GROUP 04
DIFFICULT AREA CONCEPT THEIR REMEDIES
Chapter / Content / Probable errors committed by students / RemediesChapter - I (Relationsand functions)
(i)Relations reflexive symmetric & Transitive
(ii)Transitivity
(iii)Bijectivity
(iv)EQUIVALNCE RELATIONS / •Students prove relations using numbers.
•Simplywrite without proof or
•Commit errors in proving the result
•While proving onto, Children do not consider domain properly.
•Confusion of use of counter example for proof or verification. / •Students should use the definition/ property of the relation.
•If (a,b) R & (b,c) ϵ R then relation is also transitive as transitivity is not contradicted here.
•More emphasis should be given on domain & range while teaching Bijectivity.
Use of counter example for verification and checking.
•Ex.
Chapter –II
(Inverse Trigonometricfunctions)
(i) Principal Value / •Students write directly
Sin -1(Sin ) = without understanding the concept of principal values.
- WriteSin -1(x) = (Sin x) -1
•Conversion in the principal value branch while it is given beyond the PVB (principal value branch). / •While teaching the concept of principal value, more stress focus should be given on principal value branches.
- (Sin x) -1 = 1/ Sinx
•The differencebetween solving and provingmust beexplained.
•In case > PVB subtract from π the given value and in case less than PVB add π.
•Conversion of one inverse trigonometric another inverse trigonometric ratio. / •Use right angled triangle
Method as into
•Suitable substitution from algebraic function to trigonometric function.
•Confusion between prove & determination of angle. / •
•
Name of Unit / Concept / Probable errors committed by students / Remedies
MATRICES & DETERMINANTS / Order / Taken rowas columnand column asrow / Make them understand row meanshorizontal, column means vertical, more suchproblems forpractice should be given.
Productof Matrices / Notmultiplying the firstmatrix row elementswith thesecond matrix correspondingcolumn elements and not adding correctly.
ccccccccorrectly / By giving tips like Run and Jumpremember while multiplying two matrices.More practice on various order matricesfor multiplication.
Transpose of aMatrix / Convertingboth column intorows and rowsinto columns. / Stress to be given only to change rowinto columns or vice versa but notboth.
Ad joint of a Matrix / Not getting correct cofactors with proper sign. / a) Proper concept/ technique to find cofactor of a Matrix.
b) Sufficient practice on finding Transpose of a Matrix.
Applying Rules / properties
finding Inverse / 1.Directly tryto expand the determinant.
2 (a).In finding Inverse by Elementary Operations – use both row & column
Operations.
(b) Commit the mistake in selecting the proper Identity ie
A=IA or A=AI.
(c) Finding A-1
using an identity. They do not use the identity & find A-1 using Co-factor method.
- Find difficultto convert word probleminto equations.
2(a) Through- outthe process of finding the Inverse by Elementary Transformations, either use row or columnoperations but not both.
(b) To find the Inverse of A by elementary row operations, use A=IA &
by elementary column operations, use A=AI.
(c) More emphasis on pre/post multiplication by A-1
Sufficient practice should be given.
Emphasis on verification of solutions.
INTEGRALS
ERRORS COMMITTED BYSTUDENTS:
1.Students get confused with differentiation and integrationformulas.
2.Students fail to identify the method , which they have toopt
3.In substitution method students find it difficult to substitutecorrectly.
4.Making perfect square while doing the problems of thetype∫ dx / (ax2 + bx +c),
5.Students take – ve sign out from the square rootsymbol
6.Students miss the constant of integration while writing the answer & forget to usedx whileintegrating.
7.Students find it difficult to identify and use the properties of definite integral.
8.Students make mistakes in computation while evaluating the definite integral as limitof sums.
MEASURES TO OVERCOMEERRORS (INTREGALS)
1.Conduct formula test daily - oral andwritten
2.Classification of problems based on different methods using different formulas shouldbe stressed.
3.Drilling up the same method and conduct slip testfrequently..
4.Giving sufficient number of problems forpractice.
5.Concept should be made very clear.
6.Stress to use constant of integration & write dx while integrating.
7.Concept of taking limitand summation formula should be madeclear.
ERROR ANALYSIS IN LINEARPROGRAMMING
Sl.No. / COMMON ERRORSCOMMITTED / SUGGETEDREMEDIES1 / Difficulty in converting word probleminto correspondingFunction. / Drilling in conversion ofdifferent kinds ofproblems.
2 / Wrong formation of the objectivefunction. / Drilling in conversion ofdifferent kinds of wordproblems.
3 / Wrong formation of theconstraints / Give emphasis on conversion ofword problems to mathematicalterms.
4 / Forget to write non negativityrestrictions / Reminding again andagain
5 / Unable to identify the feasibleregion. / Give sufficient practice.
6 / Wrong shading of the feasibleregion / Teacher insists the correctnesswith maximumpractice.
7 / If feasible region is unbounded , then unableto identlfy whether the half plane determinedby ax+by> M or ax+by< M has a point incommon with feasible region or not. / Give them more problems involvingsuch questions.
8 / Forget to write the finalanswer / Reminding again andagain.
9 / Forget to attempt the value basedquestion / Reminding again andagain.
ERROR ANALYSIS IN PROBABILITY
Sl.No. / COMMON ERRORSCOMMITTED / SUGGETEDREMEDIES1 / Unable to identify the question(whether independent events or Bayes’ theoremor Binomialdistribution) / More practice of questions ofvarious types.
2 / Difficulty in converting word probleminto mathematicalterms / Drilling in conversion ofdifferent kinds ofproblems
3 / Mistakes in identifying different ‘EVENTS’in Bayes’theorem / More practice of suchquestions
4 / Mistakes in identifying the probabilityof different events in Bayes’theorem / Drilling in suchproblems
5 / Computationalmistakes / More concentration andattention.
6 / Inability to find out the correct randomvariable / More practice of suchquestions
7 / Unable to form the probabilitydistribution table / More practice of suchquestions
8 / Unable to identifY the values of n , p , qin binomial distribution / More practice to begiven
9 / Forget to write the finalanswer / Emphasis on writing the finalanswer.
10 / Forget to attempt the value basedquestion / Reminding again andagain
GROUP-4
S No. / NAME OF PARTICIPANTS
1 / Smt. Kamala Tiwari
2 / Shri S L Namdeo
3 / Shri Ramesh Kumar Tripathi
4 / Shri R K Patkar
5 / Shri Anand Kumar Tiwari
6 / Smt. Sarita Singh
7 / Shri Raj Kumar Vishwakarma
8 / Shri D S Rai