CBSE Continuous and Comprehensive Evaluation (CCE ... · stands for Continuous & Comprehensive...
Transcript of CBSE Continuous and Comprehensive Evaluation (CCE ... · stands for Continuous & Comprehensive...
FOR TERM 1
SEP. 2015
EXAMS
CBSE Continuous and Comprehensive Evaluation (CCE)
Published by :
Class
9
MATHEMATICSSUMMATIVE ASSESSMENT
& FORMATIVE
QUESTION BANKwith complete solutions
OUR DISTRIBUTORS
© Publisher
Typeset by : R.N. GraphicsPrinted by : Upkar Printing Unit
02
15
CONTENTS
iii
Syllabus v - viii
_______________________________________
1. Real Numbers 1 - 28
lTopic 1. Rational Number
lTopic 2. Irrational NumberthlTopic 3. n Root of Real Number
lTopic 4. Laws of Exponents with Integral Powers
lTopic 5. Rationalisation of Real Numbers
2. Polynomials 29 - 52
lTopic 1. Polynomials
lTopic 2. Remainder Theorem
lTopic 3. Factor Theorem
lTopic 4. Algebraic Identities
3. Introduction to Euclid's Geometry 53 - 63
lTopic 1. Euclid's Geometry
lTopic 2. Euclid's Postulates
4. Lines and Angles 64 - 89
lTopic 1. Different Types of Angles
lTopic 2. Transversal Line
lTopic 3. Angle Sum Property of a Triangle
5. Triangles 90 - 114
lTopic 1. Criteria for Congruence of Triangles
lTopic 2. Some Properties of Triangles
lTopic 3. Inequalities of a Triangle
6. Co-ordinate Geometry 115- 131
lTopic 1. Cartesian System
lTopic 2. Plotting a Point in a Plane
lTopic 3. Graph of Linear Equation
7. Areas 132- 147
lTopic 1. Area of Triangle
lTopic 2. Heron's Formula
lTopic 3. Application of Heron's Formula in finding Area of Quadrilaterals
_________________________________ 148 -168
Unit I : Number System
Unit II : Algebra
Unit III : Geometry
Unit IV : Co-ordinate Geometry
Unit V : Mensuration
Summative Assessment
Formative Assessment
PREFACE
iv
CBSE always believes in Global Trends of Educational Transformation. The CBSE
curriculum gets its lead from National Curriculum Framework – 2005 and Right to Free and
Compulsory Education Act – 2009. CBSE introduced CCE in the later half of 2009. CCE has
been started to improve the quality of Education and was meant to lessen the burden of
studies on Students. CCE stands for Continuous & Comprehensive Evaluation. The term
'Continuous' in CCE refers to periodicity and regularity in assessment and the term
'Comprehensive' refers to overall assessment of the learner, in both curricular & co curricular
scheme of things.
These Oswaal CCE Question Banks for Classes IX & X have been written so as to
supplement the need of the students to prepare for these progressive assessments at school
during the entire year.
CCE Question Bank has been divided into two parts: Formative assessment (FA) &
Summative Assessment (SA). Formative part of the book will assist the students to prepare for
the frequent class room based evaluation, both as an individual and as a group activity. The
various formative techniques include Quizzes, Chapter assignment, Work sheets, Projects,
Seminar, Symposium, Action Plans, etc. These activities have been elaborated by CBSE Board
on www.cbse.nic.in. The students can read through all these components while revising a
chapter to be always prepared for the surprise FA's in the class.
Question Bank is divided in 3 sections i.e. reading, writing & Grammar & Literature Reader
& Long Reading Text. Each section is updated and in line with CBSE guidelines and syllabus.
Our team has given special focus while writing for language based subjects, because this
subject is not only important from examination point of view but also improves day to day
communication through reading, writing and grammar skills. Solutions are always checked
twice and tried to make precise as per marking scheme. Practically, this book provides
students everything they need to learn. Since we believe in continuous improvement, hence
this book is updated, reviewed every year with new questions, changes in syllabus and
reader's suggestions.
At last we would like to thank our authors, editors, reviewers and specially students who
regularly send us suggestions which helps in continuous improvement of this book and
makes this book stand in the category of “One of the Best”. Wish you all Happy Learning.
For ENGLISH
CBSE always believes in Global Trends of Educational Transformation. The CBSE
curriculum gets its lead from National Curriculum Framework – 2005 and Right to Free and
Compulsory Education Act – 2009. CBSE introduced CCE in the later half of 2009. CCE has
been started to improve the quality of Education and was meant to lessen the burden of
studies on Students. CCE stands for Continuous & Comprehensive Evaluation. The term
'Continuous' in CCE refers to periodicity and regularity in assessment and the term
'Comprehensive' refers to overall assessment of the learner, in both curricular & co curricular
scheme of things.
These Oswaal CCE Question Banks for Classes IX & X have been written so as to
supplement the need of the students to prepare for these progressive assessments at school
during the entire year.
CCE Question Bank has been divided into two parts: Formative assessment (FA) &
Summative Assessment (SA). Formative part of the book will assist the students to prepare for
the frequent class room based evaluation, both as an individual and as a group activity. The
various formative techniques include Quizzes, Chapter assignment, Work sheets, Projects,
Seminar, Symposium, Action Plans, etc. These activities have been elaborated by CBSE Board
on www.cbse.nic.in. The students can read through all these components while revising a
chapter to be always prepared for the surprise FA's in the class.
Each chapter includes brief description and covers all typologies of Questions specified by
CBSE, with well-labelled and high quality figures / diagrams for easy and fast learning.
Solutions are always checked twice and tried to make precise as per marking scheme.
Practically, this book provides students everything they need to learn. Since we believe in
continuous improvement, hence this book is updated, reviewed every year with new
questions, changes in syllabus and reader's suggestions.
At last we would like to thank our authors, editors, reviewers and specially students who
regularly send us suggestions which helps in continuous improvement of this book and
makes this book stand in the category of “One of the Best”. Wish you all Happy Learning.
CBSE always believes in Global Trends of Educational Transformation. The CBSE curriculum
gets its lead from National Curriculum Framework – 2005 and Right to Free and Compulsory
Education Act – 2009. CBSE introduced CCE in the later half of 2009. CCE has been started to
improve the quality of Education and was meant to lessen the burden of studies on Students. CCE
stands for Continuous & Comprehensive Evaluation. The term 'Continuous' in CCE refers to
periodicity and regularity in assessment and the term 'Comprehensive' refers to overall assessment
of the learner, in both curricular & co curricular scheme of things.
These Oswaal CCE Question Banks for Classes IX & X have been written so as to supplement
the need of the students to prepare for these progressive assessments at school during the entire
year.
CCE Question Bank has been divided into two parts: Formative assessment (FA) & Summative
Assessment (SA). Formative part of the book will assist the students to prepare for the frequent class
room based evaluation, both as an individual and as a group activity. The various formative
techniques include Quizzes, Chapter assignment, Work sheets, Projects, Seminar, Symposium,
Action Plans, etc. These activities have been elaborated by CBSE Board on www.cbse.nic.in. The
students can read through all these components while revising a chapter to be always prepared for
the surprise FA's in the class.
Each chapter includes brief description and covers all typologies of Questions specified by
CBSE, with well-labelled and high quality figures / diagrams for easy and fast learning. Solutions
are checked twice and made precise as per the CBSE marking scheme. Practically, this book
provides students everything they need to learn. Since we believe in continuous improvement,
hence this book is updated, reviewed every year with new questions, changes in syllabus and
reader's suggestions.
At last we would like to thank our authors, editors, reviewers and specially students who
regularly send us suggestions which helps in continuous improvement of this book and makes this
book stand in the category of “One of the Best”. Wish you all Happy Learning.
MATHEMATICS
Class - IXFor Term I (April - September 2015)
v
Course StructureFIRST TERMTime : 3 Hours
II. ALGEBRA (Contd.) 23
III. GEOMETRY (Contd.) 17
IV. TRIGONOMETRY (Contd.) 08
V. PROBABILITY 08
VI. COORDINATE GEOMETRY 11
VII. MENSURATION 23
TOTAL 90
2 1Standard form of a quadratic equation ax + bx + c = 0, (a 0). Solution of the quadratic
equations (only real roots) by factorization, by completing the square and by using
quadratic formula. Relationship discriminant and nature of roots.
Problems related to day to day activities to be incorporated.
Motivation for studying Arithmetic Progression Derivation of standard results of finding ththe n term and sum of first n terms and their application in solving daily life problems.
Tangents to a circle motivated by chords drawn from points coming closer and closer to the
point.
(i) (Prove) The tangent at any point of a circle is perpendicular to the radius through the
point of contact.
(ii) (Prove) The lengths of tangents drawn from an external point to circle are equal.
(i) Division of a line segment in a given ratio (internally).
(ii) Tangent to a circle from a point outside it.
(iii) Construction of a triangle similar to a given triangle.
UNIT II : ALGEBRA (Contd.)
UNIT III : GEOMETRY (Contd.)
3. QUADRATIC EQUATIONS (15) Periods
4. ARITHMETIC PROGRESSIONS (8) Periods
2. CIRCLES (8) Periods
3. CONSTRUCTIONS (8) Periods
SYLLABUS
Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such
Factors and multiples. Zeros of a polynomial. State and motivate the Remainder Theorem with examples.
vi
... contd. Syllabus
UNIT IV : TRIGONOMETRY
UNIT V : STATISTICS AND PROBABILITY
UNIT VI : COORDINATE GEOMETRY
UNIT VII : MENSURATION
PRESCRIBED BOOKS :
3. HEIGHTS AND DISTANCES (8) Periods
2. PROBABILITY (10) Periods
1. LINES (In two dimensions) (14) Periods
1. AREAS RELATED TO CIRCLES (12) Periods
2. SURFACE AREAS AND VOLUME (12) Periods
Simple and believable problems on heights and distances. Problems should not involve
more than two right triangles. Angles of elevation / depression should be only 30°, 45°,
60°.
Classical definition of probability. Connection with probability as given in Class IX.
Simple problems on single events, not using set notation. '
Review the concepts of coordinate geometry done earlier including graphs of linear equations.
Awareness of geometrical representation of quadratic polynomials. Distance between two
points and section formula (internal). Area of a triangle.
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas
and perimeter / circumference of the above said plane figures. (In calculating area of segment
of a circle, problems should be restricted to central angle of 60°, 90°and 120° only. Plane figures
involving triangle, simple quadrilaterals and circle should be taken.)
(i) Problems on finding surface areas and volumes of combinations of any two of the
following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed
problems. (Problems with combination of not more than two different solids be taken.)
Mathematics - Textbook for class IX - NCERT Publication
Mathematics - Textbook for class X - NCERT Publication
Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication
Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication
A Handbook for Designing Mathematics Laboratory in Schools - NCERT Publication
Laboratory Manual - Mathematics, secondary stage - NCERT Publication
1.
2.
3.
4.
5.
6.
T
Area of cyclic Quadrilateral (with proof) - Brahma Gupta's Formula.
vii
... contd. Syllabus Q
ue
sti
on
Pa
pe
r D
esig
n F
orm
Ma
the
ma
tic
s
C
LA
SS I
X
Max. M
ark
s : 9
0T
IME
: 3
Ho
urs
(qu
esti
on
s o
f 10
Mar
ks)
.
viii
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
WRITING - NOTES
S U M M A T I V E SSA S S E S S M E N T
CHAPTER
1Real Numbers
SYLLABUS Review of representation of natural numbers, integers, rational numbers on the number line. Representation
of terminating/non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/terminating decimals.
Examples of non-recurring/non-termination decimals such as 2 , 3 , 5 etc. Existence of non-rational numbers (irrational numbers) such as 2 , 3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.
Rational numbers as recurring/terminating decimals. Existence of x for a given positive real number x (visual proof to be emphasized).
Definition of nth root of a real number. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by
particular cases, allowing learner to arrive at the general laws). Rationalisation (with precise meaning) of real numbers of the type (and their combinations).
1 + a b x
and 1
x + y, where x and y are natural numbers and a, b are integers.
INTRODUCTIONÅ Natural Numbers : Counting numbers are known as natural numbers, denoted by ‘N’.
N = {1, 2, 3, 4....... } Whole Numbers : All natural numbers together with ‘0’ (zero) form whole numbers, denoted by ‘W’.
W = {0, 1, 2, 3, 4, .......... } Integers : The collection of all whole numbers and negative of natural numbers are called integers, denoted by ‘Z’
or ‘I’.
Z Ior = {......... – 3, – 2, – 1}, 0, 1, 2, 3......,}
Negative Integers Zero Positive Integers
Real Numbers : All rational numbers and all irrational numbers taken together are known as real numbers, denoted by R. So, R = Q + Irrational numbers Irrational numbers = R – Q. In general, we can say that every real number can be represented by a unique point on the number line and vice
versa. Every point on the number line represents a unique real number.
UNIT-INumber System
2 ] OSWAAL CBSE CCE Question Bank (Term-1), Mathematics-IX
Number Line : On the right-hand side of 0, the points at distances of 1 unit, 2 units, 3 units etc. from 0 denote respectively the integers 1, 2, 3 etc.
Similarly, on the left side of 0, the points at distances of 1 unit, 2 units, 3 units etc. from 0 denote, respectively the integers –1, –2, –3 etc.
FLOWCHART
Real Number
Integer ( )Z
Whole Number ( )W
Natural Number ( )N
Non-TerminatingDecimal Number
Repeating DecimalNumber
Representation ofNumber on Real Line
RationalNumber ( )Q
IrrationalNumber
nth Root ofReal Number
Exponent ofReal Number Rationalisation
Topic-1Rational Number
QUICK REVIEWÅ Rational Number : A number ’r’ is called a rational number, if it can be written in the from p/q, where p and q are
co-prime integers and q ≠ 0, denoted by ‘Q’
For example :
12
, 34
, 45
, – 23
etc. are all rational numbers.
Symbolically, Q= , 0 and
pq p, q I
q
≠ ∈
Decimal Expansion of Real Numbers : The decimal expanation of real number used to represent a number on the number line.
If the decimal expansion of real number is either terminating or non-terminating recurring, than the real number called a Rational number.
Cases in Rational Number :
Case 1 : When Remainder becomes Zero— Every rational number
,pq
(q ≠ 0) can be expressed as a decimal. On
dividing p by q, when remainder becomes zero, then decimal is called terminating decimal.
e.g. : (i) 1
2 = 0.5
On dividing 1 by 2, we get value 0.5 i.e remainder equal to zero, so
12
is the terminating decimal.
(ii) 52
100= 0.52
On dividing 52 by 100, we get value 0.52 i.e remainder equal to zero, so
52100
is the terminating decimal.
Oswaal CBSE CCE Question Bank withcomplete solutions Mathematics For
Class 9 Term I April-Sep 2015
Publisher : Oswaal Books ISBN : 9789351274414 Author : Panel Of Experts
Type the URL : http://www.kopykitab.com/product/4252
Get this eBook
51%OFF