Hunan Education Press Grade 8 Unit 1 Mathematics Test Paper Chapter 65438 +0 Score
The concept of type I fraction
1. If the score 2a+ 1 is meaningful, the range of a is ().
A.a=0 B.a= 1
C.a？ - 1 D.a？ 0
2. When a _ _ _ _ _ _ _ _ _ the score 1a+2 is meaningful.
3. If the value of the formula 2x- 1- 1 is zero, then x = _ _ _ _ _ _
4. Find the value of x that makes the score |x|-3(x+2)(x-3) 0.
Basic properties of type dichotomy
5.a and B are rational numbers, and ab= 1. Let P=aa+ 1+bb+ 1, q =1a+1+1,then P _>? 、? & lt？ Or? =? ).
Calculation and simplification of type trisection
6. The result of simplifying1x-3-x+1x 2-1(x-3) is ().
A.2 B.2x- 1
C.2x-3 D.x-4x- 1
7. The result of simplifying X (x-1) 2-1(x-1) 2 is _ _ _ _ _ _ _.
8. Simplification: 1+ 1x? 2x- 1+x2x。
9. Let's simplify it first: 1-a- 1a? A2- 1a2+2a, and then choose an appropriate value to replace the calculation.
10. Simplify first and then evaluate: x- 1x+2? x2-4x2-2x+ 1？ 1x2- 1, where x2-x=0.
Exponential power of four integers of type
1 1. Calculation: (1) (-1) 2013-|-7 |+9? (7-? )0+ 15- 1;
(2)(m3n)-2？ (2m-2n-3)-2？ (m- 1n)3。
Type 5 scientific notation
12. During the accident of Japan's nuclear power plant, a very small amount of artificial radionuclide iodine-13 1 was detected at a monitoring point in China, with a concentration of 0.0000963beck/m3. Data? 0.000 096 3? Scientific notation can be expressed as _ _ _ _ _ _ _ _ _ _ _.
Six solutions to fractional equation
13. The solution of the fractional equation 12x2-9-2x-3= 1x+3 is ().
A.x=3 B.x=-3
C. there is no solution D.x=3 or -3.
14. Solve the equation: 2x- 1= 1x-2.
15. Solve the equation: 23x- 1- 1=36x-2.
The application of the equation of seven fractions.
16. Li Ming went to the school where he left home 2. 1km to attend the ninth grade party. When he got to school, he found that the performance props were still at home. At this time, there were still 42 minutes before the party started, so he immediately walked home at a uniform speed, took 1 minute to get the props at home, and then immediately rode back to school at a uniform speed. As we all know, Li Ming rides a bike three times as fast as he walks, and Li Ming rides a bike to school faster than he walks.
(1) What is Li Ming's walking speed?
(2) Did Li Canming get to school before the party started?
17. In order to improve the added value of products, a company plans to complete the development and production of 1 200 new products before putting them on the market. The existing factories A and B have processing capacity. The company sent relevant personnel to these two factories to understand the situation and obtain the following information:
Information1:It takes 10 days for Factory A to process this batch of products alone than it takes for Factory B to process this batch of products alone;
Information 2: The daily processing capacity of Factory B is 1.5 times that of Factory A. 。
According to the above information, ask: How many new products can Factory A and Factory B process every day?
Hunan Education Press 1.c2 Answer Analysis of Unit 1 of Grade 8 Mathematics? -2 3.3
4. To make the value of the score 0, the numerator of the score must be 0 and the denominator cannot be 0, that is, |x|-3=0 and (x+2)(x-3)? 0.
Solution: Given that the score is 0, x should satisfy |x|-3=0 and (x+2)? (x-3)？ 0. When |x|-3=0, x=3 or x=-3 is obtained. Tests show that when x=3, (x+2)(x-3)=0, and when x=-3, (x+2)(x-3)? 0, so the value of x satisfying the condition is x=-3.
5.=
6. The analytic formula of b =1x-3-1x-1(x-3) =1-x-3x-1= x-/kloc-0.
7. 1x- 1
8. solution: the original formula =x+ 1x? x2- 1x=x+ 1x？ x(x+ 1)(x- 1)= 1x- 1。
9. Solution: The original formula = 1-a- 1a? a(a+2)(a+ 1)(a- 1)= 1-a+2a+ 1 =- 1a+ 1。
When a=3, the original formula =-13+1=-14. (The value of a is 0,? 1, any value except -2)
10. The analytic problem is the fractional operation of fractional multiplication and division. Simplify it first, and then combine the simplified results with the known conditions. It is not difficult to find a calculation method.
Solution: the original formula =x- 1x+2? (x+2)(x-2)(x- 1)2？ (x+ 1)(x- 1) 1 =(x-2)？ (x+ 1)=x2-x-2。
When x2-x=0, the original formula =0-2=-2.
1 1. Analytically calculate the power first, and then multiply and divide.
Solution: (1) Original formula =-1-7+3+5 = 0;
(2) The original formula =m-6n-2? 2-2m4n6？ Molybdenum nitride
= 14m-6+4-(-3)n-2+6-3 = 14mn。
12.9.63? 10-5
13 both sides of analytic equation. C times (x+3)(x-3) to get 12-2(x+3)=x-3, and x=3.
Test: (x+3)(x-3)=0 When x=3,
That is, x=3 is not the solution of the original fractional equation,
So the original equation has no solution.
14. solution: multiply both sides of the equation by (x- 1)(x-2) to get 2( x-2)=x- 1.
Without brackets, 2x-4=x- 1,
If the term is shifted, x=3.
X=3 is the solution of the original equation.
So the solution of the original fractional equation is x=3.
15. Solution: Multiply both sides of the equation by 6x-2 to get 4-(6x-2)=3.
Simplify it and get -6x=-3, and get x= 12.
Test: when x= 12, 6x-2? 0,
So x= 12 is the solution of the original equation.
16.( 1) Equation analysis: the time to walk home from school-the time from home to school =20 minutes; (2) The total time to take props home is compared with 42 points.
Solution: (1) If the walking speed of Li Ming is x m/min, then the cycling speed of Li Ming is 3x m/min.
According to the meaning of the question, we get 2 100x-2 1003x=20, and the solution is x=70.
X=70 is the solution of the original equation.
So Li Ming's walking speed is 70 meters per minute.
(2) Because 2 10070+2 1003? 70+ 1=4 1 (min) < 42 (min),
So Li got to school before the party started.
17. The equivalent relationship of this problem is: the number of days it takes for A factory to process this batch of products alone-the number of days it takes for B factory to process this batch of products alone =10; The quantity processed by factory B every day = the quantity processed by factory A every day? 1.5, if factory a processes x products every day, then factory b processes 1.5x products every day. According to the meaning of the question, the number of days required for two factories to independently process these products can be expressed, and then the equations can be listed and solved.
Solution: If Factory A processes X products every day, then Factory B processes 1.5x products every day.
According to the meaning of the question, it means1200x-12001.5x =10.
The solution is x=40,
X=40 is the root of the original equation,
So 1.5x=60.
A: Factory A processes 40 products every day, and Factory B processes 60 products every day.