The reciprocal of 1 1. -2 Yes.
Test center: countdown.
Analysis: According to the definition of reciprocal, the reciprocal of-2 is-.
Solution: The reciprocal of 2 is-.
Comments: We mainly study the definition of reciprocal, which needs to be mastered skillfully. It should be noted that
The nature of reciprocal: the reciprocal of a negative number is negative, the reciprocal of a positive number is positive, and 0 has no reciprocal.
Definition of reciprocal: If the product of two numbers is 1, we call these two numbers reciprocal.
12. If the income of 50 yuan is recorded as +50, then -80 is the expenditure of 80 yuan.
Test sites: positive and negative numbers.
Analysis: according to the number of positive numbers and negative numbers representing opposite meanings, the income is recorded as a positive number, and the representation method of available expenditure can be obtained.
Solution: 50 yuan's income is +50, so -80 means 80 yuan's expenditure.
So the answer is: spend 80 yuan.
Comments: this question examines positive and negative numbers, and uses positive and negative numbers to represent opposite quantities.
13. All integers greater than < 3 and less than or equal to 2 are < 2, < 1, 0, 1, 2.
Test center: number axis.
Analysis: express an integer greater than -3 and less than or equal to 2 on the number axis, and then fill in the blanks according to the number axis.
Solution: As shown in the figure, there are five integers greater than | 3 and less than or equal to | 2, | 1, 0,1,2 and * *;
So the answer is: -2,-1, 0, 1, 2.
Comments: This question examines the number axis. Has this question been adopted? Combination of numbers and shapes? The mathematical thought of.
14. The income of a store last month was one yuan, and this month's income is 10 yuan is more than twice that of last month. This month's income is
2a+ 10 yuan.
Test center: column algebra.
Special topic: application problem.
Analysis: We know that this month's income is twice that of last month, that is, two years, more 10 yuan, that is, more 10 yuan, that is, this month's income.
A: A: According to the meaning of the question:
This month's income is: 2a+ 10 yuan.
So the answer is: 2a+ 10.
Comments: This question examines students' mastery of algebraic expressions according to the meaning, and the key is to analyze and understand the meaning of the question.
15. 1.45? be qualified for sth
5220 seconds.
Test center: conversion of degrees, minutes and seconds.
Special topic: calculation problems.
Analysis: According to the degree, 60 times minutes and 3600 times seconds can get the answer.
Solution: according to the degree, it becomes a minute multiplied by 60 and a second multiplied by 3600.
? 1.45? 60=87 points,
? 1.45? 3600=5220 seconds.
So the answer is: 5220.
Comments: This question mainly focuses on changing the degree to minutes multiplied by 60 and seconds multiplied by 3600, which is relatively simple.
16. As shown in the figure, AOC and? DOB is a right angle, if? DOC=28？ And then what? AOB= 152？ .
Test center: angle calculation.
Special topic: calculation problems.
Analysis: Can you see from the picture? AOC and? Add DOB and subtract DOB The doctor is what you want.
Answer: Solution: ∵? AOC=？ DOB=90？ ,? DOC=28？ ,
AOB=？ AOC+？ DOB﹣？ Doctor,
=90? +90? ﹣28? ,
= 152? .
So the answer is: 152?
Comments: This question mainly examines students' understanding and mastery of diagonal calculation. The solution to this problem is not unique, as long as it is reasonable.
17. When building a wall, construction workers often set up piles at both ends and then build a wall along the line. Can you explain the principle that two points determine a straight line?
Test center: the nature of a straight line: two points determine a straight line.
Topic: fill in the blanks by reasoning.
Analysis: According to axioms? Two points determine a straight line? , to answer.
Solution: Solution: ∵ Two points determine a straight line,
? When building a wall, builders often pile up wires at both ends and then build a wall along the line.
So the answer is: two points determine a straight line.
Comments: Does this question examine axioms? Two points determine a straight line? The application in real life, to solve this problem should not only be based on axioms, but also be linked with real life, and cultivate students' thinking habits of applying what they have learned.
18. If 3amb2 and are similar items, then = 0.
Test center: similar projects.
Special topic: calculation problems.
Analysis: according to the definition of similar terms (including the same letter and the same index of the same letter), list the equations, find out the values of n and m, and then substitute them into algebraic expressions for calculation.
Solution: Solution: 3amb2 and are similar terms.
? n=2，m= 1，
? m﹣n=0
So the answer is: 0.
Comments: This question examines the definition of similar items. Pay attention to two definitions of similar items. Same? The same letter and the same index, this is a confusing point, so it has become a common test site for the senior high school entrance examination.
19. There are 44 students in Class * * * in Grade 2 of Senior High School, including 30 boys and 0/4 girls. If you look for any student in this class, you are more likely to find a boy than a girl. Big? Or? Small? ).
Test center: the size of the possibility.
Analysis: You can compare the probability of finding boys and girls.
Answer: Solution: There are 44 students in Class * * * of Senior One, including 30 boys and 0/4 girls.
? The probability of finding a boy is =,
The probability of finding a girl is: =
? More likely to find a boy,
So the answer is: big.
Comments: This question examines the size of the possibility, requires the size of the possibility, and only needs the size of their respective proportions. When calculating the proportion, you should pay attention to remember your respective figures.
20. Observe the numbers in the following column and fill in the appropriate numbers on the horizontal line according to certain rules: 1,,,,, then the nth number is.
Test center: regular type: types of numbers.
Special topic: ordinary type.
Analysis: According to the data law, the molecular law is a continuous odd number, namely 2n- 1, and the denominator is12,22,32,42,52,? N2, so the fifth number is, the sixth number is, and the nth number is.
Solution: According to the data law, the molecular law is a continuous odd number, namely 2n- 1, and the denominator is12,22,32,42,52,? N2, the nth item is, then the fifth item is: = and the sixth item is: =.
Comments: This paper mainly examines students' ability to summarize general conclusions through special case analysis. For the topic of finding rules, we must first find out which parts have changed and according to what rules. It is difficult to express the change rule with a unified formula after finding the change rule of each part through analysis.
Third, please calculate and do it. Don't make any mistakes!
2 1. Calculation: (1)4? (﹣2)﹣(﹣8)? 2
(2)
Test center: mixed operation of rational numbers.
Special topic: calculation problems.
Analysis: (1) Negative calculation based on multiplication with the same sign and multiplication with different signs;
(2) The multiplication and distribution law is simple to calculate.
Answer: Solution: (1)4? (﹣2)﹣(﹣8)? 2,
=﹣8+4,
=﹣4;
(2) The original formula = (-3) 2? ()+(﹣3)2? (﹣),
=3﹣4=﹣ 1.
Comments: This question examines students' ability to master arithmetic. The key is (1) negative calculation based on multiplication with the same sign and multiplication with different signs. (2) The calculation by using the multiplication distribution law is relatively simple.
22. Solve the equation: (1) 6Y+2 = 3Y-4 (2)
Test center: Solve a linear equation.
Special topic: calculation problems.
Analysis: (1) This is an integral equation. As long as the term is shifted and the coefficient is changed to 1, the solution of the equation can be obtained.
(2) This is an equation with a denominator, so we need to remove the denominator first, then remove the brackets, and finally shift the term, so that the coefficient is 1, so as to solve the equation.
Solution: Solution: (1) shift term, get: 6y-3y =-4-2;
Combining with similar projects, we get: 3y =-6;
Divide both sides of the equation by 3 to get: y =-2;
(2) Remove the denominator to get: 2 (x+1)-6 = 5x-1;
Without brackets, we get 2x+2-6 = 5x-1;
If you move items and merge similar items, you get:-3x = 3;
When both sides of the equation are separated by | 3 of x = |1.
Comments: This question examines the solution of a linear equation with one variable, which is relatively simple and students should master it skillfully.
23. Simplify before evaluating: (4a2-3a)-( 1-4a+4a2), where a =-2.
Test site: addition and subtraction of algebraic expressions? Simplify the assessment.
Analysis: In this question, we should remove the parentheses in the algebraic expression, merge similar items, simplify the algebraic expression into the simplest form, and then substitute the value of A. Note that when removing the parentheses, if there is a negative sign before the parentheses, then every item in the parentheses will change sign; When merging similar items, only the coefficients are added and subtracted, and the letter index remains unchanged.
Solution: Solution: (4a2-3a)-( 1-4a+4a2) = 4a.
2﹣3a﹣ 1+4a﹣4a2=a﹣ 1，
When a =-2,
a﹣ 1=﹣2﹣ 1=﹣3.
Comments: The mixed operation of algebraic expressions is investigated, mainly focusing on the knowledge points such as addition, subtraction, brackets removal and merging of similar items. Pay attention to the operation sequence and the handling of symbols.
24. As shown in the figure, it is a pattern consisting of five cubes. Please draw its front view, left view and top view on the grid paper respectively.
Test center: Drawing-Three Views.
Special topic: drawing problems.
Analysis: the number of squares in the front view from left to right is 3 and 2 in turn;
The number of squares in the left view 1 column is 3;
The number of two columns of squares from left to right in the top view is 1 and1in turn; Just draw a picture according to this.
Answer: Solution:.
Comments: This topic examines the painting methods of the three views; The front view, left view and top view are plan views from the front, left side and top of the object, respectively.
25. A department store engages in promotional activities during the New Year's Day, and shopping does not exceed 200 yuan without discount; More than 200 yuan, but less than 500 yuan, the discount is 10%, more than 500 yuan, of which 500 yuan gives a 10% discount, and the excess part gives a 20% discount. Someone spent 134 yuan and 468 yuan on shopping twice. Q:
(1) How much is this person's goods worth if they are not discounted twice?
(2) How much money did he save in this activity?
(3) If this person buys the same goods by combining two sums of money, will it save more money or lose more money? Explain why.
Test center: the application of one-dimensional linear equation.
Analysis: (1) 134 yuan does not discount. Assuming that the original price of 468 yuan is X yuan, list the equation according to the meaning of the question and find the solution of the equation to determine the original price, you can determine how much this person's goods will cost if they are not discounted twice;
(2) Subtract the discounted amount from the undiscounted amount to get the result;
(3) It is more economical, that is, to combine the money purchased twice, find out the amount of money discounted after buying the same commodity, and compare it with the amount of money sold separately to get the result.
Answer: Solution: (1) First-time shopping 134 yuan, there is no discount if it does not exceed 200 yuan.
Therefore, when shopping for the first time, there is no discount 134 yuan.
Suppose the original price of the second shopping with 468 yuan is X yuan, then:
( 1﹣ 10%)x=468
The solution is x=520.
134+520=654 (yuan)
So this person's goods are 654 yuan twice without discount;
(2) Because 134+468=602 (yuan) 654-602 = 52 (yuan)
Another solution: 520 ~ 468 = 52 (yuan)
So, he saved 52 yuan in this activity;
(3) saving, saving 70.4 yuan.
Because the sum of the two sums is 602 yuan, and it exceeds that of 500 yuan.
So the sum of the two money is * * * with a discount of 602% (500? 0.9+ 102? 0.8)=70.4 (yuan)
Therefore, it is more economical for this person to combine the two money to buy the same goods.
Comments: This topic mainly investigates the application of one-dimensional linear equation and the discount problem in real life. The key is to use the idea of classified discussion: analyze the two situations of paying discounts clearly.
26.20 10 After the defeat of the China Men's Football World Cup, a news agency randomly surveyed 400 people's views on the football environment in China. The results are as follows:
The opinion is very dissatisfied, dissatisfied, and a little satisfied.
Number of people 200 160 32 8
per cent
(1) Calculate the percentage of each opinion in the total number of respondents (fill in the space above);
(2) Please draw a fan-shaped statistical chart reflecting the survey results;
(3) What conclusions can you draw from the statistical chart? Tell me your reasons.
Test center: fan chart.
Analysis: (1) is obtained by dividing the number of people in each school by the total number of people and then multiplying by 100%;
(2) Multiply their respective percentages by 360? , you can get the degree of the central angle of each small fan, and then make a fan chart;
(3) The fan chart can reflect the percentage of various situations, and the answer can be obtained according to the fan chart.
Answer: Solution: (1)∵? 100%=50%,? 100%=40%,? 100%=8%,? 100%=2%,
(2)∵50%? 360? = 180? ,40%? 360? = 144? ,8%? 360? =28.8? ,2%? 360? =7.2? ,
?
(3) Half of the people are very dissatisfied with the national football team. Most people are dissatisfied with the football environment in China.
Comments: This topic examines the practice and significance of fan-shaped statistical charts. The difficulty in solving problems lies in the angle of fan-shaped statistical chart, so we should pay attention to mastering the methods.
27. In the calendar of 2011as shown in the figure,
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
1 2 3 4 5 6 7
8 9 10 1 1 12 13 14
15 16 17 18 19 20 2 1
22 23 24 25 26 27 28
29 30 3 1
(1) Circle any 3 with a rectangular box. 3 numbers, if from the lower left corner to the upper right corner? Diagonal? The sum of the three numbers on the table is 39, so what is the sum of these nine numbers?
(2) Can the sum of 9 numbers circled by this rectangular box be 2 16?
(3) If the shaded part is arbitrarily selected as above, what are the rules of the four numbers A, B, C and D? Please use an equation containing a, b, c and d (where the relationship between a, b, c and d is a).
Test center: the application of one-dimensional linear equation.
Analysis: (1) Let the middle number be X, then the number in the lower left corner is x+6, and the number in the upper right corner is X-6. Diagonal? If the sum of the three numbers on the table is 39, then the sum of the two opposite numbers is twice the middle number. Then nine is nine times the middle number.
(2) Set the middle number as y and list the algebraic comparison results;
(3) Observation shows that the sum of two numbers on the diagonal of the parallelogram is equal.
Solution: Solution: (1) Let the number in the middle of the diagonal be X, then the number in the lower left corner is x+6, and the number in the upper right corner is x﹣6, then
x+x+6+x﹣6=39，
The solution is x= 13.
The sum of these nine numbers = 5+6+7+12+13+14+19+20+21=162.
(2) no.
Let the middle number be y, and then
9y=2 16，
The solution is that y=24,
Then the number in the lower right corner of the rectangle is 24+8=32, which is impossible.
So just because the sum of these nine numbers can only be 162.
(3) A = B- 1 = C-6 = D-7, or B = A+ 1 = C-5 = D-6,
Or c = a+6 = b+7 = d- 1, or d=a+7=b+6=c+ 1.
Comments: Investigate the application of linear equation of one variable. The key to solving the problem is to read the meaning of the question and find the equivalent relationship of the required quantity. Pay attention to solving the same example by analogy.
I hope this 20 16-20 17 seventh grade math final paper (including answers) can help better meet the upcoming exam!
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