MMaatthheemmaattiiccss · 2018-10-01 · Preface CBSE always believes in Global Trends of...
Transcript of MMaatthheemmaattiiccss · 2018-10-01 · Preface CBSE always believes in Global Trends of...
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Content
Formative Assessment _______________________________________ 1 - 34
Note : For detailed study material of Formative Assessment log onto : www.cbse.nic.in
_______________________________________________Summative Assessment
1. Linear Equations in Two Variables 35 - 58
2. Quadrilaterals 59 - 82
3. Area of Parallelogram and Triangles 83 - 100
4. Circles 101 - 126
5. Geometric Construction 127 - 144
6. Surface Areas and Volumes 145 - 173
7. Probability 174 - 186
A One Day Trip of Four Friends 189 - 195
Health Camp in Dune Valley School 196 - 200
UNIT II : ALGEBRA (CONTD.)
UNIT III : GEOMETRY (CONTD.)
UNIT V : MENSURATION (CONTD.)
UNIT VI : STATISTICS AND PROBABILITY
OPEN TEXT BASED ASSESSMENT (OTBA)
Unit VII : Statistics will be tested in OTBA
only as specified by CBSE
Theme 1 :
Theme 2 :
(iii)
PrefaceCBSE 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.
Every Question Bank strictly follows the latest syllabus and pattern, and contains more
than sufficient questions and brief description of chapters, which help students in practicing
and completing the syllabus. 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.
–Publisher
(iv)
Syllabus (2014 - 15)Mathematics Class-IX
For Term II (October-March)
COURSE STRUCTURE
UNIT II : ALGEBRA (Contd.)
UNIT III : GEOMETRY (Contd.)
SECOND TERM Marks : 90
II. Algebra (Contd.) 16III. Geometry (Contd.) 38V. Mensuration (Contd.) 18VI. Probability 08VII Statistics 10
Note : The text of OTBA for SA-II will be from Unit - 7 statistics
2. LINEAR EQUATIONS IN TWO VARIABLES ( 1 4 )
Periods
Recall of linear equations in one variable. Introduction to the equation in two
variables. Prove that a linear equation in two variables has infinitely many solutions
and justify their being written as ordered pairs of real numbers, plotting them and
showing that they seem to lie on a line. Examples, problems from real life, including
problems on Ratio and Proportion and with algebraic and graphical solutions being
done simultaneously.
4. QUADRILATERALS ( 1 0 )
Periods
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal and conversely.
3. (Motivate) In a parallelogram opposite angles are equal and conversely.
4. (Motivate) A quadrilateral is a parallelogram and a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram the diagonals bisect each other and conversely.
6. (Motivate) In a triangle the line segment joining the mid-points of any two sides is
parallel to the third side and (motivate) its converse.
5. AREA ( 4 )
Periods
Review concept of area, recall area of a rectangle.
1. (Prove) Parallelograms on the same base and between the same parallels have the
same area.
2. (Motivate) Triangles on the same (or equal base) base and between the same
UNITS MARKS
TOTAL (Theory) 90
(v)
6. CIRCLES ( 1 5 )
Periods
Through examples, arrive at definitions of circle related concepts, radius,
circumference, diameter, chord, arc, secant, sector, segment subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate)
its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the
chord and conversely, the line drawn through the center of a circle bisecting a
chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given non-
collinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from
the center (or their respective centers ) and conversely.
5. (Prove) The angle subtended by an arc at the center is double the angle subtended
by it at any point on the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtends equal angle at two other
points lying on the same side of the line containing the segment, the four points lie
on a circle.
8. (Motivate) The sum of either of the pair of the opposite angles of a cyclic
quadrilateral is 180° and its converse.
7. CONSTRUCTIONS ( 1 0 )
Periods
1. Construction of bisectors of line segment and angles of measure 60°, 90°, 45° etc.
equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides
and one base angle.
3. Construction of a triangle of given perimeter and base angles.
2. SURFACE AREAS AND VOLUMES ( 1 2 )
Periods
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and
right circular cylinders and cones.
(12) Periods
History, Repeated experiments and observed frequency approach to probability.
Focus is on empirical probability. (A large amount of time to be devoted to group and
to individual activities to motivate the concept; the experiments to be drawn from real
- life situations and from examples used in the chapter on statistics).
(13) Periods
Introduction to Statistics : Collection of data, presentation of data – tabular form,
ungrouped / grouped, bar graphs, histograms (with varying base lengths),
frequency polygons, qualitative analysis of data to choose the correct form of
presentation for the collected data. Mean, median, mode of ungrouped data.
UNIT V : MENSURATION (Contd.)
UNIT VI : PROBABILITY
UNIT VII : STATISTICS
(vi)
Qu
esti
on
Pap
er D
esig
n F
or
Mat
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DE
No
. 04
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LA
SS
IX
(2
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-15)
(vii)
Max
. M
ark
s–90
(viii)(viii)
Writing - Notes 1.
2.
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4.
5.
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15.
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TERM - IIFormative Assessment
UNIT - II Algebra (Continued)
Linear Equations in Two Variables
TYPE (A) : ANALYSIS FROM GRAPHS
Q. 1. Study the given graph and answer the questions given below it :
B 4
3
2
1
0
A
C
D
-4 -3 -2 -1 2 3 4 5 6 7
-1
-2
-3
1
y
y'
xx'
2 + 3 = 6x y
O
1. Write the coordinates of points A, B, C and D. 2. Which type of graph it is ? 3. Can you find two more solutions of this equation ? 4. How many solutions of the given equation are possible ? 5. Name the triangle formed by given line and coordinate axes.Ans. 1. Coordinates of A can be obtained by substituting x = 0 in the equation of the given line, as the
point lies on the line. Hence, Equation of line is 2x + 3y = 6 ∴ 2 × 0 + 3 × y = 6, as x = 0 ⇒ 3y = 6 ⇒ y = 6/3 ⇒ y = 2. So, A is (0, 2).
CHAPTER
1
2| OSWAAL CBSE CCE Question Bank (Term-2), MATHEMATICS - IX
Similarly for point C, substitute y = 0, to get C (3, 0). However, the points can also be found out simply by observation. Hence, Coordinates of D and B are (6, –2) and (–3, 4) respectively. 2. This is the graph of linear equation. 3. Yes, for x = 1 : 2x + 3y = 6 ⇒ 2 × 1 + 3y = 6 ⇒ 3y = 6 – 2
⇒ y = 43
Also, for x = 2 : 2x + 3y = 6 ⇒ 2 × 2 + 3y = 6 ⇒ 4 + 3y = 6 ⇒ 3y = 6 – 4
⇒ y = 23
.
Hence two other solutions for the given equation are : (1, 4/3) and (2, 2/3). 4. There are infinite possible solutions of this equation. 5. The triangle formed by the given line and the coordinate axes is a right angled triangle OAC.
Q. 2. Study the given graph and answer the following questions :
4
3
2
1
01 2 3 4 5
-1
-2
-3
-4
A
B
C
D
E
F
y
y'
xx'
-4 -3 -2 -1
1. Write the coordinates of points A, B, C, D, E and F. 2. What would be the equation of this line ?Ans. 1. A(1, 1), B(2, 2), C(3, 3), D(–1, –1), E(–2, –2), F(–3, –3). 2. As the line passes through origin (0, 0) and the point A(1, 1), that means, the equation can be x = y; i.e., x – y = 0.
TYPE (B) : MCQ WORKSHEETChoose the Correct Option :
Q. 1. Which of the following is not a linear equation in two variables ? (A) ax + by = c (B) ax2 + bx = c (C) 2x + 3y = 5 (D) 3x + 2y = 6
Q. 2. The graph of ax + by + c = 0 is : (A) a straight line parallel to x-axis (B) a straight line parallel to y-axis (C) a general straight line (D) a line in the 2nd and 3rd quadrant
cont inue
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z #
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