I sorted out the places where candidates are most likely to lose points in mid-term and final exams in recent years. Everyone must pay attention to it, change it if there is, and encourage it if there is no …
1. Irregular writing and copying errors.
At the beginning of rational number calculation, some students often write-1+(-5) as-1+-5 and -x as-1x, so we should pay attention to these basic writing norms.
For example, the following is a classmate's answering process. Did you get shot?
Even some students often make mistakes of "copying mistakes", such as turning the paper upside down and copying it to the answer sheet, which are all familiar "low-level" mistakes.
Suggestion: be careful when doing the questions; Keep an eye on it and don't panic (be sure to be serious)!
2. Skip the steps you don't want to write more.
Some students like to think by leaps and bounds when calculating, and often get wrong results if they don't follow the "routine" to solve problems. When you do the problem, you must calculate it step by step, not in a hurry, but step by step. Only under the premise of ensuring the accuracy and proficiency can you omit some non-critical steps.
Suggestion: when doing the problem, follow the steps, don't worry, don't jump!
3. The operation sequence is wrong and the rules are unfamiliar.
The following classmate did not calculate in the order of the algorithm, which led to the loss of points.
Operation order: parentheses take precedence, multiply first, then multiply and divide, and finally add and subtract. Addition and subtraction are first-order operations, multiplication and division are second-order operations, and power sum roots are third-order operations; The operation at the same level is from left to right, and the operation at different levels should be carried out in the first three layers, then in the second layer and finally in the last layer; If there are brackets, count the brackets first, then the brackets and finally the braces.
The above operation sequence can be abbreviated as: "from small (bracket) to large (bracket), from high (level) to low (level), from left to right (same level)".
Suggestion: Remember the formula and practice more and calculate it carefully.
4. Remove the brackets and pay attention to the changes of coefficients and symbols.
For calculation problems, the teacher found that students are most likely to make mistakes when they remove brackets! When removing brackets, students must pay attention to the coefficients and symbols in front of brackets. When the brackets are removed, when there is a "-"in front of the brackets, the symbols in the brackets will change; When there is a coefficient in front of the bracket, each item in the bracket should be multiplied by it.
For example, students often change 5-(4-3) to 5-4-3 and 5(x+6) to 5x+6 by removing brackets. This kind of problem is very common. I wonder if you have been cheated.
Suggestion: You should look at brackets, coefficients and symbols!
5. When the denominator is removed, products without denominator are omitted.
When solving equations and inequalities, it often involves removing the denominator. When both sides of the equal sign are multiplied by the least common multiple of the denominator at the same time, students must be careful not to omit the multiplication! People often make the mistake of forgetting to multiply the constant term.
For example, the following situations:
Suggestion: remove the denominator, multiply by a constant term, and leave nothing!
6. Denominator, pay attention to the hidden brackets in the numerator.
When solving the equation, we must pay attention to the fact that when several terms of the molecule are added (subtracted), after removing the denominator, the molecule is a whole. Remember that this whole has an "invisible" bracket!
The above classmate didn't pay attention to the hidden brackets when removing the denominator, which led to the error of the final result.
Suggestion: remove the denominator, find the least common multiple first, and then add the invisible brackets!
7. When moving items, pay attention to the change of signs.
When solving one-dimensional linear equations, two-dimensional linear equations and inequalities, in addition to removing the common mistakes of denominator, the change of symbols when moving terms is also a common mistake made by students!
Students must be clear that when an item moves to the other side of the (not) equal sign (using the nature of the equation, it is equivalent to adding or subtracting both sides of the equation), the sign will change. Be careful!
For example, 12≤x and -x≤- 12 are equivalent; 3x- 1=x-4。 Sequence of transfer items 3x-x =-4+1; The classmate above forgot to change the sign when moving things.
Suggestion: move what you have learned and change the symbol!
8. The problem of "odd negative even positive" in symbol judgment
When calculating, the symbol should be determined first, and then the (absolute) value should be determined. We should use the "odd negative even positive" rule to judge symbols.
Let's summarize the "odd negative even positive" we have learned:
Decymbol problem.
For example-(-2) = 2; -[-(-2)]=-2。 When the number of "-"is odd, only one "-"remains in the final result; When the number of "-"is even, there is only one "+"in the final result (the plus sign can be omitted).
Symbolic judgment in rational number multiplication (division) operation.
For example, (-2) × (-3) = 6; (-2)×(-3)×(-4)=-24。 When the number of negative factors is odd, the result is negative; When the number of negative factors is even, the result is positive.
Determination of symbols in power operation.
After mastering the symbolic judgment method of "odd negative even positive", it is more important to find the base accurately. Remember, when negative numbers and fractions are used as the base, the base must be enclosed in brackets.
For example, the above classmate calculated -4 2 as 16, and he took the base as -4, but the actual base is 4 (if the base is-4, it should be written as (-4) 2).
Suggestion: move symbols and simplify to find the base, and even and negative couples catch up again!
9. the direction of the number.
According to the nature of inequality, both sides of inequality are multiplied and divided by a positive number, and the direction of inequality remains unchanged; When both sides of inequality multiply and divide by a negative number, the direction of inequality changes; When both sides of inequality are multiplied by 0, inequality becomes equality.
Suggestion: the unequal sign is special, and the change of direction is all because of negative!
10. Common mistakes of binary linear equations
When solving binary linear equations, when the coefficient is simple (such as 1), you can choose to substitute the elimination method, but you must substitute it into the deformation-free equation to eliminate it; When the coefficients of unknowns are equal, they can be eliminated by subtraction, and when the coefficients of unknowns are opposite, they can be eliminated by addition.
No matter which way you choose, the key to solving the binary linear equation lies in "elimination", and at the same time, you should pay attention to the symbols, coefficients and other issues.
Suggestion: The following are the places where students have a high error rate when doing problems. Let's see if you made the same mistake:
(1) Error in coefficient addition and subtraction when adding and subtracting elements.
(2) When substituting for elimination, substituting into the original deformation equation, the unknown cannot be solved.