, MATHEMATICS
EXEMPLAR PROBLEMS
Class XI
, FOREWORD
The National Curriculum Framework (NCF) – 2005 initiated a new phase of development
of syllabi and textbooks for all stages of school education. Conscious effort has been
made to discourage rote learning and to diffuse sharp boundaries between different
subject areas. This is well in tune with the NPE – 1986 and Learning Without Burden-
1993 that recommend child centred system of education. The textbooks for Classes
IX and XI were released in 2006 and for Classes X and XII in 2007. Overall the books
have been well received by students and teachers.
NCF–2005 notes that treating the prescribed textbooks as the sole basis of
examination is one of the key reasons why other resources and sites of learning are
ignored. It further reiterates that the methods used for teaching and evaluation will
also determine how effective these textbooks proves for making children’s life at school
a happy experience, rather than source of stress or boredom. It calls for reform in
examination system currently prevailing in the country.
The position papers of the National Focus Groups on Teaching of Science,
Teaching of Mathematics and Examination Reform envisage that the mathematics
question papers, set in annual examinations conducted by the various Boards do not
really assess genuine understanding of the subjects. The quality of questions papers is
often not up to the mark. They usually seek mere information based on rote memorisation,
and fail to test higher-order skills like reasoning and analysis, let along lateral thinking,
creativity, and judgment. Good unconventional questions, challenging problems and
experiment-based problems rarely find a place in question papers. In order to address
to the issue, and also to provide additional learning material, the Department of Education
in Science and Mathematics (DESM) has made an attempt to develop resource book
of exemplar problems in different subjects at secondary and higher-secondary stages.
Each resource book contains different types of questions of varying difficulty level.
Some questions would require the students to apply simultaneously understanding of
more than one chapters/units. These problems are not meant to serve merely as question
bank for examinations but are primarily meant to improve the quality of teaching/
learning process in schools. It is expected that these problems would encourage teachers
to design quality questions on their own. Students and teachers should always keep in
mind that examination and assessment should test comprehension, information recall,
, analytical thinking and problem-solving ability, creativity and speculative ability.
A team of experts and teachers with an understanding of the subject and a
proper role of examination worked hard to accomplish this task. The material was
discussed, edited and finally included in this source book.
NCERT will welcome suggestions from students, teachers and parents which
would help us to further improve the quality of material in subsequent editions.
Yash Pal
New Delhi Chairperson
21 May 2008 National Steering Committee
National Council of Educational
Research and Training
(iv)
EXEMPLAR PROBLEMS
Class XI
, FOREWORD
The National Curriculum Framework (NCF) – 2005 initiated a new phase of development
of syllabi and textbooks for all stages of school education. Conscious effort has been
made to discourage rote learning and to diffuse sharp boundaries between different
subject areas. This is well in tune with the NPE – 1986 and Learning Without Burden-
1993 that recommend child centred system of education. The textbooks for Classes
IX and XI were released in 2006 and for Classes X and XII in 2007. Overall the books
have been well received by students and teachers.
NCF–2005 notes that treating the prescribed textbooks as the sole basis of
examination is one of the key reasons why other resources and sites of learning are
ignored. It further reiterates that the methods used for teaching and evaluation will
also determine how effective these textbooks proves for making children’s life at school
a happy experience, rather than source of stress or boredom. It calls for reform in
examination system currently prevailing in the country.
The position papers of the National Focus Groups on Teaching of Science,
Teaching of Mathematics and Examination Reform envisage that the mathematics
question papers, set in annual examinations conducted by the various Boards do not
really assess genuine understanding of the subjects. The quality of questions papers is
often not up to the mark. They usually seek mere information based on rote memorisation,
and fail to test higher-order skills like reasoning and analysis, let along lateral thinking,
creativity, and judgment. Good unconventional questions, challenging problems and
experiment-based problems rarely find a place in question papers. In order to address
to the issue, and also to provide additional learning material, the Department of Education
in Science and Mathematics (DESM) has made an attempt to develop resource book
of exemplar problems in different subjects at secondary and higher-secondary stages.
Each resource book contains different types of questions of varying difficulty level.
Some questions would require the students to apply simultaneously understanding of
more than one chapters/units. These problems are not meant to serve merely as question
bank for examinations but are primarily meant to improve the quality of teaching/
learning process in schools. It is expected that these problems would encourage teachers
to design quality questions on their own. Students and teachers should always keep in
mind that examination and assessment should test comprehension, information recall,
, analytical thinking and problem-solving ability, creativity and speculative ability.
A team of experts and teachers with an understanding of the subject and a
proper role of examination worked hard to accomplish this task. The material was
discussed, edited and finally included in this source book.
NCERT will welcome suggestions from students, teachers and parents which
would help us to further improve the quality of material in subsequent editions.
Yash Pal
New Delhi Chairperson
21 May 2008 National Steering Committee
National Council of Educational
Research and Training
(iv)
