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Hope cup first junior high school first grade first test questions
First, multiple-choice questions (each question 1 point, * * *1point)
1. If both A and B represent rational numbers and A+B = 0, then ()
A.a and b are both 0.b.a, and one of b is 0. C.A. and B are opposites, and D.A. and B are reciprocal.
2. The following statement is true ()
A. single item and the sum of single items are single items. B. the sum of a single term and a single term is a polynomial.
C. the sum of polynomials is polynomials. D. the sum of algebraic expression and algebraic expression is algebraic expression.
3. The following statement is incorrect ()
A. there is the smallest natural number. B. there is no minimum positive rational number.
C. there is no largest negative integer. D. there is no maximum non-negative number.
4. If A and B represent rational numbers, and the value of a+b is greater than that of a-b, then ().
A. a. b with the same number. B.a., b with different numbers. c.a > 0.d.b > 0。
5. An integer greater than-π and not a natural number is ()
A.2.B.3.C.4.D is numerous.
6. There are four kinds of statements:
A. the square of a positive number is not necessarily greater than itself; The cube of b positive number is not necessarily greater than itself;
C. the square of a negative number is not necessarily greater than itself; D. the cube of a negative number is not necessarily greater than itself.
Among these four statements, the incorrect statement is ()
A.0.b. 1.c.2.d.3
7.A stands for rational number, so the relationship between A and -A is ().
A greater than -a b less than -a c greater than -a or A less than -a d a is not necessarily greater than -a.
8. In the process of solving the equation, in order to make the obtained equation and the original equation have the same solution, you can add () on both sides of the original equation.
A. multiply by the same number. B. Multiply the same algebraic expression. C. add the same algebraic expression. D. add 1.
9. There was more than half a glass of water in the cup, which decreased by 10% on the second day and increased by 10% on the third day. So, the comparison result between the water in the cup on the third day and the first day is ().
A. as much as B.
10. This ship goes back and forth between two docks of a river. If the speed of the ship itself in still water is fixed, then when the flow speed of the river increases, the time it takes for the ship to make a round trip will be ().
A. increase. B. reduce. C. unchanged. D. increase and decrease are possible.
II. Fill in the blanks (each question 1 point, * * *1point)
1.______.
2. 1989 19902- 1989 19892=______.
3.=________.
4. The solution of the equation about X is _ _ _ _ _ _ _.
5. 1-2+3-4+5-6+7-8+…+4999-5000=______.
6. When x=-, the value of algebraic expression (3x3-5x2+6x-1)-(x3-2x2+x-2)+(-2x3+3x2+1) is _ _.
7. When a =-0.2 and b=0.04, the value of algebraic expression is _ _ _ _ _.
8. There is 60 kilograms of salt water with 30% salt, which is evaporated on the scale. When salt water becomes 40% salt, the weight of salt water is _ _ _ _ _ grams.
9. A batch of parts can be manufactured in 0/8 days as planned. If the work efficiency is improved after 4 days, it will take _ _ _ _ _ days to complete half of this batch of parts.
10. It's 4: 05 now, and in _ _ _ minutes, the minute hand and the hour hand will coincide for the first time.
Answers and tips
First, multiple choice questions
1.C 2。 D 3。 C 4 explosive D 5。 C 6。 B 7。 D 8。 D 9。 C 10。 A
Tip:
1. Let a=2, B =-2, and satisfy 2+(-2) = 0, thus
2.x2, 2x2 and x3 are all monomials. The sum of two monomials x3 and x2 is x3+x2 is a polynomial, excluding A. The sum of two monomials x2 and 2x2 is x3-x2 is a monomial, excluding B. The sum of two polynomials x3+x2 and x3-x2 is 2x3 is a monomial, so we choose D. 。
3. 1 is the smallest natural number, and A is correct. You can find the positive side.
Therefore, the statement that C "has no maximum negative integer" is incorrect. Write the expanded natural sequence, 0, 1, 2, 3, …, n, …, and it is easy to know that there is no largest non-negative integer and d is correct. Therefore, the incorrect statement should be C.
5. On the number axis, it is easy to see that there are only four integers -3, -2,-1, 0 * * * to the right of-π and to the left of 0 (including 0). Choose C.
6. From 12= 1, 13= 1, we know that A and B are correct. From (-1) 3 =- 1, we know that d is also correct. The squares of negative numbers are all positive numbers, that is, negative numbers.
7. If a=0, you can immediately exclude A, B, C and choose D..
8. For the deformation of the same solution of the equation, both sides of the equation are required to be multiplied by a number that is not equal to 0. So we ruled out a.
When we consider the equation X-2 = 0, it is easy to know that its root is x=2. If both sides of the equation are multiplied by an algebraic expression X- 1, we get (X- 1) (X-2) = 0, its root is x= 1, and x=2. If it is not the same solution of the original equation, B is excluded.
9. Let the original amount of water in the cup be A, which can be obtained according to the meaning of the question.
The next day, the amount of water in the cup is a× (1-10%) = 0.9a;
On the third day, the amount of water in the cup is (0.9a) × (1+10%) = 0.9 ×1.1× a;
The ratio of water in the cup on the third day to that in the first day.
So on the third day, there was less water in the cup than on the first day, so C was chosen.
10. Suppose the distance between two docks is s, the speed of the ship in still water is A, the water speed is v0, and the round-trip time is
Let the river speed increase to v, and (V > v>v0), and the time for a round trip is
Because v-v0 > 0, a+v0 > a-v0, a+v > a-v.
So (a+v0) (a+v) > (a-v0) (a-v)
∴ t0-t < 0, that is, t0 < T. Therefore, it takes more time to increase the river speed, so choose A. 。
Second, fill in the blanks
Tip:
2. 1989 19902- 1989 19892
=( 1989 1990+ 1989 1989)×( 1989 1990- 1989 1989)
=( 1989 1990+ 1989 1989)× 1=39783979.
3. Because (2+1) (22+1) (24+1) (28+1) (216+1).
=(2- 1)(2+ 1)(22+ 1)(24+ 1)(28+ 1)(2 16+ 1)
=(22- 1)(22+ 1)(24+ 1)(28+ 1)(2 16+ 1)
=(24- 1)(24+ 1)(28+ 1)(2 16+ 1)
=(28- 1)(28+ 1)(2 16+ 1)
=(2 16- 1)(2 16+ 1)=232- 1.
2 ( 1+x)-(x-2) = 8，2+2x-x+2 = 8； x=4
5. 1-2+3-4+5-6+7-8+…+4999-5000
=( 1-2)+(3-4)+(5-6)+(7-8)+…+(4999-5000)
=-2500.
6.(3x 3-5x 2+6x- 1)-(x3-2 x2+x-2)+(-2 x3+3 x2+ 1)= 5x+2
7. Takes note of:
When a =-0.2 and b=0.04, A2-B = (-0.2) 2-0.04 = 0, B+A+0.16 = 0.04-0.2+0.16 = 0.
8.60× 30% (kg) salt water with a salt content of 30% is changed into x grams of water with a salt content of 40% by evaporation, that is, 0.00 1x kg. At this time, 60×30% = (0.00 1x) × 40%.
Solution: x=45000 (grams).
10. At 4 o'clock sharp, the angle between the hour hand and the minute hand is 120.
The first test question of the second day and the first day of the second day of Hope Cup.
First, multiple-choice questions (each question 1 point, *** 15 point)
Only one of the four conclusions A, B, C and D of each topic below is correct. Please fill in the English letter code of the correct conclusion in brackets.
1. 1 This number is ()
A. the smallest integer. B. Minimum positive number. C. Minimum natural number. Minimum rational number.
2. if a > b, then ()
A.； B.-a|b|。 D.a2>b2。
3. If A is a rational number, the relationship that must be established is ().
A.7a>a. B.7+a>a.C.7+a>7D.|a|≥7。
4. The algebraic expression of the shaded area in the figure is ().
A.D.+B.C. b . c(b-d)+d(a-c). c . ad+c(b-d). d a B- CD。
5. Among the results of the following operations, the largest number is ().
A.(- 13579)+0.2468; b .(- 13579)+；
C.(- 13579)× ; (- 13579)
The value of1416× 7.5944+3.1416× (-5.5944) is ().
A.6. 1632。 b . 6.2832 c . 6.5 132。 D.5.3692
7. If the sum of four numbers is 8 and the three numbers are -6, 1 1, 12, then the four numbers are ().
A. 16。 B. 15。 C. 14。 D. 13。
8. Among the following scores, () is greater than-and less than-.
A.- ; b .-； c .-； D ...
9. Equation A: (x-4)=3x is the same as the solution of Equation B: x-4=4x, which is based on ().
A. add the same algebraic expression x.b. multiply both sides of party a's schedule by x;
C. Both sides of Party A's schedule are multiplied; D. multiply both sides of party a's schedule.
10. As shown in the figure, the positions of rational numbers A, B and C are marked on the number axis, where O is the origin, then the size relationship of is ().
A.； b . >； & gt； c . >； & gt； d . >； & gt。
1 1. The root of the equation is ()
The 27th.
12. When x = and y =-2, the value of the algebraic expression is ().
A.-6.b-2。 C.2. D.6
13. Among the five numbers -4,-1, -2.5, -0.0 1 and-15, the product of the largest number and the number with the largest absolute value is ().
a . 225 b . 0. 15。 C.0.000 1。 D. 1。
14. The solution set of inequality is ()
A.x< 16。 B.x> 16。 C.x< 1。 D.x & gt- .
15.p% concentration of M kg physiological saline and q% concentration of N kg physiological saline mixed solution concentration is ().
A.； b； c； d。
II. Fill in the blanks (each question 1 point, *** 15 point)
1. Calculation: (-1)+(-1)-(-1) × (-1) ÷ (-1) = _ _.
2. Calculation:-32 ÷ 6× = _ _ _ _ _.
3. Calculation: = _ _ _ _ _ _.
4. Evaluation: (-1991)-|-31| = _ _ _.
5. Calculation: = _ _ _ _ _ _.
6.n is a positive integer, and the last four digits of1990n-1991are arranged in order, and the four digits are 8009. Then the minimum value of n is equal to _ _ _.
7. Calculation: = _ _ _ _.
8. Calculation: [(-1989)+(-1990)+(-1991)+(-1992)] = _
9. In (-2)5 and (-3)5, the largest number is _ _ _ _ _.
10. The largest integer not exceeding (-1.7)2 is _ _ _ _.
1 1. Solve the equation
12. Evaluation: = _ _ _ _ _ _.
13. The prime number is a two-digit number, and the difference between its one-digit number and its ten-digit number is 7, so this prime number is _ _ _ _ _.
14. If the negative reciprocal of the reciprocal of a number is, then the number is _ _ _ _ _.
15. As shown in the figure 1 1, a, b, c, d, e and f are rational numbers. The sum of three numbers in each row, column and two diagonal lines in the figure is equal, so it is = _ _ _.
Answers and tips
First, multiple choice questions
1.C 2。 B 3。 B 4。 C 5。 C 6。 B 7。 B 8。 B 9。 C 10。 B 1 1。 D 12。 A 13。 B 1 4。 A 15。 D
Tip:
1. Integer has no minimum number, excluding a; Positive numbers have no minimum number, excluding b; There is no minimum number for rational numbers, except that D. 1 is the minimum natural number. Choose C.
There are | 2 | < |-3 |, excluding c; If 2 >-3 has 22 < (-3) 2, exclude D; In fact, a > b must have-a.
3. If a=0, 7×0=0 excludes A; 7+0=7 excludes C | 0 | < 7 excludes D. Actually, because 7 > 0, there must be 7+A > 0+A = A. Choose B.
4. If the figure is filled into a big rectangle, the area of the shaded part is equal to AB-(a-c) (b-d) = AB-[AB-ad-c (b-d)] = AB-AB+AD+C (b-d) = AD+C (b-d). Choose C.
5. For negative numbers, the smaller the absolute value, the larger the value.
6.3. 14 16×7.5944+3. 14 16×(-5.5944)
=3. 14 16(7.5944-5.5944)=2×3. 14 16
= 6.2832. Choose B.
32 years. The fourth number = 32-(-6+11+12) =15. Choose B.
The new equation x-4=4x has the same solution as the original equation. Choose C.
13. -4,-1, -2.5, -0.0 1 and-15, the maximum number is -0.0 1, and the absolute number is-15,-0.06438.
15. let the concentration of mixed solution be x, then m× p%+n× q% = (m+n) X.
Second, fill in the blanks
Tip:
1.(- 1)+(- 1)-(- 1)×(- 1)÷(- 1)=(-2)-(- 1)
=- 1
4.(- 199 1)-|3-|-3 1||=- 199 1-28=-20 19.
6. The last four digits of 1990n should be the last four digits of 199 1+8009, that is, 0000, that is, the last digit of1990n should have at least four zeros, so the minimum value of n is 4.
(- 1993)]=- 199 1.
10.(- 1.7) 2 = 2.89, and the largest integer not exceeding 2.89 is 2.
Denominator
4(2x- 1)-( 10x+ 1)= 3(2x+ 1)- 12。
8x-4- 10x- 1 = 6x+3- 12。
8x- 10x-6x = 3- 12+4+ 1。
13. There are 708 1 92 digits with decimal places greater than single digits, and there are18,29 digits with decimal places greater than single digits, of which only 29 digits are prime numbers.
B+d+7=- 1+3+7=9, so the sum of three numbers on two diagonal lines in each row and column is equal to 9. It is easy to get a=4, e= 1, c=5 and F = 0.
Hope cup, grade three, grade one examination questions.
First, multiple-choice questions (each question 1 point, * * *1point)
1. rational number-definitely not ()
A. positive integer. B. negative integer. C. negative score. D.0。
2. Among the four pairs of monomials given below, the similar one is ().
A.x2y and-3x2z; B.3.22m2n3 and n3m2C.0.2a2b and 0.2a2d.11ABC and ab.
3. (x-1)-(1-x)+(x+1) equals ().
A.3x-3。 B.x- 1。 C.3x- 1。 dx-3。
4. The sum of two polynomials of degree 10 is ()
A.A.20 polynomial of degree 20 B.1polynomial of degree 0. C./kloc-polynomial of degree 0/00. D. Polynomials with degree not higher than 10.
5. If a+ 1 < 0, then among the four numbers below each group, the group arranged in descending order is ().
A.a，- 1， 1，-a.B.-a，- 1， 1，a.C.- 1，-a，a， 1.D.- 1，a， 1，-a。
6.A =- 123.4-(- 123.5)，b= 123.4- 123.5，c= 123.4-(- 123.5)。
a c > b > a b c > a > b c a > b > c d b > c > a
7. If a < 0, b > 0 and | a | < | b |, the result in the following formula is positive ().
A.(a-b)(ab+a)。 b .(a+b)(a-b)c .(a+b)(a b+ a)。 D.(ab-b)(a+b)。
8.2a+5b minus half of 4a-4b, you should get ().
A.4a-b. B.b-a.C.a-9b。 D.7b
9.a, B, C and M are rational numbers. a+2b+3c=m and a+b+2c=m, then B, C ().
A. Countdown. Countdown. C. Countdown. D. equality.
10. Zhang Mei wrote five rational numbers, the average of the first three rational numbers is 15, and the average of the last two rational numbers is 10, so the average of the five rational numbers written by Zhang Mei is ().
A.5B.8c . 12； D. 13。
II. Fill in the blanks (each question 1 point, * * *1point)
1.2+(-3)+(-4)+5+6+(-7)+(-8)+9+ 10+(- 1 1)+(- 12)+ 13+ 14+ 15=______.
2.=_________________.
3.=_________________.
4. If P=a2+3ab+b2 and Q=a2-3ab+b2, substitute it into the algebraic expression P-[Q-2P-(-P-Q)], and it will be simplified as _ _ _ _.
5. 1992-{ 199 1- 1992[ 199 1- 1990( 199 1- 1992) 1990]}=_______________.
6. The sum of the digital coefficients of the six monomials 15a2, xy, a2b3, 0.1m3, -ABC,-is equal to _ _ _ _ _ _.
7. Xiaohua writes four rational numbers, in which the sum of every three numbers is 2 17,-1 and -3 respectively, so the product of the four rational numbers written by Xiaohua is equal to _ _ _ _ _.
8. When a wheat is ground into flour, its weight will be reduced by 15%. In order to get 4250 kilograms of flour, at least _ _ _ _ kilograms of wheat are needed.
9. Among the satisfied x values, the sum of those integers whose absolute values do not exceed 1 1 is equal to _ _ _ _ _.
10. Fill in an integer in each box shown below:
And the sum of the numbers filled in any three adjacent cells is equal to 5, then = _ _ _ _ _ _.
Answers and tips
First, multiple choice questions
1.D 2。 B 3。 C 4 explosive D 5。 A six. B 7。 An eight. D 9。 A 10。 D
Tip:
So choose D.
2. according to the definition of similar items, choose B.
3.(x- 1)-( 1-x)+(x+ 1)
= x-1-1+x+x+1= 3x-1,and choose C.
4. The sum of polynomials x 10+x and-x/kloc-0+x2 is x2+x is a polynomial with a degree lower than 10, so exclude A, B and C and choose D.
5. from A+ 1 < 0, we know A 1. So the order from small to large should be A.
6. It is easy to see that a =-123.4+123.5 = 0.1B = 123.4- 123.5 < 0, c =123.
7. because a < 0, b > 0. So |a|=-a, | b | = B Because | a | 0, a-b < 0. A-b+a < 0。 AB-b < 0。
=2a+5b-2a+2b=7b, choose D. 。
9. Because a+2b+3c=m=a+b+2c, b+c=0, that is, B and C are reciprocal, so choose A. 。
10. The sum of the first three numbers = 15×3,
The sum of the last two numbers = 10× 2.
So the average of five rational numbers is
Second, fill in the blanks
Tip:
The number before 1. 12 is divided into four groups, and the sum of each group is 0. So the total is 14+ 15 = 29.
4. Because P-[Q-2P-(-P-Q)]
=P-Q+2P+(-P-Q)
=P-Q+2P-P-Q
=2P-2Q=2
Substitute P=a2+3ab+b2, Q=a2-3ab+b2,
Original formula = 2 (p-q) = 2 [(A2+3ab+B2)-(A2-3ab+B2)]
=2(6ab)= 12ab。
6. The coefficients of the six monomials are:
7. Xiaohua wrote that the sum of four rational numbers is
After subtracting the sum of every three numbers respectively, these four rational numbers are 3,-12, 6 and 8. So the product of these four rational numbers = 3× (-12 )× 6× 8 =-1728.
Suppose you need x kilograms of wheat, according to the meaning of the question, you must
Solve the equation to get x = 5000.
It needs 5000 kilograms of wheat.
Divide by the denominator to get 3(2+x)≥2(2x- 1).
Remove the brackets and get 6+3x≥4x-2.
If you move things, you will get 3x-4x≥-2-6.
Merge similar projects -x≥-8
So x ≤ 8.
The sum of integers whose absolute value does not exceed 1 1 is (-9)+(-10)+(-11) =-30.
10. It is easy to draw a conclusion that the two numbers adjacent to X are 9 and 2 respectively, namely
Because 9+x+2=5, then x=-6. According to the fact that the sum of the numbers filled in any three adjacent cells is equal to 5, the numbers filled in each cell are determined as follows:
Y=-6, z = 9. therefore
The 4th Hope Cup (1993), the first day of junior high school.
1. Multiple choice questions: (65438+ 0 for each question, *** 15)
1. If a is a rational number, it must not be [].
A. positive integer. B. negative integer. C. negative score. Zero points.
2. The value of1993-{1993-[1993-(1992-1993)]} is equal to [].
A.- 1995.B. 199 1。 C. 1995。 D. 1993。
3. if a < b, (a-b)|a-b| equals []
A. (A-B) 2. B.b2-a2。 C.a2-b2。 d .(a-b)2。
4. If n is a positive integer and rational numbers A and B satisfy a+ =0, there must be [].
a . an+= 0； b . a2n+= 0； c . a2n+= 0； D.a2n+ 1+ =0。
5. If rational numbers A and B satisfy =0, one of the following statements is incorrect []
The sum of a.a and b is 0.b and the difference between a and b is positive.
The product of c.a and b is negative. When d is divided by b, the quotient is-1.
6. The six cards of Party A are -4,-1, -2.5, -0.0 1, -3,-15, and the six cards of Party B are -5,-1, 0. 1.
7.a is a rational number, so the correct one of the following statements is [].
A.-A is negative. B.A2 is positive. C.-| A2 | is negative. D. (a.-a1993) 2+0.001is positive.
8. The value of-is equal to []
A.-3; b .-； c .- 1； d-。
9. Under the following conditions, it is [] that can make AB < B hold.
A.b>0，a>0。 B.b c > b . c . b > c > a . d . c > b > a .
1 1. Rational numbers A and B are less than zero, and (A-B) 3 is less than zero, then []
A.； b .-a & lt； -b； C. 买 a 买 > 买 b 买; D.a2 & gtb4。
12.M represents the sum of squares of a and b, and n represents the sum of squares of a and b, so when a=7 and b=-5, the value of M-N is [] a.-28.b.70.c.42.d.0. 。
13. Rational number, 8 is exactly the root of the following three equations: 3 (2y+1) = 2 (1+y)+3 (y+3), then the value of [].
A.- ; b .-； c； d。
14. Figure 22 is a schematic diagram of the famous "Yanghui Triangle" in ancient China. The sum of all the figures in the figure is equal to [] A. 126. B. 127。 C. 128。 D. 129。
15. In natural numbers: 1, 2, 3, 4, 5, …, the negative reciprocal of the sum of the first 15 prime numbers is equal to [].
A.- ; b .-； c .-； D ...
II. Fill in the blanks (each question 1 point, *** 15 point)
1. If a > 0, there are exactly 1993 integers between -a and a, then the value range of a is _ _ _ _ _.
2. If the square difference between two adjacent positive integers is equal to 999, the product of these two positive integers is equal to _ _ _ _.
3.=_________.
4. A bus * * * passes 8 stops (including these two stops) from the starting station to the terminal station. It is known that there are 0/00 people getting on the bus at the first six stops, and 80 people getting off at the first six stops except the terminal, so there are _ _ _ _ _ passengers getting on the bus at the terminal.
5.(32-22)2+(42-32)2+(52-42)2+(62-52)2=______.
6. In the polynomial1993 umvn+3xmyn+U3mv2n-4xn-1Y2M-4 (where m and n are positive integers), there are exactly two similar terms, so m? n=______。
7. If A, B, C and D are all integers and (a2+b2)(c2+d2)= 1993, then A2+B2+C2+D2 = _ _ _ _.
8. The root of the equation is x = _ _ _ _ _ _
9.(- 1)÷ =______.
10.A and b Distance between two railway stations 189 km. An express train and a local train leave from two stations, A and B, respectively, in opposite directions. 1.5 hours later, the two trains met at a distance of 2 1 km. If the express train travels more than the local train12km,
1 1. in the equation y=kx+b, when x=0, Y = 2；; When x=3 and y=3, then = _ _ _ _.
12. The product of all non-negative integers satisfying inequality is equal to _ _ _ _ _.
13. If rational numbers A, B, C and D make =- 1, then the maximum value of is _ _ _ _ _.
14.△ ABC is an equilateral triangle, and the algebraic expression of its side length is already in.
Marked in Figure 23, then = _ _ _ _ _ _.
15. A teacher was asked how many students were in his class. The teacher said, "Half of the students are studying math, one quarter are studying music, one seventh are studying foreign languages, and less than six students are playing football on the playground." This "super long class" has _ _ _ _ students.
Answers and tips
First, multiple choice questions
Tip:
Exclude a if a= 1 and m=3, and exclude b if a=- 1 and m=-3.
=
=1993-1992+[1993-(-1)] =1+1994 =1995 Select C.
3.A-B is less than 0, because A is less than B. At this time | A-B | = B-A.
So (a-b) | a-b | = (a-b) (b-a) =-(a-b) =-(a-b) 2, choose D.
It's B.
7. When a=0, it is obvious that A, B and C are incorrect and should be excluded, so D. In fact, for any rational number A, there is (a- 1993)2≥0, so (a-1993) 2+0.006544.
9.b = 1 > 0, a = 2 > 0, ab = 2× 1 = 2 > 1 = b, excluding a; A < 0, b < 0, ab > 0 > b, excluding b; A=0, b < 0, ab = 0 > b excludes d, so C.
10. It is easy to see that A, B and C are all negative numbers. Let's look at |a|.
1 1. From (a-b) 3 < 0, a-b < 0. Namely a < B.
∵a, b < 0, ∴| a | < | b|, choose C.
12.M=(a+b)2，N=a+b2。
m-N =(a+b)2-(a+B2)= a2+2ab+B2-a-B2 = a2+2ab-a。
14. Line 1 only has 1=20, and line 2 has1+0 = 21.
The third line is 1+2+ 1=4=22, and the fourth line is 1+3+ 1 = 8 = 23.
Line 5:1+4+6+4+1=16 = 24,
Line 61+5+10+10+5+1= 32 = 25.
Line 7:1+6+15+20+15+6+1= 64 = 26.
The sum of all the figures in the figure is1+2+4+8+16+32+64 =127, so choose B.
Second, fill in the blanks
Tip:
1.-The integer between a and a is 2n+ 1. So we know from 2n+ 1= 1993 that n=996, that is, 996 ≤ A < 997.
2. If two adjacent positive integers are set to n and n+ 1 respectively, then from (n+1) 2-N2 = 2n+1= 999, n=499 and n+ 1 = 500.
The product of two adjacent positive integers is 499× 500 = 249500.
4. Let 1 get on the bus at station 7. The passengers are a 1, a2, a3, a4, a5, a6 and A7. Passengers getting off from stop 2 to stop 8 are b2, b3, b4, b5, b6, b7 and b8, obviously.
a 1+A2+A3+A4+A5+A6+A7 = B2+B3+B4+B5+B6+B7+B8。 It is known that a1+A2+A3+A4+A5+A6 =100, B2+B3+B4.
It shows that 20 passengers got on the bus at the previous 6 stops and got off at the terminal.
5. The original formula = 52+72+92+112 = 276.
6. If 1993umvn and u3mv2n are the same item, only m=0 and n = 0. Does not meet the known conditions, so only 3xmyn and -4xn- 1y2m-4 are the same term. Then we get m=n- 1, n = 2m-4. The solution is m.
7. Since 1993 is a prime number, a2+b2 and c2+d2 are divisors of 1993, only a2+b2= 1, c2+d2= 1993, or A2+B2 =1.
Product of all nonnegative integer solutions = 0.
14. From 2x-8=x+6, we get x = 14.
So the side length of a regular triangle is 14+6 = 20.
From 3y+2=20, y=6, so
15. Suppose there are x students in this class. There are a group of students playing football on the playground. According to the conditions, x and a are natural numbers, 1 ≤ A < 6.
According to the meaning of the question, the equation is as follows:
Merge similar projects and move projects.
Because a and x are natural numbers, (3,28) =1,so 3 | a.
But A can only take the five numbers 1, 2, 3, 4 and 5, so A = 3. So X = 28.
There are 28 students in this class.
The 5th Hope Cup (1994), the first test question of Grade One.
First, multiple-choice questions (3 points for each question, ***30 points) Only one of the four conclusions of each question below is correct.
1.-│-A │ is []
A. positive number B. negative number C. non-positive number D.0.
2. On the number axis below (Figure 1), the number (? 2)? (? The point of 5) is []
royal marines
3. The negative reciprocal of the value is []
A.4b .-； c . 1； D.- 1。
4.=[ ]
A.5.5 B.5.65
5.-4×32-(-4×3)2=[ ]
72 BC? 180
6. The difference between X and X is []
A.； b； c； d。
7. If n is an integer, then the number divisible by 3 and whose quotient happens to be n is [].
A.； b . n+3； C.3nD.n3
8. If x∶y=3∶2 and x+3y=27, the smaller of x and y is [].
a . 3 b . 6 c . 9d . 12
The complementary angle of 9.200 is equal to []
A.； b； c； D.50
10.=[ ]
A. 1
Two. Fill in the blanks in Group A (3 points for each question, ***30 points)
1. There are _ _ _ _ integers with absolute values greater than 2 and less than 6.
2. In an English test, the scores of eight students were 93, 99, 89, 9 1, 87, 8 1, 100, 95, so their average score was _ _ _.
3.| | | | 1992- 1993|- 1994|- 1995|- 1996|=______.
4. Numbers:-1. 1,-1.0 1,-1.00 1,-1.0/.
5.=________.
6. Among natural numbers, from small to large, the15th prime number is n, the digital sum of n is a, and the digital product is b, so the value is _ _ _ _ _ _ _.
7. One-year fixed deposit with a monthly interest rate of 0.945%. If you deposit 100 yuan now, you can get the principal and interest of * * * _ _ _ _ yuan today next year.
8. If the root of the equation 19x-a=0 is 19-a, then a = _ _ _ _ _
9. When x = x+2, the value of 19x94+3x+27 is _ _ _ _ _ _ _.
10. There is also an addition vertical line, each □ is covered by a number, and the sum of the seven numbers covered by □ is equal to _ _ _ _ _.
Three. Group B fills in the blanks (4 points for each question, ***40 points)
1. It is known that A and B are reciprocal, C and D are reciprocal, and the absolute value of X is equal to twice its reciprocal, so the value of x3+abcdx+a-bcd is _ _ _ _ _.
2. 1992× 1994 1994- 1994× 1993 1993=___.
According to the requirements in the above table, the product of ten numbers filled in the blank is _ _ _ _ _ _.
4. Among all the unequal five-digit numbers, the difference is _ _ _ _ _ _ _ _ _ _
5. It is known that n =1992×1993×1994+1993×1995.
6. To change 20kg of salt water containing 15% into 20% salt water, it is necessary to add _ _ _ _ _ kg of pure salt.
7. An exam * * * requires 20 small questions, with 8 points for doing one right and 5 points for doing one wrong.
Do it or get 0. A student will get 13. Then there are _ _ _ _ questions that the student didn't do.
8. As shown in Figure 2, connect a small square with an area of a2 with a large square with an area of b2.
Put the squares together (a > 0, b > 0). Then the area of triangle ABC is _ _ _ _ _.
9. Choose any number n from one hundred natural numbers from 1 to 100. For at least one of these numbers to be a composite number, n must be at least _ _ _ _ _.
10. As shown in Figure 3, it is a park ABCDEF, where m is the midpoint of AB and n is the midpoint of CD.
P is the midpoint of DE and Q is the midpoint of FA, where the sum of the areas of APEQ and BNDM in the tourist area.
It's 900 square meters, the lake area in the middle is 36 1 square meter, and the rest is grassland.
Then the total area of grassland is _ _ _ _ square meters.