1. 1 positive and negative numbers

For any rational number A, what must be negative in the following categories is ()

(A)-(-3+A)(B)-A(C)-| A+ 1 |(D)-a2- 1

Any positive power is positive;

The odd power of a negative number is negative and the even power is positive.

When multiple numbers are multiplied and divided, the even number of "-"sign is positive; The odd number of "-"is negative.

Two negative numbers, the larger one has the smaller absolute value.

18. If | m+2 | and (n-4) 2 are antonyms, then (-m) n =.

1.2 rational number

Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.

Integers and fractions are collectively called rational numbers.

Numbers are usually represented by points on a straight line, which is called the number axis.

Three elements of number axis: origin, positive direction and unit length.

Take any point on a straight line to represent the number 0, and this point is called the origin.

Numbers with only two different symbols are called reciprocal (for example, the reciprocal of 2 is-2; The reciprocal of 0 is 0)

The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, and it is recorded as |a|.

The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0. Two negative numbers, the larger one has the smaller absolute value.

Rational number comparison method: 1, using the number axis; 2. Positive numbers are greater than 0 and negative numbers; Two negative numbers, the larger one has the smaller absolute value.

8. Let A be the smallest prime number, B be the largest negative integer and C be the smallest absolute number, then the sum of A, B and C is

(A)0 (B) 1 (C)2 (D)3

12, the following statement: ①0 is a rational number with the smallest absolute value; ② The number whose reciprocal is greater than itself is negative; ③ The numbers on both sides of the origin on the number axis are opposite; (4) Comparing the two numbers, the absolute value is larger but smaller. The correct one is ().

A.①②b。 ①③c。 ①②③D。 ②③④

Two opposite numbers are located on both sides of the origin on the number axis ()

Integer whose absolute value is less than 2 is _ _ _ _ _ _ _.

The number whose absolute value equals itself is _ _ _ _ _ _ _.

A negative integer with an absolute value not greater than 3 is _ _ _ _ _ _ _.

Addition and subtraction of rational number 1.3

Rational number addition rule:

1. Add two numbers with the same sign, take the same sign, and then add the absolute values.

2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0.

When a number is added with 0, it still gets this number.

Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.

1, the following statement is true ()

A. the larger the absolute value, the larger the number. B. Numbers with large absolute values are smaller.

C. two numbers with equal absolute values are equal. D. two numbers with equal absolute values are equal.

4, the following statement is correct ()

① if a < b, then | a | b, then | a | > | b |

③ If a = b, then | a | =| b | ④ If a≠b, then | a ||| b |

1。

Multiplication and division of rational number 1.4

Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.

Two numbers whose product is 1 are reciprocal.

Rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.

Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0 to get 0.

1.5 multiplication of rational numbers Finding the product of n same factors is called multiplication, and the result of multiplication is called the power in the n power of a, a is called the base, and n is called the exponent.

The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0.

Scientific counting method is used to express numbers greater than 10 as the n power of a× 10.

From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.

Chapter 2 Algebra distinguishes the number of terms in algebra, and the addition and subtraction operations of algebra merge similar terms.

Comprehensive application of comprehensive examination and simplified evaluation

4. The coefficient and degree of the monomial -23a2b are () respectively.

Article 23, paragraph 2 (b), paragraph 3 (c), paragraph 2 (d) and paragraph 3.

Is the same item, then _ _ _ _ _;

Yes _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _;

5. If the sum of -5a bn- 1 is similar, the value of (-n)m is ().

a . 9b . 8c-9D-8

7, the following deformation, the correct is ()

A. if a=b, then B. if ax=ay, then x = y.

C. if ab2=b3, then a=b D. if so, then a = B.

Chapter III One-variable Linear Equation

Shopping mall discount comparison commercial engineering problem interest rate problem

13, a dress is priced in 200 yuan. If you sell it at a 20% discount, you can still earn 20 yuan. The purchase price of this dress is RMB.

(2) You can still make a profit of 10% at a 20% discount on the marked price. The marked price of this dress is RMB.

15. After a commodity is increased by 20% on the basis of the purchase price, it is sold at a 10% discount, making a profit in 20 yuan. The purchase price is _ _ _ _ _ _.

Set the purchase price of X yuan and get the equation according to the meaning of the question.

28. A factory in Wenzhou and Hangzhou simultaneously produces several machines of a certain model. Wenzhou factory can support 10 foreign machines, and Hangzhou factory can support 4 foreign machines. Now it is decided to give Wuhan 8 and Nanchang 6. See table 1 for the freight of each machine. Let's assume that the machine transported from Hangzhou to Nanchang is X.

1, complete Table 2 (unit: 100 Yuan); 2. If the total freight is 8400 yuan, how many machines will Hangzhou transport to Nanchang?

destination

Starting point Nanchang Wuhan

Wenzhou Factory 400 yuan/set of 800 yuan/set.

Hangzhou factory 300 yuan/set of 500 yuan/set.

destination

Starting point Nanchang (6 units) Wuhan (8 units)

Wenzhou factory (10)

Hangzhou factory (4 sets) x

10. It takes 30s for a train traveling at a constant speed to enter a 600-meter-long tunnel and leave. It is known that a beam of light from a fixed lamp at the top of the tunnel vertically illuminates the train for 5s, so the length of the train is ().

(a)100m (b)120m (c)150m (d) 200m

69. Some of the same rooms need painting. Three masters painted eight rooms a day, but the 40㎡ wall was never painted before. Meanwhile, five apprentices painted the walls of nine rooms. Each master draws 30㎡ more walls than his disciples.

(1) Find the wall area to be painted in each room;

(2) Boss Zhang has 36 such rooms that need painting. If 1 master is invited to take two apprentices, how many days will it take?

(3) It is known that the daily wages of master and apprentice are 85 yuan and 65 yuan, respectively, and Boss Zhang requires that it be completed within three days. How to recruit people from these eight people?

68. Xiao Ming wants to buy two kinds of lamps, one is 10W (0.0 1KW) energy-saving lamp in 50 yuan, and the other is 100W (0. 1KW) incandescent lamp in 5 yuan. The lighting effect of the two lamps is the same, and the service life is the same (30). time

(1) Which lamp is more economical to choose for lighting for 500 hours? (2) Lighting time 1500 hours, which lamp is more economical?

(3) How long does it take to use two kinds of lights for lighting?

23. (8 points in this question) On February 26th, 2009, Wuhan-Guangzhou high-speed railway was officially put into operation. It is estimated that the one-way running time of the high-speed rail from Wuhan to Guangzhou will be 3 hours. 18 During the trial operation on February 6th, the trial operation time from Wuhan to Guangzhou was longer than expected 18 minutes, and the time for Guangzhou to return to Wuhan was the same as expected.

The third chapter is the preliminary understanding of graphics.

3. 1 color graphics

Geometry is also called volume for short. It is the surface that surrounds the body.

3.2 Lines, rays and line segments

Axiom of line segment: Of all the connecting lines between two points, the line segment is the shortest (the line segment between two points is the shortest).

The length of the line segment connecting two points is called the distance between these two points.

3.3 Angle measurement

1 degree =60 minutes 1 minute =60 seconds 1 fillet =360 degrees 1 flat angle = 180 degrees.

3.4 Angle comparison and operation

If the sum of two angles is equal to 90 degrees (right angle), they are called complementary angles, that is, each angle is the complementary angle of the other angle.

If the sum of two angles is equal to 180 degrees (flat angle), the two angles are said to be complementary angles, that is, each angle is the complementary angle of the other angle.

The complementary angles of equal angles (same angles) are equal.

The complementary angles of equal angles (same angles) are equal.

As shown in Figure 24, B and C divide the line segment AD into three parts: 2∶3∶4, where M is the midpoint of AD and CD=8, and find the length of MC.

7. There are three points A, B and C on the plane. If AB=8, AC=5 and BC=3, there is ().

(a) point c is on line segment AB; (b) Point C is on the extension of line segment AB.

(c) Point C is outside the straight line AB. (d) Point C may be on or outside the straight line AB.

50 24′×3+98 12′25″÷5;

It is known that the line segments AB=CD and overlap with each other. M and n are the midpoint of AB and CD respectively, and MN= 14cm. Find the length of AB.

If viewed from point A, B is 60 northeast, then point A is _ _ _ _ _ _.

As shown in figure ∠AOB=∠COD=90? ，∠AOD = 130？ Find the degree of ∠BOC.

1. From 2 o'clock to 4: 30, the angle of the clockwise hand of the clock is ().

A.B. C. D。

1. As shown in the figure, it is known that ∠AOB is a right angle, ON is the bisector of ∠AOC, and OM is the bisector of ∠BOC. Find the degree of ∠MON.

Xi。 As shown in the figure, C and D are any two points on the line segment AB, MC=2AM, DN=2NB. It is known that CD=3 and NM= 10. Find the length of AB.

9. As shown in the figure, it is known that straight lines AB and CD intersect at point O, OE bisects ∠BOD, OF bisects ∠COE, and ∠2=4∠ 1. Find the degree of ∠AOF.