The negative number in 1, -(-5), -|-5|, -(-5)2, (-5)2, -52, -(-5)3 is ().
a，2 B，3 C，4 D，5。
2. The total weight of a batch of goods is 1.4× 107kg, and the following applicable mode of transportation is ().
A, 10,000-ton ship B, plane C, car D, scooter.
3, geological staff, measured four highlands, their elevation is as follows, you analyze, the highest of which is ().
A,-85.6m b,-121.3m c, -25. 1 m d,-71.3m.
4. There is a scoring method: take 80 as the base, 85 points as +5 points, and a classmate gets 77 points, which should be recorded as ().
A, +3 points B, -3 points C, +7 points D, -7 points.
5. On the number axis, the number represented by point P is -3, and the number represented by point P after moving 4 units is ().
A, 1 B,-1 C, 7 D, 1 or -7
6. The corresponding points of two numbers on the known number axis are shown in the figure. In the following conclusions, ①; ② ; ③ ; ④ ; ⑤ ; The correct one is ()
a、①②⑤ B、③④ C、③⑤ D、②④
7, the following various calculation results equal to -5 is ()
A, B, C, D,
8. The distance that the earth rotates around the sun every hour is about 1 10000 kilometers, which is about () kilometers in scientific notation.
a、 1. 1× 104 B、 1× 1× 105 C、 1× 1× 106D、 1 1× 104
9. As shown in figure 1, it is an expanded view of a cubic carton. If the three squares A, B and C are filled with appropriate numbers respectively, and the two numbers on the opposite faces are opposite to each other after they are folded into cubes, then the three numbers filled in the three squares A, B and C are () in turn.
A, 1, -2, 0 B, 0, -2, 1 number 1
c 、-2，0， 1 D 、-2， 1，0
10. The ancient "river map" in China is composed of 3×3 squares, and each square has several.
Point charts for different purposes, with three point charts in each row, column and diagonal.
The sum of points is equal. Figure 2 shows the "River Map" section. Please calculate p.
The corresponding dot diagram here is ()
A, B, C, D,
Second, fill in the blanks
The reciprocal of 1 1 and -3.5 is, the absolute value is, and the reciprocal is;
12, the approximate value from 4.036 to 0. 1 is; The approximate value of two significant figures of 4.036 is:
13. Divers A and B are working underwater. The height of A is -50 meters, and B is above A 10 meters, so the height of B is meters;
14, A and B have a number guessing game: A says that the reciprocal of a number is himself, and B says that the reciprocal of a number B is himself. Please guess | A-B | = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _;
15, calculation: = =;
16, it is known that two unequal numbers are opposite and reciprocal, and the absolute value is 1, =;
17, use ">" to connect the following numbers.
(-2)2, - ,-(+2),0. 13, 0,- 1. 1, |-3|,-(- )
These two photos are here.
Algebraic expression:
1.a 16 can be written as ()
A.a8+a8 B.a8？ a2 C.a8？ a8 D.a4+a4
2. In the following categories, the correct calculation is ()
A.-a6？ (-a)2 = A8 b .(-2)5 =- 10 c . m2+m2 = 2 m4d .(-a-b)2 =(a+b)2
3. If the length of a rectangular lawn is xa+ 1 and the width is xb- 1(a and B are positive integers greater than 1), then the area of this rectangular lawn is ().
a . xa-bm2 b . xa+bm2 c . xa+b- 1 m2 d . xa-b+2 m2
4. When n is a positive integer, (-x2) 2n+ 1 equals ().
A.-x4n+2 b .-x4n+ 1 c . x4n+ 1d . x4n+2
5. if (4? 10m)(20？ 103)(5? 102)=4? 109, then m = ()
A.2 B.3 C.4 D.5
Fill in the blanks (4 points for each question, 20 points for * * *)
6. If mx4? 4x k= 12x 12, then m = _ _ _ _ _ _, and k = _ _ _ _ _.
7. If A=3x-2, B= 1-2x and C=-5x,
And then a? B+A？ c = _ _ _ _ _ _ _ _ _ _ _ _，A？ b？ c = _ _ _ _ _ _ _ _ _ _ _ _ _ _
8. The length of a rectangle is 2xcm, and the width is 4cm smaller than the length. If the length and width of the rectangle are enlarged by 3cm, the area will increase by _ _ _ _ _ _; If x=2cm, the increased area is _ _ _ _ _ _ _.
9.(x-y+z)(_______)=z2-(x-y)2
10. If x-y=2 and x2-y2= 10, then x+y = _ _ _ _.
Iii. Answering questions (60 points)
1 1. Simplification: (a2+b)(a2-b)-(-a2)? (-a2)； (8 points)
12.x4+2x3+ax2+bx+1is a completely flat form of quadratic polynomial. Try to find the values of a and b (12 points).
13. decomposition factor: a4+a2b2+b4 (10)
14. If x+y=0 and xy=2, find the value of x3y-xy3 (10 point).
15. It is proved that (x+1) (x+2) (x+3) (x+4)+1can be expressed as the square of an algebraic expression, and the conclusion of the proof reveals the law when x is a natural number. (20 points)
Example 1 The following statement is true ()
The exponent of a. is 0 b. There is no coefficient.
C.-3 is a monomial. D.-3 is a monomial.
Analysis: the correct answer should be D. This question mainly examines students' understanding of the number and coefficient of monomials. The index or coefficient 1 ignored by students who choose A or B can be omitted. Students who choose C don't understand that the number of monomials refers to the index of letters.
Example 7 If both A and B are quadratic polynomials, then A-B: (1) must be quadratic; (2) it can be four times; (3) It may be one-off type; (4) It may be a non-zero constant; (5) It cannot be zero. In the above conclusion, () is incorrect.
A.2 B. 3 C. 4 D.5
Analysis: Answer A, C and D easily, and try to solve the problem from the opposite side of each conclusion. If we can give a counterexample, we can explain that the original conclusion is not valid, so we can solve it correctly.
& lt 18 & gt； 1+2+3+……+2005=?
& lt 19 > given the square of (ab) m * (n-1of m * b of 3a) = b (square of ab) n * (m * b of 3a), how to find the value of m+n?
& lt20 >； What is the value of k? K+2/5 is higher than k-2/ 10 1.
Equation:
First of all, judge right or wrong:
(1) Determine whether the following equation is linear:
①-3x-6x 2 = 7； ( ) ② ( )
③5x+ 1-2x = 3x-2； ()④3y-4=2y+ 1。 ( )
(2) Judge whether the solution of the following equation is correct:
① Solve equation 3y-4=y+3.
Solution: 3y-y=3+4, 2y=7, y =; ( )
② Solving equation: 0.4x-3=0. 1x+2.
Solution: 0.4x+0.1x = 2-3; 0.5x=- 1，x =-2； ( )
③ Solving the equation
Solution: 5x+ 15-2x-2 = 10, 3x =-3, x =-1;
④ Solving the equation
Solution: 2x-4+5-5x=- 1, -3x=-2, x=. ()
Second, fill in the blanks:
(1) If 2(3-a)x-4=5 is a linear equation about x, then a≦.
(2) The solution of equation ax=3 about X is a natural number, so the value of integer A is:.
(3) The solution of equation 5x-2(x- 1)= 17 is.
(4) If x = 2 is the solution of equation 2x-3=m-, then m=.
(5) If -2x2-5m+ 1=0 is a linear equation about x, then m=.
(6) When y=, the algebraic expressions 5y+6 and 3y-2 are reciprocal.
(7) When m=, the solution of the equation is 0.
(8) If a≠0 is known, the solution of equation 3ab-(a+b)x=(a-b)x about x is.
Three. Multiple choice question:
The solution of (1) equation ax=b is ().
A. there is a solution x = B. There are countless solutions
C. No solution D. When a≠0, x=
(2) Solve equation (x- 1)=3. Among the following variants, the simpler one is ().
A. multiply both sides of the equation by 4 to get 3( x- 1)= 12.
B. remove the brackets and get x- =3.
C. divide both sides by the same number to get x- 1=4.
D. finish, acquire
(3) Equation 2- Denominator ()
a . 2-2(2x-4)=-(x-7)b . 12-2(2x-4)=-x-7
C.12-2 (2x-4) =-(x-7) D. None of the above answers are correct.
(4) If the algebraic ratio is greater than 1, the value of x is ().
13 BC
(5)x= 1 is the solution of equation ().
A.-
B.
C.2{3[4(5x- 1)-8]-2}=8
D.4x+ =6x+
Fourth, solve the following equations:
( 1)7(2x- 1)-3(4x- 1)= 4(3x+2)- 1；
(2)(5y+ 1)+( 1-y)=(9y+ 1)+( 1-3y)；
(3)[()-4]= x+2；
20%+( 1-20%)(320-x)= 320×40%
2(x-2)+2=x+ 1
2(x-2)-3(4x- 1)= 9( 1-x)
1 1x+64-2x = 100-9x
15-(8-5x)=7x+(4-3x)
3(x-7)-2[9-4(2-x)]=22
3/2[2/3( 1/4x- 1)-2]-x = 2
Verbs (short for verb) answer the following questions:
When (1)x is equal to what number, are the values of algebraic expressions equal?
(2) When y is equal to what number, the value of the algebraic expression is 3 less than that of the algebraic expression?
(3) When m is equal to what number, the sum of the value of algebraic expression 2m- and the value of algebraic expression is equal to 5?
(4) Solve the following equation about x:
ax+b = bx+a； (a≠b)；