition.
(Question 6)
(Question 3)
F
E
D
C
B
A
A
Question 9
B
B
A
Question 9
C
A
(Question 4)
Scoring reviewer
QuestionNo. 1 234 56 Answer
Total score of question 1231~ 67 ~121314151617.
C
Question 20
C
D
B
A
F
E
Map number 13
D
C
B
A
A
C
D
B
O
six
three
nine
12
Question 16
C
D
J
I
H
(Question 5)
G
F
E
D
C
B
A
(A) -4 (B) -2004 (C) -0.25 (D)
B
Scoring reviewer
A
B
D
C
Question 16