Absolute value test of seventh grade mathematics last semester: 1. Multiple choice questions (4 points for each small question, *** 12 points)
1.(20 12? The absolute value of Shantou senior high school entrance examination) -5 is ()
5th century to 5th century.
2.(20 12? As shown, the unit length of the number axis is 1. If the absolute values of the numbers represented by point A and point B are equal, then the number represented by point A is ().
A.-4 B.-2 C.0 D.4
3. If |a|=-a, then the value range of a is ().
A.a & gt0 B.a & lt0 C.a？ 0 D.a？ 0
Fill in the blanks (4 points for each small question, *** 12 points)
4. The inverse of │-(+4.8) │ is _ _ _ _ _.
5. It is known that |x|=20 12, |y|=20 13, x >；; 0>y, then x = _ _ _ _ _ _ y = _ _ _ _ _ _
6. a new operation is defined: for any two rational numbers a and b, there is a※b=? |b|, such as 2※3=? |3|=
? 3= ,4※(-2)= ? |-2|= ? 2=. Calculation: 3 ※ (-6) = _ _ _ _ _.
Iii. Answering questions (***26 points)
7.(8 points) Given │a-2│+│b-3│=0, find the value of a +2b.
8.(8 points) Made by the affiliated factory of Beijing Aerospace Research Institute? Shenzhou 10? The nut on the launch vehicle requires that the inner diameter of the nut can be? The error is 0.02mm, and five nuts are randomly selected. The number of millimeters exceeding the specified inner diameter is positive, and the number of millimeters not exceeding the specified inner diameter is negative. The test results are as follows: +0.0 10, -0.0 18,
+0.006,-0.002,+0.0 15.
(1) indicate which products meet the requirements? (i.e. within the error range)
(2) Point out which product meets the requirements is of better quality and which is of worse quality?
Extension extension
9. Read the material and answer the following questions:
When a>0, if a=6, |a|=|6|=6, the absolute value of A is itself;
When a=0, |a|=0, and the absolute value of a is zero;
When a<0, if a=-6, then |a|=|-6|=6=-(- 6), then the absolute value of A is its inverse.
To sum up, the absolute value of a number can be divided into three situations, namely |a|= This analysis method permeates the idea of classified discussion in mathematics. Please imitate the method of classification discussion in common examples and analyze the relationship between conjecture |a| and-a.
Analysis of the absolute value test answer of seventh grade mathematics last semester: 1. Analysis chooses A, and the absolute value of negative number is its inverse, so the absolute value of -5 is 5.
2. Analytically choose B. On the number axis, the number represented by the point whose distance to the origin is equal to 2 is -2 and 2, and the number represented by the left is -2, so the number represented by point A is -2.
3. Choose C analytically, because the absolute value of a negative number is its inverse; The absolute value of 0 is 0, so if |a|=-a, then the value range of a is a? 0.
Variant training If |x-3|=x- 3, then the following formula representing the relationship between size holds ().
a . x-3 & gt； 0 b . x-3 & lt； 0
C.x-3？ 0 D.x-3？ 0
Analytically choose C. Because the absolute value is its own number is non-negative, because |x-3|=x-3, so x-3 is non-negative, so x-3? 0.
4. Analyze the first simplification │-(+4. 8)│ Get 4.8, so the inverse of 4.8 is -4.8.
Answer: -4.8
5. Analysis Because |x|=20 12, so x=? 20 12. Because |y|=20 13, y=? 20 13. because of x>0>y, x=20 12 and y=-20 13.
Answer: 20 12 -20 13
6. Analysis 3※(-6)=? |-6|= ? 6=2.
Answer: 2
7. Analysis because │ a-2│? 0，│b-3│？ 0,
│a-2│ +│b-3│=0，
So │a-2│=0, │b-3│=0,
Since the absolute value of 0 is only 0, A-2 = 0 and B-3 = 0.
So a = 2 and b = 3.
So a+2b=2+2? 3=8.
8. Analysis (1) because |+0.0 10| = 0.0 10
0.006 & lt0.02，|-0.002 | = 0.002 & lt； 0.02，|+0.0 15 | = 0.0 15 & lt； 0.02, so all the products sampled meet the requirements.
(2) The closer the absolute value is to 0, the better the quality is, and |-0.002|=0.002 is the closest to 0, so the quality is better; |-0.0 18|=0.0 18 is the largest, so the quality is slightly worse.
9. Analysis (1) When A >: 0, the value of |a|=a is positive and -a is negative, so | a |>- A.
(2) When a=0, | a | = | 0 | = 0 a = 0, so | a | =-a. 。
(3) when a