|
| Table | |
| Plot | |
| Methodical recommendations: |
| Scheme "To view 2" | |
| Scheme "To relate the step with category " | |
| Scheme "To learn categories 1" | |
| Scheme "To view and learn categories 1" | |
| Scheme "To relate categories with the step 1" | |
| Scheme "To select for transformation 1" |
| N |
Objective of the step
|
Errors: | Hints: | Total: |
| 0 | To solve an equation means to find all its roots or to prove that there is none |
9
|
0
|
9
|
| 1 | To add up coefficients at the similar terms of polynomial means to add up, using the distributive law, the numerical coefficients at the similar monomials |
4
|
2
|
6
|
| 2 | To collect similar terms of polynomial means to group together similar monomials, using the commutative law |
5
|
1
|
6
|
| 3 | To move expressions from one side of equation to the other means to set up a new equation equivalent to the given one, using the addition principle of equations equivalence |
3
|
1
|
4
|
| 4 | To multiply polynomials means to transform an expression, using the rule of multiplication of polynomials "each by each" (a conclusion of the distributive and associative laws of multiplication) |
1
|
2
|
3
|
| 5 | To replace an equation by the aggregation of equations means to use the theorems of equivalence of equations and the definition of equation |
2
|
1
|
3
|
| 6 | To add up polynomials means to transform an expression using the definition of operation of addition and definition of polynomial |
1
|
2
|
3
|
| 7 | To account for the domain of definition means to remove all forbidden values from the solution |
2
|
0
|
2
|
| 8 | To clear a fraction means to multiply both sides of an equation (inequality) by the expression equal to the common nonzero denominator, resting on the multiplication principle of equivalence of equations (inequalities) |
1
|
1
|
2
|
| 9 | To find the domain of definition for an expression means to write a system of inequalities determining the forbidden values of argument at which the expression is undefined |
2
|
0
|
2
|
| 10 | To make a change of function means to replace the function f(x) by the new argument t according to the rule f(x)=t, where x is the old argument, t - the new argument, f (x) - the replaceable function, and to indicate the region of function f variation |
2
|
0
|
2
|
| 11 | To give an answer means to find and write down the solution of equation |
0
|
2
|
2
|
| 12 | To move an addend from one side of an equation to the other means to transform an equation applying the addition principle of equivalence of equations |
0
|
1
|
1
|
| 13 | To multiply both sides of equation by "-1" means to set up a new equation equivalent to the given one |
0
|
1
|
1
|
| 14 | To remove brackets means to delete the characters of algebraic brackets from the notation of expression according to the rule induced by the distributive law |
0
|
1
|
1
|
| 15 | To add up fractions means to make up a new fraction, using the rule of addition of fractions |
0
|
1
|
1
|
| 16 | To solve a set of equations means to find all their roots or to prove that there is none |
0
|
1
|
1
|
| 17 | To make the inverse replacement of function means to replace the argument by the function according to the rule: t=f(x), where the function and argument were defined at the forward replacement |
0
|
1
|
1
|
| 18 | To apply a formula means to transform an expression using the formula's relation, with allowance made for the region of formula definition |
1
|
0
|
1
|
| 19 | To factor a quadratic trinomial means to present it as a product of linear expressions |
1
|
0
|
1
|
| 20 | To raise a polynomial to natural power means, in general case, to apply the binomial formula |
1
|
0
|
1
|
|
|