1. Integers and fractions are collectively referred to as
.
2.
:a
Yes. -a
3. Absolute value: |a|=
4. reciprocal: reciprocal of a (a≠0)
5.
The operation of the product of the same factor is called
The odd power of a negative number is negative and the even power is positive; The power of any positive number is positive; Any degree of 0 is 0.
6.
Operation:
、
、
.
7.
:a× 10n( 1≤a< 1)。
.
8. Use basics
Number (refers to addition, subtraction, multiplication, division,
And the formula to be learned later) The formula for connecting numbers or letters representing numbers is called
.
9. The product of numbers and letters, such a formula is called
.
(1) The same is true for a single number or letter.
.
(2)
The number factor in is called this.
.
(3) The sum of the indices of all the letters in the monomial is called the number of times of the monomial.
10. The sum of several monomials is called
.
(1) inches
Each monomial is called
Among them, items without letters are called
.
(2) Generally, the degree of the term with the highest degree in a polynomial is the degree of this polynomial.
1 1. monomials and polynomials
.
12. Items with the same letter and the same letter index are called.
, a few
also
.
13.
Merge into a project called
.
14.
Rule: move the symbol on one side of the equation to the other side, and call it
.
15.
If the sum of two angles is 90 degrees, then these two angles
As in the right triangle ABC,
∠ A = 90, ∠B = 46 and ∠C = 44, then ∠B and ∠C are
.
16.
If the sum of two angles is 180, then these two angles
.
17.α
Is: 90-∠ α，∠ β。
Yes: 180-β
18. Countdown
The quality of being identical or equiangular.
Equality.
The quality of being identical or equiangular.
Equality.
The second exercise
Core learning series (1)
1.|2|
Is _ _ _ _ _, the reciprocal of -(-2) is, and the reciprocal is.
2. There are _ _ _ numbers whose absolute value is equal to 3, and they are _ _ _ _ _ _ _ _; There are _ _ _ _ integers whose absolute values are not greater than 3. They are _ _ _ _ _.
3. at
The number of monomials in,,,, and is _ _ _ _ _. If it is a monomial about, and the coefficient is 9 and the degree is 4, then the polynomial is _ _ _ _ _ _ _ _.
The antonym of 4 is ()
Eighth century BC-
5. Single item
They are ()
A.B. C. D。
6.；
7.；
8. Solve the equation: 3 (x-2)+1= x-5 (2x-1).
9. A job is completed by Party A alone for 6 hours, Party B alone for 12 hours, and Party C alone for 18 hours. If A and B do it for 3 hours first, and then B and C do it together, how many hours will it take to complete it?
10.
Xiao Li's surgery all afternoon was in the east-west direction.
If the east is positive and the west is negative, his mileage (km) this afternoon is as follows:+15, -2, -5, -l,-10, -3, -2,-12, -4, -9,.
(1) Let Xiao Li's starting point in the afternoon be O. How far is Xiao Li from the starting point in the afternoon when he sends the last passenger to his destination?
(2) If the fuel consumption of the car is O.35 liters /km, how many liters will Xiao Li * * * consume this afternoon?
Other issues
1 1. Calculation:
Core Learning Series (2)
1. In
The largest of them.
Yes, the smallest positive integer is the smallest.
Yes, the largest.
Yes
2. if.
Fill in the blanks with ">" or ","
3. A quadratic form of b.
about
It's -2,
Is -0.5,
Is 3, then this polynomial is _ _ _ _ _ _ _. The sum of is _ _ _ _ _ _.
4. In the following figures, the negative number is ().
A. BC-9th century AD.
use
According to the requirements, it is approximately 0.050 19 respectively, and the error is ().
A.0. 1 (accurate to 0. 1) B.0.05 (
)
C.0.05 (keep two
D.0.0502 (accurate to 0.000 1)
6.。
7.。
8. Simplify first, then evaluate
9. Xiaoming painted the room and hired five workers, which took 10 days to finish; Use a paint 150 liter, the cost is 4800 yuan; The painting area is 150 square meters. When the salary is finally settled, there are three schemes:
Scheme 1: according to the workload, each worker will get 30 yuan (1 worker will work for one day);
Option 2: Pay 30% of the painting cost;
Option 3: Pay per square meter for painting area 12 yuan.
Please help Xiao Ming point out which scheme should be chosen to pay the most cost-effective (economical)? (explained by calculation)
10. A food factory took 20 bags of samples from the bagged food produced, and tested whether the quality of each bag met the standard. Excess or deficiency are represented by positive numbers and negative numbers respectively, and are recorded as follows:
Difference from standard mass (unit: gram)
0 1 3 6
Number of bags 1 4 3 4 5 3
(1) Is the average mass of this batch of samples more or less than the standard mass? How many grams more or less?
(2) If the standard mass of each package is150g, then
What is the overall quality of the test?
Other issues
1 1.( 1) Known value. (2) Known value.
Core Learning Series (3)
1. Simplify the following categories:
( 1)-(+2)= ; (2)-(- 15)= ; (3)+[-(-2)]= .
2. If it is known, then _ _ _ _ _ _ _ _. If rational numbers A and B satisfy |a|=5, |b|=4, and A
3. Simplification: (1) = _ _ _ _ _ _; (2) =________; (3) =_______ (4) =__________; (5) =__________.
4. It is known that the following equation is incorrect ()
A.B. C. D。
5.
Prepare to make a cube out of paper, as shown in Figure 8.
For the sake of beauty, he wants to draw a pattern on six square pieces of paper, so that the patterns on the opposite sides of the last three groups are the same, so the correct one after drawing the pattern is ().
6.。
7. I know and ask.
8. Solve the equation:
9. One workshop of a factory has people, and the second workshop has 30 fewer people than the first workshop.
(1) How many people are there in the two workshops?
(2) If 10 people are transferred from the second workshop to the first workshop, how many people are there in the first workshop after the transfer?
10. A factory in Beijing and a factory in Shanghai made several computers at the same time. The factory in Beijing can support 10 foreign computers, and the factory in Shanghai can support 4 foreign computers. It is now decided to give Chongqing 8 sets and Hankou 6 sets. If the freight rates from Beijing to Hankou and Chongqing are 400 yuan/set and 800 yuan/set respectively, then the freight rates from Shanghai to Hankou and Chongqing are 300 yuan/set and 500 yuan/set respectively.
(1) Set up a factory in Shanghai and transport it to Hankou Taiwan Province, which means the total freight (100 yuan).
(2) If two sets are shipped from Shanghai factory to Hankou, what is the total freight?
Other issues
1 1. Observe the following equation ("!" In the equation, this is a kind of mathematics.
No), 1! = 1,2! =2× 1,3! =3×2× 1,4! = 4× 3× 2× 1, ... Try to calculate the value.
Core Learning Series (4)
The reciprocal of 1 -Yes _ _ _ _ _ _ _; The opposite number is your own number, and it is _ _ _ _ _ _ _ _; If the absolute value of a number is equal to itself, such a number is _ _ _ _ _ _ _.
2. Known and contrary to each other, and then _ _ _ _ _ _ _ _ _.
3. The index of is _ _ _ _
For _ _ _ _; The index of is _ _ _
It's _ _ _.
4. The following two groups belong to the same category ().
A. and B. and ...
5. The following statement is true ()
A. In the connection between two points, the straight line is the shortest B. If P is the midpoint of the line segment AB, then AP=BP.
C. if AP=BP, then p is the midpoint d of the line segment AB. The line segment between two points is called the distance between two points.
6.。
7.。
8. Solve the equation:
9. Guanghua
There are 50 leasing companies.
, including 20 A and 30 b. Now these 50 sets are
Sent to A and B to harvest wheat, 30 of them were sent to A and 20 were sent to B.
Sum of two regions
The daily rental price agreed by the leasing company is shown in the following table:
Every a
The rent for each B.
rent
Zone A 1800 yuan 1600 yuan
Zone B 1600 yuan 1200 yuan
(1) set X B in area a.
, lease these 50 joints of the company.
The rent earned in one day is Y (yuan). Write the relationship between x and y.
(2) Calculate the values when the rent y is equal to 28, 29 and 30 respectively.
10. The store has a backlog of certain goods. In order to dispose of the goods as soon as possible, the store has adopted the following sales plan: first, increase the price to twice the original price, and then reduce the price three times, the first time, the second time and the third time. The sales of the three price reductions are as follows:
Number of price reductions one, two, three
Number of sales pieces
Grab it and throw it away.
(1) What is the percentage of the original price after the third price reduction?
(2) The goods are sold according to the new sales plan, which plan is more profitable than the original price?
Other issues
1 1. It is known that A and B are rational numbers, and a+b and a-b are reciprocal when certain conditions are met.
Core Learning Series (5)
1. Calculation: =. (The result was used.
Say).
= 3.141592653 ..., if
3. 142, accurate to a point,
Yes
2. If n is a positive integer, (-1) 2n = _ _ _, (-1) 2n+1= _ _ _.
3. If the polynomial does not contain cubic terms and linear terms, then _ _ _ _ _ _ _ _ _ _ _.
4. If a is a rational number, the relationship between 2a and 3a is ().
A.2a & gt3a B. 2a & lt3a C. 2a=3a D. Not sure.
5. In 2007 10, 3 1, 17: 25, China's first satellite circled the moon.
the third time
, satellite
The altitude rises from 120000km to 370000km, and enters 1 14 hours.
Among them, the data is "more than 370,000 kilometers"
The correct meaning is ()
A. Remaining kilometers
6.(23 - 14 -38 )×(-48).
7. Subtract Polynomial A from the known Polynomial A to get Polynomial A. 。
8. If the solution of the equation is the same as that of the equation, find the value of the equation.
9. It took two hours for a ship to travel downstream from Pier A to Pier B; It took 2.5 hours to travel upstream from Pier B to Pier A. Given the current speed of 3 km/h, find the speed of the ship in still water.
10. The admission price of the park is as follows:
The number of tickets purchased is more than1~ 5051~100100.
The price of each ticket is 13 yuan 1 1 yuan 9 yuan.
A school (1) and (2) two classes *** 104 people went to the garden, of which (1) class was less than 50 people. It is estimated that if both classes purchase tickets by class, then a * * * should pay 1240 yuan. Q:
( 1)
How many students are there in each school?
(2) If
How much can you save by joining hands to buy tickets?
(3) If 1 class (1) organizes a garden activity alone, how can you save the most money as an organizer?
Other issues
1 1. Real numbers A, B and C are in
The position on the | a |-| a+b |+c-a |+b-c | is simplified.
Core Learning Series (6)
1. Simplified: _ _ _ _ _ _, = _ _ _ _ _.
2. Known to be the same category, equal to _ _ _ _ _ _ _ _.
3. In the equation 3x-= 5, use the formula containing x.
Y means: y =, when x = 3, y =.
4. In the algebraic expressions,,,,, the number of monomials is ().
A. 1 B.2 C.3 D
5. Scoring rules for football matches: a game wins 3 points, a game draws 1 point, and a game loses 0 points. A team played 14 games, lost 5 games and scored 19 points, then the team won () games.
(A)3 (B)4 (C)5 (D)6
6.。
7. If |x|=2, find the value of the following formula: 3x2-[7x2-2 (x2-3x)-2x].
8. Solve the equation:
9. It is produced by 22 workers in a workshop
and
Average output per person per day
1200 or
In 2000, one
To match two nuts, how many workers should be assigned to produce them, so that the daily products can just match?
How many workers produce nuts?
10. The mall plans to allocate 90,000 yuan to buy 50 TV sets from manufacturers. It is known that this manufacturer produces three different models of TV sets, and the apparent price is 1500 yuan, 2 100 yuan per set and 2,500 yuan per set.
(1) If the shopping mall buys 50 TV sets of two different models at the same time, and it costs 90,000 yuan, please study the shopping plan of the shopping mall;
(2) If a shopping mall sells Class A TV sets with a profit of 150 yuan, Class B TV sets with a profit of 200 yuan and Class C TV sets with a profit of 250 yuan, which purchase scheme should be chosen to obtain the maximum profit?
Other issues
1 1. Specific dimensions: ①12 _ _ 21; ②23____32; ③34____43; ④45____54; ⑤56____65……
(1) Guess the relationship between nn+ 1 and (n+ 1)n;
(2) Comparison: 2007-2008.
Core Learning Series (7)
1. and-15 are opposites, so the value of is _ _ _ _ _ _ _ _. If -(-3) = 6, the value of is _ _ _ _ _ _ _ _ _ _.
2. Sum is opposite to each other, and then _ _ _ _ _ _ _ _ _.
3. There are 8.64× 104 seconds in a day, and if there are 365 days in a year, there are _ _ _ _ _ _ _ seconds in a year.
A number with two significant digits indicates the result)
4. The following statement is true ()
A. a positive number must be a negative number, and c means no temperature.
C. The weight of floret increased by -2 kg, that is to say, the weight of floret decreased by 2kg D. The degree of polynomial is 3.
5. The correct calculation is ()
A.B.
C.D.
6.。
7. Find the value of algebraic expression, in which
8. Given that the value of the algebraic expression is -2, find the value.
9. A series of numbers arranged regularly: 2, -4, 8,-16, 32, -64, …, in which the sum of some four adjacent numbers is -640. What is the difference between the maximum number and the minimum number of these four numbers?
10. The mall * * * sells 50 pieces of A and 50 pieces of B, with a total purchase price of 108000 yuan, of which the purchase price of commodity A is 1800 yuan, and the profit after the sale is 200 yuan; The purchase price of commodity B is 2,400 yuan per piece, and there will be profits in 300 yuan after it is sold. Beg the mall to sell these 50 pieces of * * * and get it done.
Less yuan?
Other issues
1 1. Equation:.
Core Learning Series (8)
1. If, the value of ab is. If, A must be _ _ _ _ _ _ _.
2. Polynomial plus _ _ _ _ _ equals.
3. If the value of the algebraic expression is 2, the value of the algebraic expression is.
4. The sum of all integers whose absolute value is greater than 3 and less than 7 is ().
30 (B) 15 (C)0 (D)20
5. If yes
, which is equal to ().
(A) 1 (B)2 (C) 1 or 2 (D) any number
6.-24× .
7. Know and ask.
8. Solve the equation:
9. A milk factory has 8 tons of fresh milk. If you sell fresh milk directly in the market, you can make a profit of 500 yuan per ton; Made into yogurt for sale, the profit per ton can reach 1200 yuan; manufacture
Sales, profit of 2000 yuan per ton. the factory's
Yes: if it is made into yogurt, it can process 3 tons a day; manufacture
Processing per day 1 ton; Limited by personnel, the two treatment methods cannot be carried out at the same time; Due to the temperature conditions, this batch of milk must be sold or processed within 4 days.
Therefore, the factory has designed two feasible schemes:
Option 1: Do as much as possible.
, the rest is sold directly.
Option 2: Make part of it into milk slices and the rest into yogurt, which can be sold in exactly 4 days.
Which scheme do you think is more profitable? Why?
10. A shop sells a kind of shirt, in April.
Five thousand yuan. In order to expand sales, every shirt was sold at 20% off the original price in May, and the sales volume increased by 40 pieces compared with April.
More than in April, 600 yuan. Ask the price of each shirt in April.
Other issues
1 1. Solve the equation:
│x- 1│+│x-5│=4
Core Learning Series (9)
1. In the algebraic formula:,,,,,, has _ _ _ _ _ _ _ _,
There is _ _ _ _ _.
2. If the monomial is quintic, then X = _ _ _ _ _ _ A monomial contains the letters x and y, and its coefficient is four times. Try to write this monomial _ _ _ _ _ _ _ _.
3. In equations ①, ②, ③, ④, ⑤, ⑤, it is
_ _ _ _ _ _ _ _ _ _ _ _ _ _ (fill in the serial number).
4. When solving the equation,
The correct one is ().
(A) (B)
(C) (D)
5. Fix a piece of wood on the wall. Xiao Ming said that only two nails are needed. The mathematical truth used here is ().
A. between two points, the line segment is the shortest; B. two points determine a straight line;
C. The line segment has only one midpoint; Two straight lines intersect and there is only one intersection.
6.。
7. Given, find the value.
8. Solve the equation:
9. In the mid-term exam, the information technology teacher asked each teacher for 40 minutes.
The students finished typing an article. You know it's the same size when you finish it independently.
Bao Xiao needs 50 minutes, and Beckham only needs 30 minutes. In order to complete the task, Bao Xiao played for 30 minutes and asked Beckham for help and cooperation. Can he finish the game within the specified time?
10.GSM mobile phone card charges 0.20 yuan per minute, and the monthly rental fee is 20 yuan per month;
There is no monthly fee for mobile phone cards, which is 0.40 yuan per minute. If you buy a mobile phone:
(1) If the estimated monthly call time is 75 minutes, which mobile phone recharge card should I choose?
(2) If the estimated monthly call time is 120 minutes, which mobile phone recharge card should I choose?
(3) How many minutes is the monthly call time?
The same fee?
Other issues
1 1. Party A and Party B respectively advance from Party A and Party B at the same speed. They met for the first time at a distance of 700 meters from point A, and then moved on. After A arrives at point B, B returns immediately and meets at a place 400 meters away from point B for the second time. What is the distance between A and B?