MMaatthheemmaattiiccss · 2018-10-01 · Preface CBSE always believes in Global Trends of...

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Mathematics Mathematics OSWAAL BOOKS Published by :

Transcript of MMaatthheemmaattiiccss · 2018-10-01 · Preface CBSE always believes in Global Trends of...

MathematicsMathematics

OSWAAL BOOKSPublished by :

Our Distributors

Code : 0714

(ii)

© Publisher

Typeset by : Narendra DTP

Printed by : Aadhya Printers

09

09

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)

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(vii)

Max

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(viii)(viii)

Writing - Notes 1.

2.

3.

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6.

7.

8.

9.

10.

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12.

13.

14.

15.

16.

17.

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30.

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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