For example, the math test of senior one: Building A is 24.5 meters higher than Building C, and Building B is 15.6 meters higher than Building C, so Building B is _ _ _ _ meters lower than Building A (the math test of Hope Cup Senior One in 2000).
Solution: If building C is x meters high, building A is (x+24.5) meters high and building B is (x+ 16.5) meters high.
(x+ 16.5)-(x+24.5)=-8.9, that is, Building B is 8.9 meters lower than Building A. 。
Second, the calculation of rational numbers.
Example of junior high school math test: calculation (11998-1) (11997-1) (11000).
Analysis of senior one mathematics test questions: subtraction rule of reverse rational number, multiplication of transformation component number.
Solution: The original formula =-(1997/1998) (1996/1997) (999/1000) =-1/2.
Third, the parity and divisibility of numbers
For example: 1998 A person's age is exactly equal to the sum of the years he was born, so his age should be _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Solution: Let this person's birth year be abcd, thus,1998-ABCD = A+B+C+D.
A+b+c+d9=36, so abcd 1998-36= 1962. When a= 1 and b=9, there is 1 1c+2d=88.
So c is an even number, and 1 1c88, c8, 1 16+288, c=8, d=0. This person's age is 18 years old.
Fourth, use non-negativity.
Example of senior one math test: It is known that A, B and C are all negative numbers and |x-a|+|y-b|+|z-c|=0, then the value of xyz is ().
(a) negative numbers (b) non-negative numbers (c) positive numbers (d) non-positive numbers
(Examination questions of the 10th Hope Cup Junior One Mathematics Invitational Tournament)
Solution: from the nature of non-negative numbers, we know that x = a, y = b and z = c.
Xyz=abc, and both abc are negative numbers, xyz0, so choose (a).
Fifth, the issue of comparative scale.
For example, a=989898/999999, b=979797/989898, compare the sizes of A and B, (1998 Hope Cup Mathematics Invitational Tournament)
Solution: a = (98101)/(991010) = 98/99, b = 97/98,
a-b = 98/99-97/98 = 1/(9899)ab。
Six, reciprocal, reciprocal problem
For example, if A and B are reciprocal, and C and D are negative reciprocal, then (A+B) 1996+(CD) 323 = _ _ _. (7th Hope Cup Mathematics Invitational Tournament)
Solution: A+B = 0, CD =-1(A+B)1996+(CD) 323 =-1.
Seven, the combination of number and shape number axis problem
For example, the positions of the three numbers A, B and C on the number axis are as shown in the figure, then the following formula is correct ().
(A) 1/(c-A) 1/(c-B) 1/(A-B)(B) 1/(c-A) 1/(c-B) 1/(B-A)
(c) 1/(b-c) 1/(c-a) 1/(b-a)(d) 1/(a-b) 1/(a-c)65438。
Several problems that often appear in mathematics learning in junior one.
1, the understanding of mathematics knowledge points in grade one of junior high school stays at the level of a little knowledge;
2. The key math skills can never be grasped when solving math test questions in senior one, and each problem is treated in isolation, lacking the ability to draw inferences from others;
3. There are too many small mistakes in solving the math test questions in senior one, and the problems can never be completely solved;
4. The efficiency of solving math test questions in the first grade is low, and a certain number of questions can not be completed within the specified time, which is not suitable for the examination rhythm;
5. I haven't formed the habit of summarizing and summarizing, and I can't habitually summarize the knowledge points I have learned;