Error analysis - Methodical analysis of task performance

Performance analysis and methodical recommendations

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EMMentor_Algebra

This page demonstrates how one-task performance is analysed. Shown are the results of step by step analysis of errors. You can see a summary of errors for each solution step. This option is only available in the program EMMentor. EMMentor shows you why you are struggling in math and how to improve. At the bottom of this page we offer you to try examples of learning techniques available in the programs EMSolution and EMMentor.

Multifactor error analysis and methodical recommendations

Methodical recommendations are based on a joint multifactor analysis of a set of performed tasks. Multifactor analysis means that user's errors are analysed with regard to multiple parameters - to formulas, definitions and rules used in the performed tasks, to applied techniques, topics and types of tasks. Such comprehensive analysis enables EMMentor to detect vacancies in user's knowledge and skills and generate an optimal set of tasks to close the revealed gaps. EMMentor helps you find out why you are struggling in math and provides a qualified guidance in training problem solving skills.

Journal

The Journal keeps a record of performed tasks with grades (marks) and summaries of errors and activates the results of multifactor error analysis with concluding methodical recommendations.

Methodical analysis of task performance

23.2.2005

3:10:11

Educational task:

	Rational inequalities
	Strict linear inequalities
	Strict linear inequalities. Factorization of quadratic trinomial
	Solve the inequality

\frac{(- 18 r^{2} + 15 r + 25) \cdot (2 r - 6)}{- 6 r - 5} - \frac{(- 14 r^{2} - 32 r - 8) \cdot (3 r - 6)}{- 7 r - 2} < 0

Methodical task:

To select the transformation

The task was discharged by:	xxx yyy zzz
Affiliation:	xxx yyy zzz
Number of errors made:	7
Number of used hints:	9
Mark/grade (USA):	E 39

The task is not accomplished

Too much errors. Try a simpler educational task. Select a task from the listed groups of methods:

	Scheme "To transform 2"
	Scheme "To transform 1"
	Scheme "To select for transformation 7"

Methodical analysis of task performance

	Analysis of solution steps
	Analysis of math categories

The course of solution was either wrong or nonoptimal in the selection of the following transformations:

0. Solve the inequality

2. Let's solve linear equation(s), applying the addition and multiplication principles of equations equivalence

3. Let's factor quadratic trinomial(s), using the theorem of factorization of quadratic trinomial

4. Applying the main property of fractions, let us reduce fractional expression by the linear nonzero polynomial (expression of the form "ax+b")

6. Applying the main property of fractions, let us reduce fractional expression by the linear nonzero polynomial (expression of the form "ax+b")

7. Let's multiply polynomials by each other, using the distributive law

8. Let's combine polynomials, using the definition of operation of addition

9. Let's collect similar terms of polynomial

10. Let's add up coefficients at the like terms

11. Let's multiply both sides of inequality by "-1"

12. Let's divide both sides of inequality by the greatest common divisor of coefficients of polynomial forming the inequality

13. Using the addition principle of equivalence of inequalities, let us move the numeric addend from the left-hand side of the inequality to its right-hand side

14. Using the multiplication principle of equivalence of inequalities, let us divide both sides of the inequality by numerical coefficient at the argument

15. Let's apply the method of intervals to the obtained inequality

Educational task:

0. Solve the inequality

\frac{(- 18 r^{2} + 15 r + 25) \cdot (2 r - 6)}{- 6 r - 5} - \frac{(- 14 r^{2} - 32 r - 8) \cdot (3 r - 6)}{- 7 r - 2} < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	1	0

1. Let's find the domain of definition D(f) for the considered expression, taking into account that the division by zero is not defined

{\begin{matrix} - 6 r - 5 \neq 0 \\ - 7 r - 2 \neq 0 \end{matrix}

Methodical task:	Errors:	Hints:	C
To select the transformation	0	0

2. Let's solve linear equation(s), applying the addition and multiplication principles of equations equivalence

{\begin{matrix} r \neq - \frac{5}{6} \\ r \neq - \frac{2}{7} \end{matrix}

Methodical task:	Errors:	Hints:	C
To select the transformation	2	0

3. Let's factor quadratic trinomial(s), using the theorem of factorization of quadratic trinomial

\frac{((- 18) \cdot (r - \frac{5}{3}) \cdot (r + \frac{5}{6})) \cdot (2 r - 6)}{- 6 r - 5} - \frac{(- 14 r^{2} - 32 r - 8) \cdot (3 r - 6)}{- 7 r - 2} < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	2	0

4. Applying the main property of fractions, let us reduce fractional expression by the linear nonzero polynomial (expression of the form "ax+b")

(3 r - 5) \cdot (2 r - 6) - \frac{(- 14 r^{2} - 32 r - 8) \cdot (3 r - 6)}{- 7 r - 2} < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	1	0

5. Let's factor quadratic trinomial(s), using the theorem of factorization of quadratic trinomial

(3 r - 5) \cdot (2 r - 6) - \frac{((- 14) \cdot (r + \frac{2}{7}) \cdot (r + 2)) \cdot (3 r - 6)}{- 7 r - 2} < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	0

6. Applying the main property of fractions, let us reduce fractional expression by the linear nonzero polynomial (expression of the form "ax+b")

(3 r - 5) \cdot (2 r - 6) - (2 r + 4) \cdot (3 r - 6) < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	1	0

7. Let's multiply polynomials by each other, using the distributive law

(6 r^{2} - 18 r - 10 r + 30) - (6 r^{2} - 12 r + 12 r - 24) < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

8. Let's combine polynomials, using the definition of operation of addition

(6 r^{2} - 18 r - 10 r + 30 - 6 r^{2} + 12 r - 12 r + 24) < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

9. Let's collect similar terms of polynomial

6 r^{2} - 6 r^{2} - 18 r - 10 r + 12 r - 12 r + 30 + 24 < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

10. Let's add up coefficients at the like terms

- 28 r + 54 < 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

11. Let's multiply both sides of inequality by "-1"

28 r - 54 > 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

12. Let's divide both sides of inequality by the greatest common divisor of coefficients of polynomial forming the inequality

14 r - 27 > 0

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

13. Using the addition principle of equivalence of inequalities, let us move the numeric addend from the left-hand side of the inequality to its right-hand side

14 r > 27

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

14. Using the multiplication principle of equivalence of inequalities, let us divide both sides of the inequality by numerical coefficient at the argument

r > \frac{27}{14}

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

15. Let's apply the method of intervals to the obtained inequality

Methodical task:	Errors:	Hints:	C
To select the transformation	0	1

16. Let us account for the domain of definition

Methodical task:	Errors:	Hints:	C
To select the transformation	0	0

17. Answer

\forall r \in (\frac{27}{14}; \infty)

Methodical task:	Errors:	Hints:	C
To select the transformation	0	0

Analysis of math categories

Step

Errors:	Hints:	Mathematical categories
1	0	What is called an equation?
0	1	Let's multiply polynomials by each other, using the distributive law
0	1	Let's add up coefficients at the like terms
2	0	Let's solve linear equation(s), applying the addition and multiplication principles of equations equivalence
0	1	Using the addition principle of equivalence of inequalities, let us move the numeric addend from the left-hand side of the inequality to its right-hand side
0	1	Using the multiplication principle of equivalence of inequalities, let us divide both sides of the inequality by numerical coefficient at the argument
2	0	Let's factor quadratic trinomial(s), using the theorem of factorization of quadratic trinomial
2	0	Applying the main property of fractions, let us reduce fractional expression by the linear nonzero polynomial (expression of the form "ax+b")
0	1	Let's combine polynomials, using the definition of operation of addition
0	1	Let's collect similar terms of polynomial
0	1	Let's multiply both sides of inequality by "-1"
0	1	Let's apply the method of intervals to the obtained inequality
0	1	Let's divide both sides of inequality by the greatest common divisor of coefficients of polynomial forming the inequality

More...

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