summative assessment i - studiestoday · delhi public school assignment booklet indirapuram,...

DELHI PUBLIC SCHOOL Assignment Booklet

Indirapuram, Ghaziabad (Class - IX : MATHS)

#1#

SYLLABUS

SUMMATIVE ASSESSMENT I

S. No. Chapter‟s Name

(i) Number Systems

(ii) Heron’s Formula

(iii) Polynomials

(iv) Lines and Angles

(v) Coordinate Geometry

(vi) Triangles

(vii) Euclid’s Geometry

SUMMATIVE ASSESSMENT II

S. No. Chapter‟s Name

(i) Areas of Parallelograms and Triangles

(ii) Linear Equations in two Variables

(iii) Surface Areas and Volumes

(iv) Quadrilaterals

(v) Probability

(vi) Circles

(vii) Constructions

(viii) Statistics

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CHAPTERS

Chapter 1 : Number Systems Contents :

Introduction Irrational Numbers Real Number and their decimal expansions Representing real numbers on the number line Operations on real numbers Laws of exponents for Real numbers

Learning Objectives After studying contents students will be able to apply mathematical knowledge and skills to solve problems by developing abilities to analyse, think and reason to rationalize the denominator and simplify the surd.

Key Terms (i) Terminating and Non terminating Decimals (ii) Simplest Rationalizing Factor.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 2 : Heron‟s Formula Contents :

Introduction Area of triangle - by Heron’s formula Application of Heron’s formula in finding area of quadrilaterals. Learning Objectives

To help the students to select the appropriate method for the solutions of the problems

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 3 : Polynomials Contents :

Introduction Polynomials in one Variable Zeroes of a polynomial Remainder Theorem Factorization of Polynomials Algebraic Identities

Learning Objectives

To develop understanding of basic algebra skill. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



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Chapter 4 : Lines and Angles Contents :

Introduction Basic terms and definitions

Intersecting lines and non intersecting lines Pairs of angles Parallel lines and a transversal Lines parallel to the same line Angle sum property of a triangle

Learning Objectives

To develop the ability to articulate logically.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 5 : Coordinate Geometry

Contents :

Introduction Cartesian System

Plotting a point in the Plane if its coordinates are given

Learning Objectives

To make the students understand and develop understanding in the Cartesian System.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 6 : Triangles Contents :

Introduction Congruency of Triangles

Criteria for congruency of Triangles Some properties of a Triangle Some more criteria for congruence of triangles Inequalities in a triangle

Learning Objectives

To acquire the knowledge and understanding of the terms, symbols, concepts, principles etc.

Key Terms

Alternate and corresponding angles

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



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Chapter 7 : Introduction to Euclid‟s Geometry Contents :

Introduction Euclid’s definitions, Axioms, Postulates Equivalent versions of Euclid’s fifth Postulate

Learning Objectives

To make the students understand the Axioms and Postulates given by Euclid.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 8 : Areas of Parallelograms and Triangles Contents :

Figures on the same base and between the same parallels Parallelograms on the same base and between the same parallels

Triangles on the same base and between the same parallels

Learning Objectives

After studying the contents students will be able to apply mathematical knowledge and skills to solve problems by developing abilities to analyse, think and reason.

Key Terms

Area of parallelogram and triangle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 9 : Linear Equation in two Variables Contents :

Introduction Linear equations

Solutions of a linear equation Graph of a linear equation in two variables Equation of lines parallel to x- axis and y- axis

Learning Objectives

To make the students understand and acquire the knowledge of solutions of linear equations.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 10 : Surface Areas and Volumes Contents :

Introduction Surface area of a cuboid and a cube

Surface area of a right circular cylinder



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Surface area of a right Circular cone Surface area of a sphere Volume of cuboid Volume of a cylinder Volume of a right circular cone Volume of a sphere

Learning Objectives

After studying the contents the students will be able to apply mathematical knowledge and skills to solve mathematical problems by developing abilities to analyse.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 11 : Quadrilaterals Contents:

Introduction Angle sum property of a Quadrilateral

Types of Quadrilateral Properties of a parallelogram Another condition for a Quadrilateral to be a parallelogram The Mid Point Theorem

Learning Objectives

To acquire the knowledge and understanding particularly by way of motivation and visualization of basic concepts terms, principles, symbols and underlying processes and skills.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 12: Probability Contents :

Introduction Probability – an experimental approach

Learning Objectives

To feel the flow of reasons while proving a result or solving the problem. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Chapter 13 : Circles Contents :

Introduction Circles and its related terms

Angle subtended by a chord at a point Perpendicular from the centre to a chord



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Circle through three points Equal chords and their distances from the centre Angle subtended by an arc of the circle Cyclic Quadrilaterals

Learning Objectives

To consolidate the mathematical knowledge and skills acquired at the upper primary stage.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 14: Constructions of Triangles Contents :

Basic Constructions Some Constructions of Triangle

Learning Objectives

To make children do constructions with ease.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Chapter 15: Statistics Contents :

Introduction Collection of data

Presentation of data Graphical representation of data Measures of central tendency

Learning Objectives

To acquire the skills of drawing graphs, reading charts etc. Also to acquire the knowledge of new terms, concepts and definition.

Key Terms

(i) Frequency (ii) Mean (iii) Mode (iv) Median

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



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ASSIGNMENTS

Chapter -1 NUMBER SYSTEM

Q.1. Convert the decimal numbers into the form p/q. (i) 18.48 (ii) 32.1235

Q.2. Find a rational and an irrational no. between.

(i) 9

3 and

6

5 (ii) 3 and 4

Q.3. If

2 3x then find the value of

(i) 1

xx

(ii) 22

1x

x

Q.4. Rationalise the denominator :

1429

27

Q.5. Express with rational denominator.

123

1

Q.6. Prove that

43

1

32

1

21

1 is rational.

Q.7. If = a + b √6 find the value of a & b.

Q.8. Find the simplest rationalization factor of 3

1

3

1

22

Q.9. Multiply (4√5 3√2) by (3√5 + 5√2) Q.10. What is the rationalization factor of

(i) 2 3 (ii) 2 5 3

(iii) 125 (iv) 37 2

(v) 4 25

=============================================

Chapter – 2 POLYNOMIALS

Q.1. Factorise :

(i) 1 + a + b + c + ab + bc + ca + abc

(ii) 2x (a + b) + 3y (6a + 6b) – 5z (3a + 3b)

(iii) x2 + y2 + 2 (xy + xz + yz)

(iv) x2 +

(v) a2 – b2 – c2 + d2 – 2 (ad – bc)

√2 + √3 3√2 2√3

4 x2



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#8#

(vi) x2 – 24x 180

(vii) (p + q)2 – 20 (p + q) – 125

(viii) 2x2 – +

(ix) (2a + 3b)3 – (2a – 3b)3

(x) 2√2a3 + 16√2b3 + c3 – 12abc

Q.2. Prove that : = 1

Q.3. If the polynomials px3 + 4x2 + 3x – 4 and x3 – 4x + p are divided by (x – 3) then the remainder in each case is the same. Find the value of p.

Q.4. Find the value of a if (x – a) is a factor of the polynomial

x6 – ax5 + x4 – ax3 + 3x – a + 2

Q.5. Find the values of a and b so that the polynomial x3 + 10x2 + ax + b is exactly divisible by (x – 1) as well as (x – 2).

Q.6. Factorise using factor theorem (i) y3 – 2y2 – 29y – 42 (ii) y3 – 7y + 6

Q.7. What must be added to 3 23 4 13x x x to obtain a polynomial which is exactly divisible by x – 3?

Q.8. What must be subtracted from 3 24 16 5x x x to obtain a polynomial which is exactly divisible by x + 5.

Q.9. If 3 22 6x ax bx has 1x as a factor and leaves a remainder 2 when divided by x – 2, find the value of ‘a’ and ‘b’.

Q.10. If both (x – 2) and 1

2x

are factors of 2 5 ,px x r show that p = r.

=============================================

Chapter – 3 CO-ORDINATE GEOMETRY

Q.1. Find the image of point (2, 5) under x-axis and y-axis.

Q.2. Plot the points A(6, 4), B(3, 3), C(2, 2). Join AB, BC and AC. What figure do you obtain?

Q.3. Plot the points A (4, 4), B (- 4, 4) and join OA, OB and BA. What figure do you obtain?

Q.4. Which of the following points lie on X-axis and which on Y-axis?

P (1, 1), Q (1, 0), R (0, 1), S (0, 0), T (-1, 0), U (4, 0)

5x 6

1 12

0.96 × 0.96 × 0.96 + 0.04 × 0.04 × 0.04 0.96 × 0.96 – 0.96 × 0.04 + 0.04 × 0.04



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Q.8. Find four solutions of the equation 2(x+3)3(y1)=0

=============================================

Chapter – 5 INTRODUCTION TO EUCLID‟S GEOMETRY

Q.1. Define :-

(i) Axioms (ii) Theorems (iii) Collinear Points (iv) Concurrent lines

Q.2. Differentiate between parallel lines and intersecting lines.

Q.3. Given two distinct points A and B, can there be a line that passes through A and B? How many such lines are there?

Q.4. If l and m are intersecting lines, l|| p and m || q, show that p and q also intersect.

Q.5. If line segments AB, AC, AD and AE are parallel to a line l, then points A, B, C, D and E are collinear. Is it true?

Q.6. Two lines which are both parallel to the same line, are parallel to each other. Prove it.

Q.7. Give the correct statement (if required)

(i) Two distinct points always determine a line.

(ii) The ray AB is same as ray BA . (iii) Only a single line may pass through a given point. (iv) Two lines are coincident if they have only one point in common.

Q.8. Name the following :-

(i) Any five line segments (ii) Any two rays (iv) Four collinear points (iv) A pair of non-intersecting lines

============================================= Chapter – 6 LINES AND ANGLES

Q.1. The measure of an angle is twice the measure of its supplementary angle. Find its measure.

Q.2. The sides BA and DC of a quadrilateral ABCD are produced. Prove that a+b=x+y if AB || DC.

Q.3. If two parallel lines are intersected by a transversal, then the bisectors of any pair of alternate interior angles are parallel.

C

A

B

D

P R

Q

L S

A B

a

C D

b

y

x



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#11#

Q.4. In the fig, BD || CE, find x, y, z.

Q.5. In fig, PQ || RS, find the value of x.

Q.6. In the fig, ∠1 = 600 and ∠2 = of a right angle. Prove that l || m.

Q.7. In fig, AB || CD, if ∠2 = (2x + 30), ∠4=(x + 2y) and ∠6 = (3y + 10) find 5 .

Q.8. In the fig PQ || MN, if the complement of ∠5 equals the supplement of ∠4, find

the measures of ∠4 & ∠5.

=============================================

B0

E0

C0

x0

z0

y0

1200

700

A0

P

R S

Q

400

O

•

• 800

x

2 3

A B

C D

1 2

3 4

5

8 7

6

P Q

M N

1 2

3 4

5

8 7

6

l

m

1

2

3



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#12#

Chapter – 7 TRIANGLES

Q.1. Prove that the medians of an equilateral ∆ are equal. Q.2. The sides EF, FD and DE of ∆DEF are produced in order forming three exterior

angles ∠DFP, ∠EDQ and ∠FER respectively, Prove that –

∠DFP + ∠EDQ + ∠FER = 3600.

Q.3. In a ∆ABC if 2A = 3B = 6C. Determine A, B and C

Q.4. Prove that the sum of any two sides of a triangle is greater than the third side.

Q.5. In ∆ABC, AD is the median. Prove that AB + AC > 2AD. Q.6. Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Q.7. In a ABC if A+B=1100 and B+C = 1320, then find A, B and C.

Q.8. In a ABC, AD is the perpendicular bisector of BC. Show that ABC is an isosceles

triangle in which AB = AC.

=============================================

Chapter – 8 QUADRILATERALS

Q.1. ABCD is a parallelogram. L and M are points on AB and DC respectively and AL=CM. Prove that LM and BD bisect each other.

Q.2. If ABCD is a quadrilateral in which AB || CD and AD = BC prove that A = B.

Q.3. ABCD is a parallelogram and X and Y are the midpoints of sides AB and DC respectively. Show that AXCY is a parallelogram.

A L

B

C D M

O

D

A B

C

X A B

C D Y



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#13#

Q.4. In ABC, AD is the median through A and E is the mid-point of AD. BE produced meets AC at F.

Prove that 1

3AF AC

Q.5. In a quadrilateral ABCD, CO and DO are the bisectors of C and D respectively.

Prove that COD=21

[A+B].

Q.6. ABCD is the parallelogram. AB is produced to E so that BE = AB. Prove that ED bisects BC.

Q.7. In a parallelogram ABCD, the bisector of A also bisects BC at P. Prove that AD=2AB.

Q.8. Two opposite angles of a parallelogram are (3x2)0 and (50x)0. Find the measure of each angle of the parallelogram.

=============================================

Chapter – 9 AREA OF PARALLELOGRAMS AND TRIANGLES Q.1. If the medians of a ABC intersect at G, show that

ar(AGB) = ar(AGC) = ar(BGC) = 3

1 (ar ABC)

Q.2. In ABC, D is the mid point of AB and P is any point on BC. If CQ||PD meets AB

in Q, prove that ar(BPQ)=21

ar(ABC)

Q.3. ABCD is a quadrilateral. Prove that – ar (∆ ABO) × ar (∆ CDO) = ar (∆ADO) × ar (∆ CBO)

Q.4. Prove that area of a rhombus = ½ × product of its diagonals.

Q.5. In a parallelogram ABCD, AB=8cm. The altitudes corresponding to sides AB and AD are respectively 4cm and 5cm. Find AD.

Q.6. Prove that area of an equilateral ∆ is equal to a2, where a is the side of the triangle.

=============================================

√3 4

A B

C D

O

A

B P

C

D

Q

A

F

B C

E

D



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#14# A B

C E D

Chapter – 10 CIRCLES

Q.1. AB and CD are two parallel chords of a circle, which are on opposite sides of the centre, such that AB = 10 cm, CD = 24 cm and the distance between AB and CD is 17 cm. Find the radius of the circle.

Q.2. Two equal chords AB and CD of a circle with centre O, when produced meet at point E. Prove that BE = DE and AE = CE

Q.3. O is the centre of the circle and PO

bisects the ∠APD.

Prove that AB = CD

Q.4. P is the centre of the circle. Prove that ∠XPZ = 2 (∠XZY + ∠YXZ)

Q.5. ABC is a triangle, in which ∠BAC = 300.

Show that BC is the radius of the circumcircle of ∆ABC, whose centre is O.

Q.6. If a side of cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle.

Q.7. Prove that the sum of the angles in the four segments exterior to a cyclic quadrilateral is equal to 6 right angles.

Q.8. ABCD is a parallelogram. The circle through A, B and

C intersects CD produced at E, prove that AE = AD.

A

C

O

B

D

E

.

Y

Z X

P

A

B C

O •

300

A B

C D

R

Q S

P

A

B

D

C

O

F E

P



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#15#

=============================================

Chapter – 11 CONSTRUCTIONS

Q.1. Construct a triangle ABC in which AB = 7 cm, BC + CA = 9 cm and ∠A = 450.

Q.2. Construct a ∆ABC in which BC = 5 cm, ∠C = 600, AC – AB = 1.5 cm.

Q.3. Construct a ∆ABC whose perimeter is 14 cm and B = 600 and C = 450

Q.4. Construct a ∆ABC in which BC = 5 cm, ∠B = 450. AB – AC = 2.8cm.

=============================================

Chapter – 12 HERON‟S FORMULA

Q.1. Find the area of a quadrilateral ABCD whose sides are 9 m, 40 m, 28 m and 15 m respectively and the angle between the first two sides is a right angle.

Q.2. If each side of a scalene triangle is tripled then prove that ratio of their area will be 1:9.

Q.3. Find the area of a trapezium whose parallel sides are 34cm, 20cm and the other sides are 13cm and 15cm.

Q.4. Find the area of a triangular field, the lengths of whose sides are 275 m, 660 m and 715 m. What is the cost of cultivating the field at the rate of Rs. 200 per hectare?

Q.5. The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. Find the length of perpendicular from the opposite vertex to the side whose length is 13 cm.

Q.6. The diagonals of a rhombus are 24cm and 10cm. Find its perimeter and area.

=============================================

Chapter – 13 SURFACE AREAS AND VOLUMES

Q.1. The length of a cold storage is double its breadth. Its height is 3 m. The area of its four walls is 108 m2. Find its volume.

Q.2. The total surface area of a solid right circular cylinder is 231cm2. Its curved surface

area is 3

2 of the total surface area. Determine the radius of its base and height.

Q.3. The area of the base of a right circular cylinder is 15400 cm2 and its volume is 92400 cm3. Find the area of the curved surface.

Q.4. A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises.

Q.5. A well 14 m inside diameter is dug 15 m deep. Earth taken out is spread all around to a width of 7 m to form an embankment. Find the height of the embankment.



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#16#

Q.6. A right circular cone is 8 cm high and the radius of its base is 2cm. The cone is melted and recast into a sphere. Determine the diameter of the sphere.

Q.7. A cylinder of radius 12cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball.

Q.8. A semicircular thin sheet of metal of diameter 28 cm is bent and an open conical cup is made. Find the capacity of the cup.

=============================================

Chapter 14 STATISTICS

Q.1. The daily earnings of 50 workers are given below.

Daily earnings in ` No. of workers

125 – 134 02 135 – 144 07 145 – 154 10 155 – 164 15 165 – 174 10

Draw a histogram to depict the given information.

Q.2. Find the value of ‘a’ if the mean of the following is 15.

x 5 10 15 20 25

f 6 a 6 10 5

Q.3. Find the median of first ten prime numbers.

Q.4. For what value of x is the median of the following data 34? The data is 20, 22, 27, 28, 32, x+2, 39, 40, 41, 50.

Q.5. Given for the data 11, 15, 17, x + 1, 19, x – 2, 3, the mean is 14. Find the value of x. Using the value of x, also find the mode of the data.

Q.6. Find the median of the following data: 19, 25, 59, 48, 35, 31, 30, 32, 51. If 25 is replaced by 52, what will be the new median?

Q.7. Construct a frequency polygon of the following data:

Age : 0–4 4–8 8–12 12–16 16–20 20–24 24–28 28–32 32–36 No. of

Person : 1 3 6 8 10 8 5 3 2

Q.8. The class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82. Determine

(i) Class size (ii) Class limits



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#17#

=============================================

Chapter – 15 PROBABILITY

Q.1. Find the probability that a number selected at random from the numbers 1 to 25 is not a prime number when each of the given number is equally likely to be selected.

Q.2. Find the probability of getting a number less than 5 in a single throw of a die.

Q.3. Two coins are tossed simultaneously. Find the probability of getting:

(i) two heads (ii) at least one head (iii) no head (iv) at most one head

Q.4. An urn contains 6 oranges, 7 apple and 11 mangoes. A fruit is drawn at random. What is the probability of drawing

(i) an orange (ii) a mango (iii) an apple or a mango (iv) not orange (v) not apple

Q.5. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing.

(i) an ace (ii) a face card

Q.6. Given below is the frequency distribution of wages of 30 workers in a factory.

Wages 110-130 130-150 150-170 170-190 190-210 210-230 230-250

No of Workers

3 4 5 6 5 4 3

A worker is selected at random. Find the probability that his wages are :-

(i) at least Rs. 150 (ii) at most Rs. 190 (iii) more than or equal to 150 but less than Rs. 210

Q.7. If the probability of winning a game is 0.3, what is the probability of losing it?

Q.8. On tossing three coins at a time, find.

(i) All possible outcomes (ii) Probability of 3 heads coming up (iii) Probability of at least one head coming up (iv) Probability of getting more tails than heads

============================================= ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=============================================



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#18#

VERY SHORT ANSWER QUESTIONS

Real Numbers

Q.1. Give two irrational numbers lying between 0.2 and 0.3

Q.2. Find x if 2 30 25 0.6

3x

Q.3. Multiply: 5√2, 2√10 & 3√15

Q.4. Solve: (− 5789 )0

Q.5. What is the rationalizing factor of : 5 732 zyx

Q.6. π being 22/7 not considered a rational number. Why?

Q.7. For what value of x 3x − 2= 4

Q.8. √0.9 = ________________.

Q.9. √3√64 = ________________.

Q.10. If a = cz, b = ax and c = by, show that xyz = 1

Polynomials

Q.1. Write the coefficient of x in 333

43

1

2 xx .

Q.2. Find the zero of the polynomial: p(x)=11−5x

Q.3. Evaluate: 102 × 98 without multiplying directly.

Q.4. Find the remainder when 4x3−12x2+14x−3 is divided by 2x−1

Q.5. Factorize: 2x4 − 32

Q.6. If a + b + c=0, find a3 +b3+c3

Q.7. What will be the degree of the resulting polynomial when 24 7 x and

32534 2 xx are multiplied?

Q.8. Factorize: 1− 4a2 + 4ab − b2

Q.9. Give the possible expression for the length and breadth of the rectangle with area

123525 2 aa

Q.10. Write a quadratic polynomial whose zeroes are 3 and 3 .

∛



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#19#

Co-Ordinate Geometry / Linear Equations

Q.1. Point of intersection of vertical and horizontal axis is known as ________________.

Q.2. If the abscissa and the ordinate are the same (not equal to zero), where will the point lie?

Q.3. A linear equation in one variable has ________________ solution/s.

Q.4. If (m, 2m+1) is a solution of the equation 4x+3y=8. Find the value of m.

Q.5. General equation of a line parallel to y axis is ________________.

Q.6. x−9=√5y is in the form ax + by + c = 0. Write the values of a, b, c.

Q.7. Write a solution of 7x−6y=8

Q.8. If the point is in 2nd Quadrant then the point will be of the form ________________, ________________.

Q.9. Point of intersection of lines 032 yx and 073 yx is origin (True/False)

Q.10. What must be the nature of x if (x, 4) lies on the line 3x+y=10?

Euclid‟s Geometry

Q.1. How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Q.2. In the given figure are have 1=3, 3=4, 2=4. Show that 1=2

Q.3. Write the number of dimensions of the following:

(i) Surface (ii) Line (iii) Solid (iv) Point.

Q.4. Name the book written by Euclid.

Q.5. Write Euclid’s five postulates. Lines And Angles

Q.1. Find the angle whose complement is itself.

Q.2. If one angle of a linear pair is acute, then its other angle will be ________________.

Q.3. It one angle of triangle is equal to the sum of the other two then which kind of a triangle is it?

Q.4. In the given figure if AB║CD. will a+b = x+y ?

y

x C D

b

A B

a

3 4

1 2



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#20#

Q.5. If two lines are intersected by a transversal, then the sum of interior angles on the same side of transversal is 1800 (True/False)

Q.6. If the measures of a pair of alternate angles are (6a−80˚) and (a+15˚). Find the value of a.

Q.7. Sum of all interior angles of any polygon of n sides is (n2)1800. (True/False)

Q.8. If the sum of two adjacent angles is 180˚, their non-common arms form a

________________.

Q.9. Find the angle if 5 times its complement is 24 less than twice of its supplement.

Q.10. In figure, if AOC +BOD + BOC = 338˚

Find AOD.

Triangles And Quadrilaterals

Q.1. In a ∆ PQR if R>Q then PQ<PR. (True/False)

Q.2. The point of concurrence of the median of a triangle is called ________________ of the triangle.

Q.3. In the given figure, name the line which is giving the shortest distance between a point O and a line AB.

Q.4. Are the ∆ ABC and ∆ PQR congruent?

If yes, name the congruence condition.

Q.5. How many parallelograms are there in the adjacent figure?

M N L A

O

B

B C

A

35˚ Q R

P

55˚

B C

A

R P

Q

•

•

A

D

B

C •

• O



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#21#

Q.6. What is the measure of each exterior angle of an equilateral triangle?

Q.7. In PQR, PS and RT are medians and SM || RT. Prove that QM = 4

1PQ

Q.8. If PQRS is a rhombus with PQR = 550, find PRS.

Q.9. Prove that a cyclic trapezium is always an isosceles trapezium.

Q.10. Consecutive angles of a parallelogram are ________________.

Probability

Q.1. In tossing a die, what is the probability of getting an odd number or a number less than 4?

Q.2. What is the probability of getting a prime number when a die is rolled once?

Q.3. What is the probability of having a boy in a family having two children?

Q.4. Probability of getting 5 Sundays in the month of January is ________________.

Q.5. Event of getting an even prime number from numbers 3 to 28 is named as ________________.

Q.6. How many possible outcomes are there if a coin is tossed thrice?

Q.7. If P (E) = 0.07, what is P (E)?

Q.8. P(A) + P( A ) = 1. (True/False)

Q.9. Find the probability of getting the sum as 9 when two dice are thrown simultaneously.

Q.10. A bag contains tickets which are numbered from 1 to 100. Find the probability that a ticket number picked up at random is a multiple of 7.

Area of Parallelograms And Triangles

Q.1. Name the two triangles equal in area.

B

C E

F

D

A

P

Q R S

M

T



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#22#

Q.2. If ar (∆ ADP) = 48cm2

and ar (∆ BCP) = 30cm2.

Find ar (║gm ABCD).

Q.3. Diagonals AC and BD of a trapezium ABCD intersect at O and AB||DC. Prove that ar(AOD) = ar(BOC)

Q.4. PQR is a triangle in which PS is median and A is any point on PS. Show that ar(PQA)=ar(PRA)

Q.5. The area of a parallelogram ABCD is 40cm2. If X be the mid-point of AD, find the area of AXB.

Circles

Q.1. If A, B, C and D are four points such that BAC = 450 and BDC = 450 then A, B, C, D are concyclic (True/False)

Q.2. In the given figure, O is the centre of the circle. Find BDC.

Q.3. From the given figure, find a.

Q.4. In the figure ABC = 450. Prove that OA OC.

Q.5. Two parallel chords of a circle whose diameter is 13 cm are respectively 5cm and 12cm. Find the distance between them if they lie on opposite sides of centre.

B

P D

A

C

A B

C D

O 300

700

A

B

C

O

P

Q R S

A

450

O a

400

600 .



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#23#

Statistics

Q.1. Find the mean of all the factors of 12.

Q.2. Out of a total of 15 observations, arranged in ascending order, the 8th and 9th observations are 25 and 27. What is the median?

Q.3. Find the modal marks:

Marks : 33 35 37 39 42 Frequency : 30 29 36 20 40

Q.4. For what value of x, is the mode of the following data 7?

3, 5, 6, 7, 5, 4, 7, 5, 6, (x+1), 8, 7

Q.5. 10 numbers are given as:

9.6, 10.0, 9.4, 10.3, 8.8, 9.1, 9.7, 10.2, 8.1, 9.8

Find the range.

Q.6. The class marks of a distribution are:

37.5, 42.5, 47.5, 52.5, 57.5, and 62.5

Find the class size & class limits of first class interval.

Surface Areas and Volumes

Q.1. The perimeter of one face of a cube is 28 cm. Find its surface area.

Q.2. The dimensions of a hollow box are 40 cm, 32cm and 16cm. Find the length of the longest rod that can be kept inside the box.

Q.3. The area of the flat surface of a hemisphere is 154cm2. Find its total surface area.

Q.4. Find the formula for the total surface area of the figure?

Q.5. Find the perimeter of an equilateral triangle when its area is 144√3 cm2.

=============================================~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=============================================

r

l



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#24#

MULTIPLE CHOICE QUESTIONS 1. Number System:

Q.2. If n=23×34×54×7, then the number of consecutive zeroes in n, where n is a natural number is

(i) 3 (ii) 2 (iii) 4 (iv) 5

Q.3. If x is a positive real number then 4 3 2x is

(i) x1/24 (ii) x1/6 (iii) x1/2 (iv) x1/20

Q.4. 32.0 expressed in the form q

p , where p&q are integers and q≠0 is

(i) 25

8

(ii) 90

29

(iii) 99

32

(iv) 199

29

Q.5. Value of (625)0.16 (625)0.09 is

(i) 25 (ii) 5

(iii) 125 (iv) 625.25

Q.6. Every rational number is

(i) A natural number (ii) A real number

(iii) A whole number (iv) None of these

2. Polynomial:

Q.1. Degree of a zero polynomial is (i) 0 (ii) 1

(iii) Any natural number (iv) Not defined

Q.2. A polynomial of degree 5 in x has at most

(i) 5 terms (ii) 10 terms

(iii) 6 terms (iv) 4 terms

Q.3. Zeros of the polynomial p(x)=x(x1)(x2) are

(i) 0, 1, 2 (ii) 0, 1, 2

(iii) 0, 1, 2 (iv) 0, 1, 2

Q.4. If a = 7, then degree of the polynomial p(x)=(xa)3+343 is

(i) 0 (ii) 2

(iii) 3 (iv) None of these

Q.5. If (x+1) is a factors of the polynomial p(x)=2x2+Kx, then K is equal to

(i) 3 (ii) 4

(iii) 2 (iv) 3



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#25#

3. Co-ordinate Geometry

Q.1. Point (0, 2) and (0, 2) lie

(i) On the x-axis (ii) On the y-axis

(iii) In the first quadrant (iv) In the third quadrant

Q.2. Ordinate of all the points on the y-axis is

(i) 1 (ii) 0

(iii) 1 (iv) Any number

Q.3. The perpendicular distance between of the point P(3, 4) from the x-axis is (i) 3 units (ii) 4 units

(iii) 1 unit (iv) 7 units

Q.4. Signs of the coordinates of a point in the 3rd quadrant are

(i) (+, +) (ii) (, +)

(iii) (+, ) (iv) (, )

Q.5. Number of quadrants of a Cartesian plane are

(i) 2 (ii) 4


4. Linear Equations in Two Variables:

Q.1. x=3, y=1 a solution of the linear equation

(i) x+y=3 (ii) 2x+y=3

(iii) x+2y=1 (iv) None of these

Q.2. Straight lines represented by linear equations x+y=2 and 5x3y=2 intersect at the point

(i) (1, 2) (ii) (1, 1)

(iii) (2, 1) (iv) (0, 0)

Q.3. Equation 2x y = 4 meets

(i) x axis at (4, 0) (ii) y axis at (0, 2)

(iii) x axis at (2, 0) (iv) y axis at (0, 4)

Q.4. If (2p1, p) is a solution of the equation 10x9y=12, the value of p is

(i) 1 (ii) 4 (iii) 2 (iv) 3

Q.5. Linear equation such that each point on its graph has its ordinate equal to twice its abscissa is

(i) x+y=2 (ii) y=2x

(iii) x=2y

(iv) xy=2



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#26#

5. Euclid‟s Geometry:

Q.1. In ancient India, the shapes of altars used for household rituals were (i) Square and rectangular (ii) Square and circular

(iii) Triangular and rectangular (iv) Square and triangular

Q.2. The number of interwoven isosceles triangles in sriyantra is (i) Seven (ii) Eight

(iii) Nine (iv) Ten

Q.3. Euclid derived his famous treatise “The Elements” into (i) 9 chapters (ii) 11chapters

(iii) 12chapters (iv) 13chapters

Q.4. Which of the following needs a proof? (i) Axiom (ii) Theorem

(iii) Definition (iv) Postulates

Q.5. The number of dimensions, a point has (i) None (ii) 1

(iii) 2 (iv) 3

6. Lines and Angles:

Q.1. The measures of an angle which is 260 more than its complement is

(i) 640 (ii) 320

(iii) 580 (iv) 1140

Q.2. If two complementary angles are in the ratio 2:3, then the angles are

(i) 580, 320 (ii) 500, 400

(iii) 560, 340 (iv) 360, 540

Q.3. In the given figure, if l ||m, then x =….. (i) 1450 (ii) 1250


Q.4. The value of x that will make POQ a straight line is

(i) 30 (ii) 25 (iii) 35 (iv) 40

l

m y x

550

Q

O

B

P (3x)0 (2x+30)0



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#27#

Q.5. If l || m and n m then the measure of P is

(i) 350 (ii) 550 (iii) 750 (iv) 650

7. Triangles:

Q.1. In triangles ABC and PQR, AB=QR, C=P, B=Q. The two triangles are

(i) Isosceles but not necessarily congruent (ii) Neither congruent nor isosceles. (iii) Isosceles and congruent. (iv) Congruent but not isosceles.

Q.2. In PQR if R>Q then (i) QR>PR (ii) PQ>PR

(iii) PQ<PR (iv) QR<PR

Q.3. In ABC, we have (i) AB>BC (ii) AB+AC>BC

(iii) AB+AC=BC (iv) None of these

Q.4. In ABC, A=1000, B=300 and C=500, then (i) AB>AC (ii) AB<AC

(iii) BC<AC (iv) AB+AC=BC

Q.5. The perimeter of a triangle is (i) Equal to the sum of its altitude (ii) Greater than the sum of its altitudes (iii) Less than the sum of its altitudes (iv) None of these

8. Areas of Parallelograms and Triangles

Q.1. The median of a triangle divides it into two –

(i) Congruent triangles (ii) Isosceles triangles

(iii) Right triangles (iv) Triangles of equal areas.

1250 m

l

n

P



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#28#

Q.2. Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is

(i) 1:2 (ii) 2:1

(iii) 1:1 (iv) 3:1

Q.3. ABCD is a parallelogram. P is any point on CD. If ar (DPA)=15cm2 and ar(APC)=20cm2, then ar (APB) is

(i) 15cm2 (ii) 20cm2

(iii) 35cm2 (iv) 30cm2

Q.4. If AD is a median of ABC and P is a point on AC such that

ar (ADP): ar (ABD)= 2:3, then ar (PDC): ar (ABC) is

(i) 2:5 (ii) 1:6 (iii) 1:5 (iv) 3:5

Q.5. D and E are mid points of BC and AD respectively. If ar (AEC)=4cm2, then ar(BEC) is (i) 6 cm2 (ii) 12 cm2 (iii) 8 cm2 (iv) 4 cm2

9. Quadrilaterals:

Q.1. In a quadrilateral ABCD, if AB=BC and CD=DA, then quadrilateral ABCD is a

(i) Trapezium (ii) Rhombus

(iii) Kite (iv) Parallelogram

Q.2. In quadrilateral ABCD, if A=600 and B:C : D=2:3:7, then D=……. (i) 1750 (ii) 1350

(iii) 1500 (iv) None

Q.3. If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to (i) 16 cm (ii) 15 cm

(iii) 20 cm (iv) 17 cm

Q.4. If the angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a

(i) Rhombus (ii) Trapezium

(iii) Square (iv) Any parallelogram

A

P

C D

B

A

E

B C D



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#29#

Q.5. AD is the median of ABC. E is the midpoint of AD. BE produced meets AC at F. If AC=10.5 cm, then the length of AF is

(i) 3 cm (ii) 3.5 cm

(iii) 2.5 cm (iv) 5 cm

10. Circles:

Q.1. O is the centre of the circle. If 21ˆˆˆ lll , then

(i) x>z (ii) x<y (iii) x+y=2z (iv) None of these

Q.2. O is the centre of the circle, AB is a chord of the circle. OM AB. If

AB=20cm, OM= 112 cm, then radius of the circle is

(i) 15 cm (ii) 10 cm (iii) 12 cm (iv) 11 cm

Q.3. The value of x in the given figure is (i) 350 (ii) 450 (iii) 250 (iv) 300

Q.4. If a straight line APQB is drawn to cut two concentric circles, then (i) AP>BQ (ii) AP=BQ (iii) AP<BQ (iv) AQ>PB

Q.5. Angle formed in minor segment of a circle is

(i) An acute angle (ii) An obtuse angle

(iii) A right angle (iv) A straight angle

11. Constructions:

Q.1. LM is an arc of a circle having radius = r. If AL=AM=AN=LM=r and

LN=2

1LM, then CAB=

(i) 600 (ii) 450 (iii) 300 (iv) 150

O

M A B

• B A

O

P Q

B •

C •

A

M N

L

l1 l2

l

x y z

o

B

A

C

D

O

1100

x



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#30#

Q.2. If BAC=900, BAD=CAD and DAE=CAE. Then BAE=…. (i) 650 (ii) 750

(iii) 672

1 0

(iv) None of these

Q.3. With the help of a rules and compass, it is not possible to construct an angle of

(i) 7.50 (ii) 82.50

(iii) 350 (iv) 67.50

12. Heron‟s Formula:

Q.1. The length of each side of an equilateral triangle having an area of 325cm2 is

(i) 25 cm (ii) 5 cm

(iii) 10 cm (iv) 15 cm

Q.2. The area of a triangle with base 8 cm and height 10 cm is

(i) 80 cm2 (ii) 40 cm2

(iii) 20 cm2 (iv) 18 cm2

Q.3. If the side of an equilateral is 4 cm, then its area is

(i) 316 cm2

(ii) 34 cm2

(iii) 312 cm2

(iv) 38 cm2

Q.4. In a triangle the sides are 9 cm, 28 cm and 35 cm. The area of the triangle is

(i) 630 cm2

(ii) 636 cm2

(iii) 2108 cm2 (iv) None of these

Q.5. The area of an equilateral triangle of side „a‟ is given by (i)

2

3a2

(ii) 3

2a2

(iii) 3

4a2

(iv) 4

3a2

B A

C E

D



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#31#

13. Surface Areas and Volumes:

Q.1. The number of 6 m cubes that can be formed from another cuboid measuring 18m × 12m × 9m is

(i) 9 (ii) 10 (iii) 12 (iv) 15

Q.2. The radius of a sphere is 2r, then its volume will be –

(i) 3

3

4r

(ii) 4 r3

(iii) 3

3

32r

(iv) 3

3

8r

Q.3. The total surface area of a cone whose radius is 2

r and slant height is 2l

is

(i) 2 r l

(ii) r (l + r)

(iii) r (l + 4

r)

(iv) 2 r (l + r)

Q.4. The curved surface area of a right circular cylinder which just encloses a sphere of radius r is

(i) 2r2

(ii) 4r2

(iii) 8r2

(iv) 6r2

Q.5. If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is

(i) 6 : (ii) : 6

(iii) 4 : (iv) : 4

14. Statistics:

Q.1. The range of the data 20, 8, 20, 18, 16, 15, 30, 12, 22, 6, 11, 17, 25, 32, 10, 19 is (i) 16 (ii) 18 (iii) 15 (iv) 26

Q.2. The mean of the data x1, x2, …., xn is 102, then mean of the data 5x1, 5x2,…,5xn is

(i) 102 (ii) 204 (iii) 606 (iv) 510

Q.3. The mean of the data x1, x2,…,xn is „a‟. Then the mean of the data x1+a, x2+a,…, xn+a is

(i) ‘a’ (ii) 2a (iii) a2

1 (iv) a2

Q.4. Let m be the mid point and l be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is



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#32#

(i) 2m+l

(ii) 2ml (iii) ml

(iv) m2l

Q.5. One of the sides of a frequency polygon is (i) The x-axis (iii) The y-axis (ii) Either of the coordinate axes (iv) Neither of the coordinate axes

15. Probability:

Q.1. The probability of an impossible event is (i) 1 (ii) 0

(iii) Not defined (iv) Negative

Q.2. The probability of a sure event is (i) 1 (ii) 0

(iii) Not defined (iv) Negative

Q.3. The total probability of an event of a trial is (i) 1 (ii) 0 (iii) Not defined (iv) Between 0 and 1 (both inclusive)

Q.4. In n trials of a random experiment, if an event E happens m times, then P(E) is equal to

(i) n

m

(ii) m

n

(iii) nm

m

(iv) nm

n

Q.5. Two coins are tossed simultaneously. Then, the probability of getting at least one head is

(i) 4

3 (ii)

4

1 (iii)

3

1 (iv) 1



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# 33 #

Value Based Questions (Term - I)

Q.1 How many rational or irrational numbers are there between any two rational numbers and irrational numbers? What values you conclude?

Solution : There are infinitely many rational / irrational numbers between any two rational / irrational numbers.

Values : • We should have a nature of accommodating infinite happenings between any two parts of society or life which increase the tendency of accepting and accommodating.

Q.2 Mr. Dass bought few mangoes from market where x € N, N 3. He distributed these mangoes among his son and daughter equal in number. {where x2- 4x + 4 is the product of mangoes to be distributed in two equal parts} Find share of each and values.

Solution : x2- 4x + 4 = (x - 2) (x - 2) So share of each is (x- 2).

Values : • Eating mangoes is good for health. • We should distribute equally without doing any partiality of gender.

Q.3 Find the image of point (2, 3) under the line x axis. How it relate to values.

Solution : Image of point (2, 3) under x axis is (2, -3).

Values : • Life is a part of two coins one positive and other negative so always look its both faces and live it.

Q.4 How many coordinate are there whose sign can not be changed? Also deduce value.

Solution : Origin (0, 0)

Values : • One can never change the truth. Q.5 A farmer has piece of land in the form of an scalene triangle. He want to distribute

it into three equal parts one to his son second to his daughter and rest for a park. Explain how will he do it and also write value learned.

Solution : Let ABC is the field of farmer to divide into 3 equal parts he will draw three medians AD, BE and CF. These three median meet at G so area AGB = arBGC = ar AGC.



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# 34 #

Values : • Equality of shares for both boys and girls is a good positive thought for society. • Keeping reserve place for park so that multiuse of park can be made for children youngsters and old persons for their activities.

Value Based Questions (Term - II) Q.1 What happens to the graph of line 2x + y = 3. If this equation is multiplied by 2

and if this equation is divided by 3. What values are reflected? Solution :

Graph of equation in both situations will remain same as it was of original equation 2x + y = 3.

Values : • We should not change our path of morality, duty and dedication if situation is changed uniformly.

Q.2 From a quadrilateral ABCD a teacher asked the students to cut out a piece in the shape of parallelogram so that its area is half of the area of quadrilateral. Deduce values.

Solution :

In the figure ABCD is a quadrilateral P, Q, R and S are mid points of sides AB, BC, CD and DA respectively. Then the shape PQRS will be a parallelogram whose area is half of area of quadrilateral ABCD.

Values :

• Geometry give such skills to a student so that each one can resolve the such situational problems.

Q.3 A father want to divide his plot of land which is in the shape of parallelogram into 4

equal parts to his son, daughter, wife and Gram Panchayat. Explain how will he do it and also discuss the values. Solution :



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# 35 #

As shown in the figure a parallelogram can be separated into 4 equal parts.

arAOB = arBOC=arCOD = arAOD.

Values : • Thought of equal division to son and daughter without partiality of gender. • Kindness towards village Panchayat. • Making meaning of Mathematical use. • Developing skills of Maths.

Q.4 Name the shape which is required for running each type of mode of transportation.

Solution : Circle

Wheel of cycle, Bus, Truck, Bike or Aeroplane are always circular. Values : • Maths is the subject which gives the power of running. • Maths helps in technology. Q.5 Name the shape shown in the centre of our National flag . In how many parts it is

divided? Also explain the value shown.

Solution :

It is a circle (Ashok Chakra) divided into 24 spoke wheel. Values :

• It gives us inspiration of patriotism and keep telling us that we should be alret 24 hours for our self, our society and for our nation.

=============================================



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# 36 #

MODEL TEST PAPER SUMMATIVE ASSESSMENT – I (UNSOLVED)

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section-A

comprises of 8 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-

C comprises of 10 questions of 3 marks each and Section-D comprises of 10 questions of 4 marks

each.

(iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are required to select

one correct option out of the given four.

(iv) There is no overall choice. However, internal choices have been provided in 1 question of two marks,

3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of

the alternatives in all such questions.

(v) Use of calculator is not permitted.

=========================================================================================

SECTION: ‘A’ Q.1 The decimal which represents the fraction

8

7 is :

(A) 0.775 (B) 0.875 (C) .0875 (D) 0.845

Q.2 Expression which represents a polynomial is :

(A) 156 2 xx (B) 13 2 xx (C) 213x

(D) 125 xx

Q.3 Value of 9596 is :

(A) 8120 (B) 8210 (C) 9210 (D) 9120

Q.4 One of the factor of 8a3 b3 12a2b + 6ab2 is :

(A) (2a b) (B) (8a b) (C) (2a + b) (D) (8a + b)

Q.5 In the given figure, the value of x for which AOB is a straight line is:

(A) 500 (B) 300 (C) 400 (D) 600

Q.6 In the given figure ABC is isosceles triangle in which AB = AC. If measure of B = 500,

then measure of A is:

(A) 500 (B) 1300 (C) 800 (D) 700 Q.7 The point (0, 5) lies:



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# 37 #

(A) on the x-axis (B) on the y-axis (C) in the II quadrant (D) in the IV quadrant

Q.8 Co-ordinates of the origin are:

(A) (0, 1) (B) (1, 0) (C) (0, 1) (D) (0, 0)

SECTION B

Q.9 Find the product of 252325 .

Q.10 Find the remainder when 2x2 x + 1 is divided by 2x + 1.

Q.11 Without actually calculating the cubes, find the value of (8)3 + (15)3 + (7)3.

Q.12 If a point C lies between A and B, such that AC = CB then prove that AC = 2

1AB.

Explain by drawing the diagram.

Q.13 In the given figure PQ||RS, PAB = 700 and ACS = 1000. Find the measure of BAC

and CAQ.

OR

In the figure, PT is the bisector of QPR in PQR and PS QR. Find the value of x,

when PQS = 500 and PRT=300.

Q.14 The longest side of a right triangle is 90 cm and one of the remaining two sides is 54

cm. Find its area.

SECTION C

Q.15 Evaluate : 223825

OR

Find the values of a and b if : 2246

246ba

Q.16 If 5131 32842 xx , find the value of x.

Q.17 Factorise : 3223

27

1

6

1

4

1

8

1babbaa

OR

If 92 y

x and 4xy find 8

33 y

x

Q.18 If (a + b + c) = 15, (ab + bc + ca) = 35 find a2 + b2 + c2.



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# 38 #

Q.19 In the given figure, AC||DE and AD||CE find x and y, when it is given that

BAC=700 and DEC=550.

OR

In the given figure AB||CD, BAC = 720 and CEF = 400. Find CFE.

Q.20 If diagonal AC of a quadrilateral ABCD bisects A and C, then prove that AB = AD and CD = CB.

Q.21 In the figure, prove that CD + DA + AB + BC > 2AC.

Q.22 In figure PS = PR, TPS = QPR. Prove that PT = PQ.

Q.23 In the given figure, CBF = 1000, DCB = 450 and BDA = 1100. Find the measure of

ABD, DCE and BAC.

Q.24 A field is in the shape of a trapezium, whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.



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# 40 #

MODEL TEST PAPER

SUMMATIVE ASSESSMENT – I (SOLVED)






each.



(iv) There is no overall choice. However, internal choices have been provided in 1 question of two marks,

3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of

the alternatives in all such questions.


==========================================================================================

SECTION: ‘A’ Q.1 A real number which has a terminating decimal expansion is :

(A) 125

31 (B)

455

64 (C)

343

8 (D)

30

11

Q.2 The zeroes of the polynomial x2 2x are :

(A) 0, 0 (B) 0, 2 (C) 0, 2 (D) 2, 2

Q.3 The remainder when the polynomial p(x) is divided by 2x 5 is :

(A) p(5) (B) p(5) (C) p

2

5 (D) p

5

2

Q.4 If a + b + c = 0, then a3 + b3 + c3 is equal to :

(A) 0 (B) abc (C) 2abc (D) 3abc

Q.5 In the figure, if POQ is a straight line, then POR is :

(A) 200 (B) 600 (C) 1000 (D) 1200

Q.6 Which of the following is not a criterion for congruence of triangles :

(A) SAS (B) ASA (C) SSA (D) SSS

Q.7 The abscissa of the point (2, 7) is :

(A) 2 (B) 7 (C) 2 (D) 7



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# 41 #

Q.8 The co-ordinates of a point whose ordinate is 3 and which lies on y-axis are :

(A) (0, 3) (B) (0, 3) (C) (3, 0) (D) (3, 0)

SECTION B

Q.9 Find the value of 23333 321 .

Q.10 For what value of m, is the polynomial x3 2mx2 + 16 divisible by (x + 2) ?

Q.11 Without actually calculating the cubes, find the value of (12)3 + (7)3 + (5)3.

Q.12 In the figure, if PR = QS, then prove that PQ = RS.

Q.13 In the figure PQ and ST intersect at T. Find QOT :

OR

In the figure, PQ and RS intersect at the point T such that PRT = 400, RPT = 850 and

TSQ = 750. Find SQT.

Q.14 Find the area of a triangle whose, two sides are 8 cm and 11 cm and its perimeter is 32

cm.

SECTION C

Q.15 Find the values of a and b if : 2246

246ba

OR

Evaluate : 223825

Q.16 Represent 3.9 on the number line.

Q.17 Factorise : 5(2a + b)2 (2a + b) 4 OR

If p(x) = x3 + 3x2 2x + 4, find the value of p( 2) + p(1) + p(0)

Q.18 If the polynomial 3x3 + kx2 + 2x 3 leaves a remainder 5, when divided by x 2, find the value of k, using Remainder Theorem. Is x + 1 a factor of this polynomial?



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# 42 #

Q.19 In the figure, AB||CD, EF||DQ. Determine PDQ, AED and DEF.

OR

In the figure, if AD||BC, BAD = 620, BDC = 320 and DCE = 700, then find x, y and z.

Q.20 In the figure, ABCD is a quadrilateral such that AB = AD and AC is the bisector of the

angle A. Show that ABC ADC and BC = DC.

Q.21 In the figure BC AB, DE AD and BC produced meets DE at E. If AB = DE and AC = CE, prove that

(i) CED = CAB (ii) BC = CD

Q.22 In figure PR > PQ and PS bisects QPR. Prove that PSR > PSQ.



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# 45 #

SOLUTION

SUMMATIVE ASSESSMENT – I

SECTION: ‘A’ Q.1 A Q.2 B Q.3 C Q.4 D Q.5 D Q.6 C Q.7 C Q.8 A

SECTION: ‘B’

Q.9 32 3 1

1 8 27 6216

Q.10 2 0 8 8 16 0p m

8 8 1m m

Q.11 12 7 5 0 If a + b + c = 0 3 3 3 3a b c abc

3 3 312 7 5 3 12 7 5

1260

Q.12 PR = QS PQ + QR = QR + RS PQ RS [If equals are sub from equal the wholes are equal]

Q.13 7 40 180 20x x OR

180 85 40 55PTR [Angle Sum] = QTS (vert. opp.)

180 3 180 60 120QOT x 50SQT

Q.14 3rd side = 32 8 11 = 13

2

a b cS

area S S a S b S c

8 11 13 3216

2 2S

16 16 8 16 11 16 13area

24 4 4 2 5 3 8 30cm

SECTION: ‘C’

Q.15 LHS 2

2

6 4 2 6 4 2 36 32 48 2

36 326 4 2



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# 46 #

68 48 22

4a b

68 48 22

4 4a b

68

174

a

48 22

412

b

b

OR

5 2 2 10 8 3 2 24

4 2 10 2 24 4 2 10 4 6

Q.16 9.3 on number line

Q.17 Let 2a b x 25 4 5 4 1x x x x

2 5 4 2 1a b a b

OR 2 8 12 4 4 12p

1 6; 0 4p p 2 1 0 22p p p

Q.18 2 5p

3 8 4 4 3 5 5k k 1 3 5 2 3 0p k+1 is not a factor

Q.19 CD||AB

AED = 430 DEF = 720 PDQ = DEF = 720 [corresponding s] OR x + 320 = 700 [ext ] x = 380 y + 320 = 700 [alt int] y = 380 z = 1800 62 y [angle sum] = 800

Q.20 In ABC, ADC AB = AD (given) BAC = DAC [AC is angle bisector] AC common ABC ADC (SAS) BC = DC (cpct)

Q.21 In CED, CAB

CDE = CBA (given 900) ED AB

givenEC AC



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# 47 #

CED CAB (RHS) CED = CAB BC = CD by c.p.c.t.

Q.22 Given PR > PQ

1 = 2 T.P. 4 > 5 Soln PR > PQ 6 > 3 6 + 1 > 3 + 2 [ 1 = 2] 4 > 5 [4 = 1 + 6 5 = 2 + 3 ext ]

Q.23 EA AB EAB = 900

AEF = 900 [co int s] x = 650 CD || EF x + y = 1800 y = 1150

z = y = 1150 [corresponding s]

Q.24 Const. Draw BE || AD ABED is a ||gm ED = AB = 10m EC = 25 10 = 15m AD = BE = 14cm, BC = 13m In BEC ;

2

ar BEC S S a S b S c

a b cS

13 14 1521

2S

ar (BEC) = 21 21 13 21 14 21 15

= 7 3 8 7 6

= 27 3 4 84m

Let BF EC: 1

842

EC BF

2 84

15BF

ar(ABCD) =2

1 sum of parallel sides distance

287 21 2 8435 196

2 15 3m

SECTION: ‘D’

Q.25 2 1 3 2 4 3 5 4

2 1 3 2 4 3 5 4

1 5

6 5

1

2

3 4

P

Q R

S

A

D

E F C

B



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# 48 #

OR

5 3 3x 1 5 3 3 5 3 3

25 27 2x

22

2

1 12x x

x x

2

5 3 35 3 3 2

2

2

9 3 5 8 260 90 3

4 4

Q.26

3 3 34 24 2

4 2

3 5 5

2 3 2

3 3 33 5 5

2 3 2

8 27

127 8

Q.27 3 24 3 4p z az z z ; 3 4q x z z a

27 36 9 4 27 12 4a 26 26 1a a

Q.28 3 22 2 1p y y y y

1 0p y 1 is a factor

21 2 3 1p y y y y 1 2 1 1y y y

Q.29 2 1 5 1 6 1x x x x x

21 5 6x x x 21 3 2 6x x x x 1 3 2x x x

Q.30 R(4, 3)

Area = 9 unit2

Q.31 RS is a line

4 75 180b b [S on st line] 21 ; 4 84b b a (vert. opp.)

75 + b = 2c (vert. opp) C = 480 Q.32 Given: AB = AD, AC = AE

BAD = EAC To show : BC = DE Soln In ABC, ADE BAD + DAC = EAC + DAC BAC = DAE AB = AD, AC = AE given ABC ADE (SAS) BC = DE (cpct) OR



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# 49 #

In ABD, ACD AB = AC (given) ADB = ADC = 900 AD is common ABD ACD (RHS) BD = CD (cpct) In AED, AFD ADE = ADF = 900 AD is common ½BD = ½CD ED = DF [E & F are mid points] AED AFD (SAS) AE = AF (cpct) In ABE, ACF AB = AC, AE = AF, BE = CF [½BD = ½CD] ABE ACF (sss) BAE = CAF (cpct)

Q.33 In PQR, PSR PQ = PS, RQ = RS (given ) PR common PQR PSR (sss) ------- (i) QRP = SRP (cpct) ------- A In RQT, RST RQ = RS (given) RT common QRT = SRT from A RQT RST (SAS)

Q.34 Let AB & CD intersect at O

To prove 1 = 3, 2 = 4 Proof AB is a line 2 + 3 = 1800 [linear pair] 1 + 4 = 1800 CD is a line 1 + 2 = 1800 [linear pair] 3 + 4 = 1800

2+3 =3 + 4 2 = 4 1+4 =3 + 4 1 = 3 Hence proved

1

2

3 4

B

C

D

A

O



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# 50 #

MODEL TEST PAPER SUMMATIVE ASSESSMENT – II (Unsolved)

Time : 3hrs. Maximum Marks: 90






each.



(iv) There is no overall choice.


==========================================================================================

SECTION: ‘A’ Q.1 If 3 2 1x x , then x is equal to:

(A) 1

3 2 (B) 1

2 3 (C) 1 (D) 3 2

Q.2 The point (a, b) is the solution of the linear equation : (A) ax – by = a2 + b2 (B) ax + by = a2 + b2 (C) bx – ay = a2 – b2 (D) bx + ay = a2 + b2

Q.3 In figure, if BAC is an equilateral triangle. BDC is equal to:

(A) 100 (B) 600 (C) 1200 (D) 1400

Q.4 Sum of all interior angles of a quadrilateral is :

(A) 360° (B) 4 × (Right angle)

(C) 2 × (Straight) (D) All of these (A), (B) and (C)

Q.5 The ratio of volumes of two spheres is 1 : 8. The ratio of their surface areas is: (A) 1: 2 (B) 8:1 (C) 4:1 (D) 1:4

Q.6 Internal and external radii of a hollow wooden cylinder 10cm high are 4cm and 5cm respectively. The volume of material of the hollow cylinder is:

(A) 45 cu.cm (B) 9 cu.cm (C) 90 cu.cm (D) 900 cu.cm



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# 52 #

Q.17 The given figure shows a cyclic quadrilateral ABCD in which BAD = 750, ABD =

580and ADC = 770. Find BDC, BCD and BCA.

Q.18 Two parallel chords AB = 4 cm and CD= 6 cm are on opposite sides of the centre. If distance between AB and CD is 5 cm, find the radius of the circle.

Q.19 In the given figure, ABCD is a parallelogram in which DAC= 40°, BAC= 30° and

DOC= 95°. Find the measure of CDO.

Q.20 In the figure PQRST is a pentagon. A line through Q parallel to PR meets SR produced at F. Show that ar(PRQ) = ar(PRF)

Q.21 The total surface area of a ·cylinder is 6512 cm2 and the circumference of its base is

88cm. Find the volume of the cylinder. 22

7

Q.22 The radius and height of a right circular cone are in ratio 5 : 12. If its volume is 314

cm3, find slant height and curved surface area (use = 3.14)

Q.23 A die is thrown 500 times. The frequencies of the outcomes are recorded in the following frequency distribution table:

Outcome 1 2 3 4 5 6

Frequency 120 50 65 70 80 115

Find the probability of the occurrence of (a) a number between 3 and 6 (b) an even number (c) an odd

number

Q.24 Given below are the seats won by different political parties in the polling outcome of a state assembly election:

Political Parties A B C D E F

Seats Won 75 55 37 29 10 37

Draw a bar graph to represent the polling result



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# 53 #

SECTION D

Q.25 Present age of a woman is two years more than three times the age of her daughter. Write a linear equation to represent this statement. Draw its graph. If the daughter is 8 years old, what is the age of the mother?

Q.26 Draw the graph of the equation 2x + 4 = 3x + 1 in (i) one variable (ii) two variables.

Q.27 In the given figure, two circles intersect each other at A and B. The centre of the

smaller circle is O and lies on the larger circle. If PAC and PBD are straight lines and

APB = 70°, find AOB, ACB and ADB.

Q.28 Construct a PQR; in which QR = 3cm; Q = 60° and PQ + PR = 6cm. Name the type

of triangle.

Q.29 In the figure, ABCD is a parallelogram. Find ar(ADE) + ar(BEC).

Q.30 In the figure, LPEA is a parallelogram. Points M, N and O, are taken on LP such that LM = MN = NO = OP and AL||BM||CN||DO||EP prove that ar(OPR) = ar(ABF).

Q.31 A man divides his rectangular plot of length 204m and width 106m into four equal triangular plots and gives each triangular plot to his four sons. The third son decides to build a Health Centre on his plot but falls short of money. They youngest one sells his plot and gives him the money. Answer the following questions: (i) What is the area of the rectangular plot? (ii) How could the rectangular plot be divided into equal triangular plots and what is the

area of each plot? (iii) What value of the third son and the youngest son can be seen here?



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# 54 #

Q.32 The water for a factory is stored in a hemispherical tank whose internal diameter is 14m. The tank contains 50 kl of water. Water is pumped into the tank to full to its capacity. Calculate the volume of water pumped into the tank.

Q.33 An iron cone of diameter 8cm and height 12cm is melted and recast into spherical iron shots each of radius 4mm. How many shots are made?

Q.34 Draw a histogram representing the following frequency distribution.

Marks: 0-10 10-20 20-30 30-40 40-50 50-60

No. of students: 3 5 8 10 7 2



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# 55 #

MODEL TEST PAPER

SUMMATIVE ASSESSMENT – II (Solved)

Time : 3hrs. Maximum Marks: 90






each.



(iv) There is no overall choice.


==========================================================================================

SECTION – A

Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. Q.1

Q.2

Q.3



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# 56 #

Q.4

Q.5

Q.6

Q.7

Q.8

SECTION-B

Question numbers 9 to 14 carry two marks each.

Q.9

Q.10

Q.11



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# 57 #

Q.12

Q.13

Q.14

SECTION-C Question numbers 15 to 24 carry three marks each.

Q.15

Q.16

Q.17

Q.18

Q.19



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# 58 #

Q.20

Q.21

Q.22

Q.23

Q.24

SECTION-D Question numbers 25 to 34 carry four marks each.

Q.25

Q.26

Q.27

Q.28



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# 59 #

Q.29

Q.30

Q.31

Q.32 A well is 6m deep. The cost of plastering its inner surface at the rate of

`20 per m2 is `1320. Determine the diameter of the well.

Q.33



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# 60 #

Q.34

=============================================~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=============================================



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# 61 #

SOLUTION

SUMMATIVE ASSESSMENT – II

SECTION: ‘A’

Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1 (A) 2 (B) 3 (A) 4 (B) 5 (B) 6 (B) 7 (C) 8 (B)

SECTION: ‘B’

Question numbers 9 to 14 carry two marks each.



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# 62 #

SECTION: ‘C’

Question numbers 15 to 24 carry three marks each.



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# 63 #



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# 64 #



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# 65 #

SECTION: ‘D’

Question numbers 25 to 34 carry four marks each.



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# 66 #

Y

Y

X X



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# 67 #

BC]

m2



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# 68 #



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# 69 #

IMPORTANT FORMULAE

A. Algebraic Expression:

(i) (a + b)2 = a2 + b2 + 2ab

(ii) (a – b)2 = a2 + b2 – 2ab

(iii) (a2 – b2) = (a + b) (a – b)

(iv) (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(v) (a3 + b3) = (a + b) (a2 + b2 – ab)

(vi) (a3 – b3) = (a – b) (a2 + b2 + ab)

(vii) (a + b)3 = a3 + b3 + 3ab (a + b)

= a3 + b3 + 3a2b + 3ab2

(viii) (a – b)3 = a3 – b3 – 3ab (a – b)

= a3 – b3 – 3a2b + 3ab2

(ix) a3 + b3 + c3 – 3abc = (a + b + c) (a2 +b2 + c2 – ab – bc – ca)

(x) a3 + b3 + c3 = 3abc if a + b + c = 0

B. Heron‟s Formula : Area of triangle = √S (S – a) (S – b) (S – c)

Where, S =

C. Surface Area :

(i) Total Surface Area of a cube = 6a2

(ii) Total Surface Area of a Cuboid = 2 (lb + bh + hl)

(iii) Lateral Surface Area of Cube = 4a2

(iv) Lateral Surface Area of Cuboid = 2(l+b)h

(v) Curved Surface Area of Cylinder = 2πrh

(vi) Total Surface Area of Cylinder = 2πrh + 2πr2

(vii) Total Surface Area of a hollow Cylinder = 2πRh + 2π (R2 – r2) + 2 πrh

(viii) Curved Surface area of a cone = πrl (ix) Total Surface are of a cone = πr (l + r)

(x) Surface Area of a sphere = 4πr2

a + b + c 2



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# 70 #

(xi) Curved Surface Area of a hemisphere = 2πr2

(xii) Total Surface Area of a hemisphere = 3πr2

D. Volume :

(i) Volume of Cube = a3

(ii) Volume of cuboid = l × b × h

(iii) Volume of cylinder = πr2h

(iv) Volume of hollow cylinder = πR2h – πr2h = π (R2 – r2) h

(v) Volume of cone = πr2h

(vi) Volume of a Sphere = πr3

(vii) Volume of a hemisphere = πr3

(viii) Volume of Spherical shell (hollow sphere) = π (R3 – r3)

E. Mean :

x =

Probability :

P (E) =

O < P (E) < 1

P (not E) = 1 – P (E)

F. Median :

(i) When n is odd

Median = ( )th term

(ii) When n is even

( )th term + ( + 1)th term

2

1 3

4 3

2 3

4 3

∑fixi ∑fi

No. of favourable outcomes . Total no. of possible outcomes

n + 1 2

n 2

n 2

Median =



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# 71 #

IMPORTANT CONVERSIONS

Kilo

Hecto

Multiply Deca Divide

× 10 m/g/l ÷ 10

deci

centi

milli

For any conversion from upwards to downwards multiply in the multiple of 10 for every step and for any conversion from downwards to upwards divides in the multiples of 10 for every step respectively.

1 hectare = 10000 m2 1 are = 100 m2 1 litre = 1000 cm3 1 kilo litre = 1 m3 = 1000 litre

m/sec to km/hr => Multiply by ( )

km/hr to m/sec => Multiply by ( )

=============================================~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=============================================

18 5

60 × 60 1000

5 18

1000 . 60 × 60



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