FORMATIVE ASSESSMENT-I [50 Marks] MCQ HOLIDAY …...Chapter: Visualising solid shapes (Maths Lab...

DELHI PUBLIC SCHOOL Assignment Booklet

Indirapuram, Ghaziabad (Class – VII : Mathematics)

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BREAKUP OF Formative Assessment MARKS =========================================================

FORMATIVE ASSESSMENT-I [50 Marks]

MCQ [20 Marks] LAB ACTIVITY [15 Marks (3 × 5)] HOLIDAY HOMEWORK [15 Marks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

FORMATIVE ASSESSMENT-II [50 Marks]

PEN & PAPER TEST [30 Marks] MCQ [10 Marks] CLASS PERFORMANCE/ NOTEBOOK ASSESSMENT [10 Marks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ FORMATIVE ASSESSMENT-III [50 Marks]

PEN & PAPER TEST [30 Marks] MCQ [10 Marks]

CONSTRUCTION TEST [10 Marks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

FORMATIVE ASSESSMENT-IV [50 Marks]

MCQ [20 Marks] PROJECT WORK [10 Marks] LAB ACTIVITY [15 Marks (10 + 5)] NOTEBOOK ASSESSMENT [5 Marks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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SYLLABUS

Summative Assessment-I

1. Integers 2. Fractions and decimals 3. Lines and Angles 4. The Triangle and Its Properties 5. Algebraic Expressions 6. Exponents and powers 7. Data Handling

Lab Activities (SA- I)

1. To find the product of two fractions. 2. To verify that the sum of the three angles of a triangle is 180°. 3. The sum of the square of the hypotenuse of a right angles triangle is equal to

the sum of the square of the other two sides. ------------------------------------------------------------------------------------------------------------------

Summative Assessment-II

1. Rational Numbers 2. Congruence of Triangle 3. Simple Equations 4. Comparing quantities 5. Practical Geometry 6. Perimeter and Area 7. Rotational Symmetry (Only Project Work)

Lab Activities (SA- II)

1. Visualising Solid Shapes 2. Project Work on Rotational Symmetry 3. To Determine Area Of a Circle



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Test Papers

1 MCQ Assignments 2 Model test paper – Summative Assessment I (Solved) 3 Model test paper – Summative Assessment I (Unsolved) 4 Model test paper – Summative Assessment II (Solved) 5 Model test paper – Summative Assessment II (Unsolved) 6 Worksheets

MODULES

Module – 1 Chapter – Integers Contents: Need of integers and their introduction Representation of integers on number line Properties of addition and subtraction of integers Additive identity Multiplication and division of integers

Properties of multiplication and division of integers.

Learning Objectives: Students develop understanding of integers and operation on integers. Develop skill in using and solving operation on integers.

Key Term: Additive inverse Absolute value Multiplication inverse Closure, Associative, Commutative and distributive properties. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Module – 2 Chapter – Fraction And Decimals Contents : Multiplication of a fraction by a whole number. Fraction as an operation ‘of’. Multiplication of a fraction by a fraction Division of whole number by a fraction Division of fraction by whole number Division of fraction by another fraction Multiplication of decimal numbers



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Division of decimal numbers Learning Objectives : Students learn about fractions and decimals along with the operation of

multiplication and division on fractions as well as on decimals.

Key Term : Proper fraction Improper fraction Mixed fraction ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Module – 3 & 4 Chapter - Lines And Angles Contents: Concept of point, line, line segment, ray, plane Complementary and Supplementary angles. Linear pair and vertically opposite angles Pairs of lines Angles made by a transversal Types of Angles

Checking of parallel lines

Key Terms: Adjacent angles Linear pair Vertically opposite angles Transversal Alternate interior angles Corresponding angles Chapter – The Triangle And Its Properties Contents :

Medians of a triangle Altitudes of a triangle Angle sum property of a triangle Exterior angle of a triangle and its property Sum of the length of two sides of a triangle

Pythagoras property



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Learning Objectives: Children acquire the concept of Pythagoras theorem and the use of it in daily

life situations.

Key Term : Median Altitude Exterior and Interior angles Hypotenuse Equilateral triangle and isosceles triangle Pythagoras Property ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Module – 5 Chapter – Algebraic Expressions Contents : Variables and Constant Factors of a term Coefficients Like and unlike terms Monomials, Binomials, Trinomials, and Polynomials Addition and subtraction of algebraic expressions Finding the value of an expression.

Learning Objectives : Students will understand the concept of addition and subtraction in algebra. Key Term : Variable and constant Coefficient Like term, Unlike term Monomial, Binomial, Trinomial

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Module – 6 Chapter – Exponents And Powers Contents:

Definition of exponents Positive exponent Laws of exponent



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Zero exponent Use of exponential notation in expressing large numbers and small numbers. (Scientific notation).

Learning Objectives : The students will acquire the basic knowledge of exponents. They learn how to express a rational number in its exponential form and to change a number into its power notation form.

Key Term : Exponent or index Base Power Power notation Exponential form

Reciprocal

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

Module – 7 Chapter – Data Handling Contents:

Definiion of Statistics Organization of data Reading of a given bar graph

Interpretation from a given bar graph

Learning Objectives:

Students learn recording and organization of data. They also acquire knowledge of use bar graphs in various daily life situations.

Key Terms:

Statistics Data Arithmetic mean Range

Mode Median Bar graph

Double bar graph



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

Module – 08

Revision for Half Yearly Examinations

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

Module – 09 Chapter – Rational Numbers Contents: Recall of fractions Definition of rational numbers Standard form of rational numbers Comparison of rational numbers Representation of rational numbers on the number line. Equality and order of rational numbers. Absolute value of a rational numbers.

Operations on rational numbers


The pupil acquire the skill of differentiating between fractions and rational numbers. They learn how to compare two fractions, change them to standard form learn how to apply the knowledge acquired to compare the rational numbers.

Key Terms and Formulae:

Equivalent rational numbers. Negative and Positive rational numbers Standard form

Absolute value of a rational number.

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

Module – 10 & 11 Congruence Of Triangles Contents:

Meaning of congruency Congruence among line segments Congruence of two circles.



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Congruence of triangles (SSS/SAS/ASA/RHS/ Congruence condition)

Learning Objectives :

The children will be able to define the meaning of congruency of two figures. The children will be able to test for the congruency of – 2 line segments, 2 angles, 2 circles and 2 triangles and solve simple related problems. The children will be able to test for the congruency of 2 triangles using any one of the following congruency conditions- SSS, ASA, SAS and RHS

Key Term :

Congruency SSS, SAS, ASA and RHS Congruency conditions. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Module – 12 Chapter – Simple Equations Contents : Definition of an equation Degree of a polynomial of one variable. Solution or root of the equation Rule for solving linear equation in one variable. Transposition Verification of the solution of an equation obtained Solving of word problems formatting linear equations for them.

The various examples of word problems will be taken up for explaination.


Acquire the knowledge of an equation. Apply this knowledge to solve real life problems. Establish the relationship among the data given in the problems.

Apply the mathematical skill to analyse and solve the word problems.

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



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Module – 13 & 14 Chapter – Comparing Quantities Contents :

Equivalent ratios. Percentage- another way of comparing quantities Converting decimals to percentage Converting percentages to fractions or decimals. Use of percentages Profit or loss as a percentage

Simple interest.

Learning Objectives: Acquire the knowledge of percentage, C.P., S.P. Profit and Loss. Learn different formulae involving C.P.,S.P. , Profit, Loss, Gain % and Loss% Apply the knowledge and mathematical skill to solve real life problems involving different situations.

Acquire the knowledge and understanding of simple interest.

Key Term :

Selling Price (S.P.) Cost Price (C.P.) Gain% Loss % Simple Interest (S.I.)

Principal, Time, Rate and Amount

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

Module – 15 Chapter – Practical Geometry Contents :

Construction of a line parallel to a given line to a point not on the line. Constructing a triangle when the lengths of its three sides are known (SSS criterion). Constructing a triangle when the length of two sides and the measure of the angle between them is known (SAS criterion) Constructing a triangle when the measures of two of its angles and the length of the side included between them is known (ASA criterion)



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Constructing a right angled triangle when the length of one side and its hypotenuse are given (RHS criterion).

Learning Objectives :

Children learn the method of drawing a triangle, using indirectly the concept of congruence of triangles.

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

Module – 16 Chapter – Perimeter And Area Contents : Perimeter and area of a rectangle/square. Area of a triangle. Area of a parallelogram Circumference of a circle Area of a circle

Area of rectangular paths.

Learning Objectives : Students learn the difference between area and perimeter. The learn to find the area of a parallelogram and triangle and the use of them in daily life situations.

Key Term : Area Base Height/Altitude Parallelogram

Circumference

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

Module – 17 Chapter – Symmetry Lines of symmetry for regular polygons Rotational symmetry Students get an idea about the symmetrical objects in daily life, mirror

reflection leading to symmetry and rotational symmetry.



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Key Term :

Line symmetry Centre of rotation Angle of rotation Rotational symmetry

Chapter: Visualising solid shapes (Maths Lab activity)

Through this activity students understand the difference between the plane figure and the solid figures.

Solid shapes drawn on a flat surface realistically (2- D representation of a 3- D solid) is understood by oblique sketch and isometric sketch

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

Module – 18 Revision For Annual Examination

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



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ASSIGNMENTS

Assignment – 1

Integers

Q.1. Fill in the blanks:

(i) All natural numbers are __________ integers. (ii) The product of –7 and 7 is __________ (iii) (–5) × (–1) × (–2) = ___________ (iv) 36 ÷ (–9) = __________ (v) –6 × (–3 + 6) = [(–6) × __________] + [ (–6) × 6] (vi) The successor and predecessor of –380 is __________ and ________

respectively. (vii) A pair of positive and negative integer whose sum is –10 is (________) (viii) The additive inverse of –23 is __________ (ix) The integer whose product with (–2) is (–150) is __________. (x) –3 + 7 = 7 + (–3) is true by __________ property.

Q.2. Verify the following result: 20 × [5 + (–16)] = (20 × 5) + 20 × (–16) Q.3. Subtract (–42 + 39) from 100

Q.4. I was 8 km to the north of my home. Now, I am 4 km to the south of my home. How many kilometers did I travel?

Q.5. The temperature of Delhi which was 42°C fell by 2°C each day for a week. What is the temperature after the whole week?

Q.6. Compare (– 2 –5 ) × (– 6) and (–2) – 5 × (–6). Which is greater?

Q.7. In a quiz based programme, there are three teams A,B and C. There are total five rounds in a game. 20 marks are given for each correct answer and – 10 marks for each wrong answer. No marks are deducted for not attempting a question. Which team won the game, if Team A gave 3 correct and 2 wrong answers? Team B gave 2 correct and 2 wrong answers and they didn’t attempt

1question? Team C gave 3 correct and 1 wrong answers and they didn’t attempt 1question?



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Q.8. Using suitable properties solve:

(i) (–15) × (–37) (ii) 423 × (–63) – [63 × (–423)]

Assignment – 2

Fractions And Decimals Q.1. A bucket contains 24 litres of water. How many litre jugs can be filled from the

bucket to get it emptied?

Q.2. A carton contains 40 boxes of nails and each box weighs 3 kg. How much would a carton of nails weigh?

Q.3. Do as directed

(i) 4 – 13

2 (ii)

4

1 of a rupee

(iii) 27

6 ÷15 (iv) 10.199 ÷ 4.7

Q.4. Fill in the blanks:–

(i) 2 + 3 = 3 + _____________.

(ii) ( + ) + = ______________ + ( + )

(iii) 8 + 0 = ____________.

Q.5. If I go to school on bicycle it takes me 4

1hour and if I go on foot it takes me

hour. Find the time taken if I go on bicycle and return on foot.

Q.6. of Rs. 1240 were spent on food. Find the money spent on food.

Q.7. 20 litres of milk was divided equally among some children. If each child got ¼ litre of milk, find the number of children.

3 4

3 4

3 4

3 4

1 5

1 5

2 3

3 5

3 4

3 5

3 4

1 3

3 8

3 8



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Q.8. Fill in the blanks:–

(i) 0.03 × __________ = 3

(ii) 11.11 × 7.3 = ___________

(iii) 1.3 × ( ________× 2.6) = (1.3 x 7.96) × 2.6

(iv) 108.54 ÷ 9 = 1085.4 ÷ ___________

(v) 0 ÷ 17.3 = __________ (vi) 231.61 ÷ 100= _________

Assignment – 3

Lines and Angles Q.1. Have you ever noticed that

(i) The simplest diagram for a pair of corresponding angles is an F shape.

t

(ii) The simplest diagram for a pair of alternate angles is a Z shape.

t mt

l

t

t

mt

l

t

t

mt

l

t

t l

t

mt

Fig. 9.58

Fig. 9.57



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(iii) The simplest diagram for a pair of interior angles is a U- shape.

Q.2. Fill in the blanks-

(i) A ___________ occupies a position and its location can be determined. (ii) A ___________ is straight and extends indefinitely in both directions. (iii) A ____________ is a flat surface which extends infinitely in all directions. (iv) Through a given point in a plane, __________ lines can be drawn. (v) Exactly _____________ line passes through two distinct given points in a plane

and it lies wholly in that plane. (vi) Two lines in a plane either _________ at exactly one point or are _________. (vii) Three or more points in a plane are ___________ if all of them lie on the same

line. (viii) Three or more lines are __________ if all of them pass through the same

point. This point is called their point of ___________. (ix) A _________ is a portion of a line and its end points are fixed. (x) A ________ starts from a fixed point and extends endlessly in one direction. (xi) An __________ is a figure formed by two rays with the same initial point. (xii) Two angles with a common vertex, a common arm and the other arms lying

on the opposite sides of the common arm form a pair of _________ angles. (xiii) Adjacent angles whose two non-common arms are opposite rays form a

_______ pair. (xiv) Two angles whose sum is 1800 are called __________ angles. (xv) A line which intersects two or more given lines at distinct points is called a

____________ to the given lines. (xvi) Lines in a plane which do not intersect are called _________ lines. (xvii) The distance between two parallel lines is ____________.

Fig. 9.59



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Q.3. In which of the following figures, the pairs of angles are adjacent? Complete the table on the basis of your observations: -

Figure Common vertex

Common arm

Non common arms

Are the angles adjacent?

(i)

(ii)

(iii)

Q.4. In the given figure, PQ║RS, find y.

'

A B

y x

C O (i)

A

B C

1 2

P

(ii) A

B

2 1

C Q (iii)

32°

x1

x2



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Q.5. Name the pair of angles in the following figures. Q.6. In the given figure DE ||BC. Find the measure of x and y. Q.7. In figure if AB || CD and CD || EF

Find ∠ACE.

•

•

•

•

A B

C D

F E

700

1300

• A

•



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Assignment – 4

The Triangle and its properties

(i) The six parts, namely three sides and three angles of a triangle taken together are called the six _________ of the triangle.

(ii) In a triangle an _________ angle equals the sum of the two interior opposite angles.

(iii) The sum of any two sides of a triangle is _________ than the third side. (iv) In a triangle if two angles are 300 and 600 then the third angle is _________. (v) The figure formed by the three line segments by joining three non-collinear

points in pairs is called a _________.

Q.1 In figure, the sides of ∆ ABC are produced in order. Complete each of the statements given below:- (i) ACX = CAB + ______

(ii) BAY = _____ + ______

(iii) CBZ = ______ + ______

Q.2 In the given figures below, the measures of some angles are given. Find the values of

x and y :

(i) (ii)

Q.3 Match the following:-

A B (i) A triangle having no two sides equal (a) Right angled triangle (ii) A triangle having two sides equal (b) Acute angled triangle (iii) A triangle having all sides equal (c) Scalene triangle (iv) A triangle all of whose angles are acute. (d) Obtuse angled triangle (v) A triangle one of whose angles is a right angle. (e) Equilateral triangle (vi) A triangle one of whose angle is obtuse. (f) Isosceles triangle



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Q.4 State whether statements are true or false? Give reason. (i) Can an isosceles triangle be a right triangle? (ii) Can a right triangle be a scalene triangle? (iii) Can a right triangle be an equilateral triangle? (iv) Can an obtuse triangle be an isosceles triangle?

Assignment – 5

Algebraic Expressions

Q.1 Add x2 + 2xy + y2 to the sum of x2 – 3y2 and 2x2 – y2 + 9

Q.2 If P = 7x2 + 5xy – 9y2, Q = 4y2 – 3x2 – 6xy and R = – 4x2 + xy + 5y2 show that P

+ Q + R = 0

Q.3 How much is 2a2 – 7a + 5 less than a3 – 3a2 + 2a – 3?

Q.4 What should be subtracted from x2 – xy + y2 – x + y + 3 to obtain

– x2 + 3y2 – 4xy + 1?

Q.5 Fill in the blanks:-

(i) A number or a combination of numbers (including literal numbers), using the signs of fundamental operations, is called an ___________ expression.

(ii) An expression which contains one term is called a _______________. (iii) An expression which contains two terms is called a _____________ and which

contains three terms is called a _____________. (iv) The terms having same literal factors are called __________ terms, otherwise

they are called _______ terms. Q.6 Get the algebraic expressions in the following cases using variables, constants and

arithmetic operations: - (i) The sum of the numbers 6 and x ______________

(ii) 3 more than a number y __________

(iii) One third of a number x ____________

(iv) One half of the sum of the numbers x and y ____________

(v) Number y less than a number 7 ___________

(vi) 3 more than twice a number x ___________



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(vii) number x multiplied by itself ____________

(viii) 5 more than of number y _______________

Q.7 Subtract 3abc – a2 – b2 from c2 + 2a2 – b2 + abc

Q.8 Find the value of 2y3 – 3y2 + y – 1 if y = – 2

Q.9 The perimeter of a triangle is 7x – 10. One of the sides is x – 6 and another is 3x + 2. Find the third side.

Assignment – 6

Exponents and Powers

Q.1 Express 3600 as product of powers of its prime factors.

Q.2 Simplify using laws of exponents – (i) {(22)3 × 36} × 56

(ii)

Q.3 Complete the following table: –

S. No. Usual Form Exponential Form Standard

Form

Expanded Form

1.

2.

682403056

___________

_____________

_____________

________

________

_____________

1 104 + 4 103

+3 104 + 3 01 +

5 100

Q.4 Fill in the blanks:- (i) If a is any non-zero rational number then ao = _____________.

(ii) a × a × a × ____________ m times = am where a is called the

_____________ and m is called the ____________.

1 3

124 ×93 × 4 63 × 82 × 27



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(iii) (–1)odd positive integer = _______________.

(iv) (–1)even positive integer = _______________.

(v) ( )0 × (– 3)0 = _______________.

(vi) = _______________.

(vii) ( )4 × ( )5 = _______________.

(viii) × × = _______________.

(ix) 47 ÷ 43 = _______________.

(x) [( )2]5 =_______________.

(xi) The standard form for 70, 00, 000 is _______________ .

Q.5 Find p so that:- (625)2 ×57= (5)5p

Q.6 State true or false :–

(i) ( )2 ×( )3 =( )6

(ii) ( )0 = 0

(iii) [( )6÷ ( )5] ÷ = 30

(iv) [( )4]5 =( )20

Q.7 Write 81 in exponential form with base as 3?

Assignment – 7

Data Handling

Q.1. Fill in the blanks-

(i) Collection of all the observations is called _________.

(ii) The difference between the highest and the lowest values of the observations in the given data is called its _________

3 5

3 5

3 5

–2 3 2 5

2 5

2 5

4 7

4 7

20 × 50 × 80 20 + 50 + 80 –3

7 –3 7

2 5

2 5

2 5

2 5

17 20



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(iii) __________ is calculated by dividing the sum of all the observations by the total number of observations.

(iv) The _________ of a set of observations is the observation that occurs most often.

(v) __________ refers to the value which lies in the middle of the data (when arranged in an increasing or decreasing order).

(vi) A ______ graph is a representation of numbers using bars of uniform widths.

Q.2. Find the MEAN of the following:

(i) 3,5,2,6,5,9,5,2,7,4 and 6

(ii) First 8 odd numbers.

(iii) First 10 two digit numbers.

(iv) First seven multiples of 9.

(v) 3, –7, 5, –13 and –2.

Q.3. Read the bar graph in figure and answer the following questions: (i) What information is

given by the bar graph?

(ii) When is the hourly traffic maximum? Also write the maximum number of vehicles.

(iii) When is the hourly traffic minimum? Also write the minimum number of vehicles.

(iv) Find the total number of vehicles.

Bar graph shows the number of vehicles passing through a particular road crossing in Delhi.



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Q.4. Following data shows the favourite snacks item of different students.

Favourite Snacks

Burger Finger Chips

Pizza Sandwich Garlic bread

Number of Student

43 19 55 49 34

Draw the bar graph of the given data and with the help of the same, answer the following:

(i) Which is the most preferred and the least preferred snack item? (ii) How many items are there in all? (iii) How many students consider pizza and burger as their favourite food item?

Q.5. If the mean of 6, 4, 7, p and 10 is 8, find the value of p.

Q.6. What is the median length of the following set of tapes? 12m, 20m, 14m, 24m, 8m, 16m, 14m.

Also find the mode of the above data.

Q.10. Arithmetic mean of 6,7,11,8,X,3,8,14 is 8. Find X.

Q.11. The mode of 2, 2, 5, 9, 7, 11, 10, 9, 9, 10, 12 and 18 is (a) 2 (b) 5

(c) 7 (d) 9

Assignment – 8

Rational Numbers

Q.1. State true or false:

(i) and are positive rational numbers.

(ii) All fractions are rational numbers.

(iii) A rational number can be a natural number.

(iv) Rational number is in the lowest form, but is not in the lowest form.

(v) If x and y are two given rational numbers such that x<y, then (x – y) is always a negative rational number.

Q.2. Fill in the blanks:-

(i) The number lies to the _____________ of 0 on the number line.

– 7 – 9

7 9

1 7

7 1

–3 10



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(ii) Rational numbers are number which can be expressed in the form of q

p such

that p and q are ______________ and q ≠ 0. (iii) in its lowest form is _____________

(iv) as a rational number with numerator –85 is _____________.

(v) = = =

Q.3. Write 3 rational numbers equivalent to:

= ___________________

Q.4. Find any three rational numbers between and

Q.5. Compare which is greater:

(i) or (ii) or

Q.6. Do as directed:

(i) × – ×

(ii) –

(iii) 2+2

1 +

4

3

(iv) (35

16)÷ (

14

15)

48 –144

17 –4

18

14

18

4 –15

–1 3

1 3

3 –14 –5 21

–5 9

11 16

–2 –3

( ) 21 9

3 7 ( )

7 8

16 14

–8 15

16 3



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Q.7. The sum of two rational numbers is –10. If one of the rational number is , find the other number.

Q.8. Fill in the blanks with correct symbol out of >, = and < :–

(i) (ii)

(iii) – 2 (iv) 0

(v)

Q.9. What should be added to

5

1

3

1

2

1 to get 3?

Q.10 What should be subtracted from

3

2

4

3 to get

6

1?

Q.11 The product of two rational numbers is 81

28. If one of the number is 27

14, find

the other.

Q.11. Divide the sum of and by the product of and ?

Assignment – 9

Congruence of Triangles

Q.1. Fill in the blanks :–

(i) If two figures have exactly the same shape and size they are said to be _________. For congruence we use the symbol ___________.

(ii) Two line segments are congruent if they have the same _________. (iii) Two angles are congruent if they have the same ___________. (iv) Two rectangles are Congruent if they have the same _________ and _______. (v) Two _________ are Congruent if they have the same radius.

Q.2. Write true or false:-

(i) All squares are congruent. (ii) If two figures have equal areas they are congruent. (iii) If two squares have equal areas they are congruent. (iv) Two triangles are said to be congruent if pairs of corresponding sides and the

corresponding angles are equal.

– 3 7

6 . – 13

5 13

– 35 91

– 13 5

– 3 – 5

– 8 – 9 – 9 10

– 13 5

12 7

– 31 7

– 1 2

–15 9



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Q.3. Which of the triangles in figure (i) and (ii) are congruent due to the SAS congruence condition. State the result in symbolic form.

(i) (ii)

Q.4. In adjacent figure line segment AB and CD bisect each other at O. Which of the following statements are true?

(i) ∆ AOC ∆ DOB

(ii) ∆ AOC ∆ BOD

(iii) ∆ AOC ∆ ODB

Q.5. In adjacent figure ∆ ABC ∆ ADC

(i) ABC = _____________ (ii) ACD = _____________ (iii) BC = _____________ (iv) ABC ADC due to the ____________ congruence condition.

Q.6. In figure AB CD and AB = DC

(i) Is ∆ ACD ∆ CAB ______________ (ii) State the three pairs of matching parts

used to answer (i)

(iii) Which angle is equal to CAD?

(iv) Is AD BC?

Q.7. In figure AX bisects BAC as well as BDC. State the three facts needed to

ensure that ∆ ABD ∆ ACD.

Q.8. In figure BC AB, AD AB and OC = OD = 4cm. Also BC = AD = 3cm.

A

B C

D

O

B

C

D

A

C

D

B

A X

A B

C D



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(i) Is ∆ OBC ∆ OAD? State the three pairs of matching parts used to answer the question

(ii) Also write the congruence condition.

Q.9. In adjacent figure equal sides have been marked by

the same signs.

(i) Is ∆ ABC ∆ DCB? Write the congruence condition used for it.

(ii) State the three pairs of matching parts used to prove ∆ ABC ∆ DCB

Assignment –10

Simple Equations

Q.1. The length of a rectangle is three times its width. If the perimeter of the rectangle is 96 metres, find the length and breadth of the rectangle. Q.2. In a class of 35 students, the number of girls is of the boys. Find the number of boys in the class. Q.3. Nadeem’s father is thrice as old as Nadeem. After 12 years he will be just twice his son. Find their present ages. Q.4. Translate each of the following statements into an equation, using ‘x’ as the unknown variable:-

A B

C

D

O

4 cm

4 cm

3 cm

3 cm

A

B C

D

2 5



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(i) 4 more than thrice a number is 22. (ii) Twice of a number subtracted from 19 is 9. (iii) A number multiplied by itself is 12 more than the number.

Q.5. Convert the following equations in statement form:

(i) 3p + 5 = 2 (ii) 3p = 180

Q.6. A number when added to its half gives 72. Find the number.

Q.7. Sum of two numbers is 75. If one exceed the other by 5, find the numbers.

Q.8. Two third of a number is greater than one third of the number by 3. Find the number. Q.9. Solve the following equations:

(i) –2 (x + 3) =8 (ii) 0 = 18 + 2 (p – 6)

Assignment –11

Comparing Quantities

Q.1. In how many years will Rs. 750 amount to Rs. 900 at 12% annum?

Q.2. A farmer borrowed Rs. 2400 at 12% interest per annum. At the end of 2½ years, he cleared his account by paying Rs. 1200 and a cow. Find the cost of the cow Q.3. Fill in the blanks: -

(i) A fraction with its denominator ________ is called a percent. (ii) When S.P.> C.P. then __________ = S.P. – C.P.

(iii) When S.P. < C.P. then __________ = C.P. – S.P.

(iv) Profit % = × 100 (v) _________ = × 100

(vi) The money borrowed from a lender is called the ___________. (vii) The additional money that is paid back after a specified period (time) in

addition to the principal is called the ____________. (viii) Total money paid back at the end of the specified period is called the

____________. (ix) Amount = ____________ + interest.

_____ C.P.

Loss C.P.



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Q.4. Convert

(i)

(ii)17.5%

(iii).75

(iv)75 %

(v)1:5

To

Percentage

Decimal

Percentage

Ratio

Percentage

Q.5. In an orchard, 16 % of the trees are apple trees. If the total number of trees in

the orchard is 240, find the other types of trees in the orchard.

Q.6. A shirt is sold at a profit of 12% for Rs 672. What is the cost price of the shirt?

Q.7. Jacob bought a plastic sheet for Rs. 800 and sold it for Rs 1000. Find his profit or loss percent.

Q.8. Neelam secured 21 marks out of 25 and Bina secured 43 marks out of 50. Calculate their percentage and find whose performance is better?

Assignment – 12

Practical Geometry

Q.1. Draw a line PQ. Draw another line parallel to PQ at a distance of 3 cm from it.

Q.2. Construct a ∆ ABC in which B = 700, AB = 4.8 cm and BC = 5.2 cm. Measure side CA.

Q.3. Construct a ∆ PQR in which Q = 1000, R = 200 and PR = 5.1 cm. What type of triangle is it according to angles.

Q.4. Construct a ∆ LMN in which LM = 5 cm, MN = 5.6 cm and NL = 4.2 cm.

Q.5. Construct a right triangle DEF in which E = 900 and hypotenuse DF = 4.2 cm and side EF= 3.8 cm. Write steps of construction.

47 50

2 3



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Assignment – 13

Perimeter and Area

Q.1. A rectangular grassy lawn measuring 40 m by 25 m is to be surrounded externally by a path which is 2 m wide. Calculate the cost of leveling the path at the rate of Rs. 8.25 per square metre. Q.2. A path 2 m wide is built along the border inside a square garden of side 10 m. Find –

(i) The area of the path. (ii) The cost of planting the grass in the remaining portion of the garden at the

rate of Rs. 10 per m2.

Q.3. A square park has each side of 100 m. At each corner of the park, there is a flower bed in the form of a quadrant of radius 14 m as shown in figure. Find the area of the remaining part of the park. (take π = )

Q.4. A paper is in the form of a rectangle ABCD is which AB = 20 cm and BC = 14 cm. A semicircular portion with BC as diameter is cutoff. Find the area of the remaining part. Q.5. Fill in the blanks: -

(i) The magnitude of a plane region is called its ______________.

(ii) The perimeter of a circle is called its ______________.

22 7

D

A B

C

14

cm

20 cm

10

0 m

100 m

14 m

100



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(iii) Area of a parallelogram = Base × ________________

(iv) Area of a ________________ = ½ × base × height.

(v) Circumference of a circle = ________________

(vi) Area of a ________________ = r2

(vii) ________________ of a parallelogram =

(viii) Height of a parallelogram = ________________

(ix) Base of a triangle =

(x) Height of a triangle =

(xi) The value of is ___________ or ____________. (Correct to two decimal places)

Q.6. Find the altitude of a parallelogram one of whose side is 6.5 cm, the area being

26 cm2.

Q.7. Find the height of a triangle whose base is 80 cm and area is 0.08 m2.

Q.8. Find the diameter of a circle whose circumference is 12.56 cm.

Q.9. A crater falls near a village creating a circular pit of diameter 200m. Find the affected area of land.

Q.10. Which has greater area, a square of perimeter 88cm or a circle with circumference 88cm?

Assignment – 14

Symmetry

Q.1. Fill in the blanks: -

(i) A figure has _________ symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

(ii) A regular _________ has 6 lines of symmetry.

(iii) A regular square has _________ lines of symmetry.

2 × . Altitude

Area Height

2 × Area _________



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(iv) Two figures that have both horizontal and vertical line of symmetry _________ & __________.

(v) An example of a geometrical figure which has no line of symmetry __________.

Assignment – 15

Visualising Solid Shapes

(Only Maths Lab Activity)

OBJECT: To make net of a cube, cuboid and a square pyramid.

Method: - NET OF A CUBE NET OF A CUBOID

Sl No.

Shape Number of faces

Number of vertices

Number of edges

1.

2.

3.

Cube

Cuboid

Square pyramid

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



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MCQ ASSIGNMENT

INTEGERS

Q.1. The successor of –12 is

(i) –11 (ii) 13

(iii) –13 (iv) None of these

Q.2. The product of (–3) (–5) 4 is

(i) 75 (ii) –75

(iii) 60 (iv) None of these

Q.3. What should be added to –13 to get –7?

(i) 6 (ii) –6

(iii) –20 (iv) None of these

Q.4. What is the sign of the product together five negative integers and one positive

integer?

(i) + (ii) –

(iii) × (iv) None of these

Q.5. On simplification 12 – 3 [ 5 + 2{ (5 – 7)– 2} ] gives

(i) 3 (ii) –3


FRACTIONS AND DECIMALS

Q.1. What is of ?

(i)

(ii) 1

(iii)

(iv) None of these

Q.2. The reciprocal of + is

(i)

(ii)

(iii)

(iv) None of these

10 12

21 32

3 4

7 8

2 3

3 4

3 2

4 3

17 12



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Q.3. If 5776 38= 152 what is quotient of 5.776 0.38?

(i) 0.152 (ii) 01.52

(iii) 15.2 (iv) None of these

Q.4. 120 0.8 is equal to __________ (i) 15 (ii) 0.15


LINES AND ANGLES

Q.1. Two angles forming a linear pair are ____________ (i) Adjacent angles and supplementary angles (ii) Complementary angles (iii) Adjacent and Complementary angles (iv) None of these

Q.2. In the adjoining figure, which of the following is a pair of supplementary angles?

(i) (1,2)

(ii) (2, 5) (iii) (4, 6) (iv) None of these

Q.3. If one angle of a linear pair is an acute angle, what type of angle is the other angle? (a) Acute angle (b) Right angle

(c) Obtuse angle (d) None of these

Q.4. If two non- common arms of two adjacent angles form a straight line, the two angles form a

(a) Right angle (b) Linear pair

(c) Reflex angle (d) None of these

Q.5. The measure of an angle whose complement is the angle itself

(a) 90 (b) 180 (c) 360

(d) None of these

7 6 8

1

5 2 3 4



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TRIANGLES AND ITS PROPERTIES

Q.1. A triangle may have all the three __________ (a) Obtuse angles (b) Acute angles

(c) Right angles (d) Reflex angels

Q.2. A triangle can be constructed by taking its two angles as (a) 80, 60 (b) 75, 115 (c) 135, 45

(d) 90, 90 Q.3. The hypotenuse of a right- angled triangle is 25 cm. If one of the remaining two sides is of length 24cm, what is the length of the other side?

(i) 1cm (ii) 4cm

(iii) 7cm (iv) 10cm

Q.4. In an equilateral triangle each angle is of measure _____________ (i) 60 (ii) 75 (iii) 90

(iv) 180

ALGEBRAIC EXPRESSIONS

Q.1. Which of the following is a binomial? (i) 2xy (ii) y2–2

(iii) xyz (iv) None of these

Q.2. What should be added to x – y + 4 to get the sum 2x – 1? (i) x–y+3 (ii) x+y–3

(iii) x+y–5 (iv) None of these

Q.3. The difference of 7a – b – 5 and – a +b –1 is (i) 8a–2b–4 (ii) –6a+2b–6

(iii) 6a–6 (iv) None of these

Q.4. A symbol which takes in various numerical values is called a (i) Constant (ii) Algebraic expression

(iii) Literal (iv) None of these



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EXPONENT AND POWERS

Q.1. ( )3 is equal to

(i)

(ii)

(iii)

(iv) None of these

Q.2. The reciprocal of (–2)7 is

(i) ( )7

(ii) (–7)2

(iii) (– )7

(iv) None of these

Q.3. (–5)3 4 is equal to

(i) 60

(ii) –60

(iii) (–5)7

(iv) None of these

Q.4. ( )6 ×( )2 ( )4 is equal to

(i)

(ii) (– )4

(iii) –

(iv) None of these

Q.5. (3 + 4 15) is equal to

(i) 1 (ii) 2


–3 7

9 15

9 125

–27 343

1 2

1 2

–3 4

–3 4

–3 4

3 4

3 4

3 4



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DATA HANDLING

Q.1. The median of 1, 2, 2, 3, 3, 3, 5 and 8 is (i) 3 (ii) 5

(iii) 8 (iv) 9

Q.2. Number of times an observation or an entry occurs in a data is called its ________ (i) Mean (ii) Median

(iii) Frequency (iv) None of these

Q.3. The mode of 2, 2, 5, 9, 7, 11, 10, 9, 9, 10, 12 and 18 is (i) 2 (ii) 5

(iii) 7 (iv) 9

RATIONAL NUMBERS

Q.1. Which of the following is the smallest rational number?

(i)

(ii)

(iii)

(iv)

Q.2. Which of the following rational number is not equivalent to ?

(i)

(ii)

(iii)

(iv) None of these

Q.3. The product of two rational number is – .If one of them is , what is the other rational number?

(i)

(ii)

(iii)

(iv) None of these

Q.4. Which of the following is a positive rational number?

(i)

(ii)

(iii)

(iv) None of these

–7 13

7 13

4 –13

–9 13

2 – 3

–2 3

8 3

4 –6 3 – 5

36 75

12 –15 20 25

4 5

–5 6

– 5 – 6

0 –6



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Q.5. The reciprocal of is

(i)

(ii)

(iii)

(iv) None of these

CONGRUENCY OF TRIANGLES

Q.1. In ΔXYZ, the angle included between the sides XZ and YZ is (i) X

(ii) Y

(iii) Z (iv) None of these

Q.2. If ΔABC ΔDEF, then which side of ΔDEF is equal to the side AC of ΔABC ? (i) DE (ii) DF

(iii) EF (iv) None of these

Q.3. If Δ ABC Δ XYZ and Δ ABC is not congruent to Δ ZXY, then which of the following is not true?

(i) AC=XZ (ii) BC=XY

(iii) AB=XY (iv) None of these

Q.4. ΔPQR and ΔTQR are on the same base QR. PQ=TR and PR=TQ which of the following correspondence gives a congruency relationship?

(i) PQR TQR (ii) PQR RQT (iii) PQR TRQ (iv) None of these

SIMPLE EQUATION

Q.1. Which of the following is a solution of the equation 4x–8=7–x? (i) x=3 (ii) x=5

(iii) x=–1 (iv) None of these

9 2

81 32

32 81

8 27

3 4

P T

Q R



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Q.2. The value of x satisfying the equation 3(x–1)+2(x–2)=3 is (i) x=1 (ii) x=2

(iii) x=–2 (iv) None of these

Q.3. An equation for the given statement: ‘Thrice a number subtracted from 20 is 2’ is __________

(i) 3(20 – x)=2 (ii) 3x – 20=2

(iii) 20 – 3x=2 (iv) None of these

Q.4. Mathematical statement for – 3q =5 is

(i) Three times q subtracted from 20 is 5 (ii) Thrice of q subtracted from quotient of 20 by p is 5 (iii) Product of 20 and q subtracted from 3q is 5 (iv) None of these

Q.5. The value of x which satisfies the equation 5x+3=4x–7 is

(i) 10

(ii) –10

(iii)

(iv) None of these

COMPARING QUANTITIES

Q.1. The ratio of 20 hrs to 2 months is

(i) 20:2

(ii) 5:36

(iii) 1:72

(iv) None of these

Q.2. If 16 girls can type 288 pages in a day, how many pages in a day can 20 girls type?

(i) 360 pages

(ii) 390 pages

(iii) 292 pages

(iv) None of these

Q.3. If 30% of a number is 75, what is this number?

(i) 45

(ii) 105

(iii) 250

(iv) None of these

Q.4. A sum of Rs 1260 was deposited in a bank for 5 yrs at the rate of interest 8% per annum. How much money will the bank pay on the maturity?

(i) Rs 504

(ii) Rs 1764

(iii) Rs 1300

(iv) None of these

20 P

–10 9



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PRACTICAL GEOMETRY

Q.1. A ΔABC can be constructed if the measures of (i) two sides and one angle are known (ii) one side and two angles are known (iii) three angles are known (iv) both one and two are correct

Q.2. In which of the cases, ΔXYZ can be constructed (i) XY=YZ=XZ=4cm (ii) XY=2cm, YZ=3cm & ZX=7cm (iii) XY=6cm, YZ=4cm & ZX=10cm (iv) XY=4cm, YZ=3cm & ZX=7.5cm

Q.3. To construct a line parallel to a given line we can make. (i) Alternate interior angles equal (ii) Co- interior angles equal (iii) Vertically opposite angles equal (iv) None of these

Q.4. To construct a right angled triangle (i) One side should be known (ii) One hypotenuse should be known (iii) one hypotenuse and a side should be known (iv) None of these

PERIMETER AND AREA

Q.1. The circumference of a circle is also called

(i) Perimeter (ii) Area (iii) Boundary (iv) Diameter

Q.2. π is (i) An integer (ii) A whole number (iii) A terminating decimal (iv) A non- terminating and non- repeating decimal



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Q.3. What is area of the adjacent figure? (i) 30 sq cm (ii) 45 sq cm (iii) 60 sq cm (iv) None of these

Q.4. The area of a square of each side 1cm is (i) 1 sq m (ii) 6 sq cm (iii) 0.0001 sq m (iv) none of these

Q.5. The area of the shaded region in the adjacent figure is (i) 70 sq m (ii) 64 sq m (iii) 66 sq m (iv) none of these

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

3cm

10cm

6cm

2m

15m

20 m

2m



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MODEL TEST PAPER

Summative Assessment I [Solved] Time: 3 hrs. Max Marks: 80

General Instructions:

Read the question paper well before answering. Each part of Q1 carry 1 mark Q2 to Q11 carries 2 marks each. Q12 to Q20 carried 3 marks each. Q21to Q25 carries 4 marks each.

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

SECTION- A Q.1

(i) Value of ‘x’ in the given figure. If l||m, is (a) 90 (b) 60 (c) 120 (d) 75

(ii) The angle which is complement of itself:

(a) 90 (b) 50 (c) 45

(d) 180 (iii) Coefficient of x in the expression y2z–2xy2+3z is

(a) 2y (b) –2

(c) –2y2 (d) –1

(iv) Exponential form of 4558 is

(a) 23 53 (b) 24 52

(c) 42 5 (d) 25 52

(v) The value of (–3)3 (–2)2 is

(a) –36 (b) 36

(c) –108 (d) 108

(vi) Which of the following statement is true

(a) –9+8=–7 (b) –8+(–8)=16

(c) –7+10=3 (d) –11+8=3

l

m

x

2x



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(vii) Which of the following statement is false

(a) Addition is commutative for integers (b) Integers are closed under subtraction (c) Multiplication is commutative for integers (d) Subtraction is commutative for integers

(viii). If m is a rational number and m 0 then m0 =

(a) 0

(ii) m

(b) 1

(iv) None of these

SECTION- B

Q.2. Find the value of ‘x’ in the figure

Q.3. Find the value of x2 – 2x+120 for x=–10

Q.4. Find the median of the following data

19, 25, 23, 9, 20, 20, 15, 10, 16, 25, 20, 24, 13

Q.5. Find two pairs of positive and negative integer whose sum is –37.

Q.6. Identify the terms and their factors in the following expression show the term and factors by tree diagram

–xy2 + 2x2 – 3y3

Q.7. Express 256 as the power of 2.

Q.8. Find the unknown angle x.

115

x

45

x

B A D

110

C



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Q.9. A rectangular field is 14 m long and 11 m wide. Find its perimeter.

Q.10. One of the angles of a triangle has measure 80 and the other two angles are equal. Find these two angles.

Q.11. Divide 44.5 by 8000.

SECTION- C Q.12. (i) Express 39087.8 in standard form.

(ii)Write the expanded form of 3006194.

Q.13. The temperature at 12 noon was 10C above zero. If it decreases at the rate of 2C per hour until midnight, at what time would the temperature be 8C below zero? What would be the temperature at mid night?

Q.14. Find m so that

(–7)m= – 343

Q.15. Simplify the expression and find the value if x is equal to 2.

4 (2x – 1) + 3x + 11

Q.16. Find the values of the angles x, y and z in the following figure.

Q.17. Simplify:-

Q.18. In figure AM is the median of Δ ABC.

Prove that AB + BC+ CA > 2 AM.

12

x

y

40 25 z

24 93 4 63 82 27

A

B C M

1 2



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Q.19. Simplify:-

(i) 3

(ii)

Q.20. In the adjoing figure 1 = 108 Find 2, 3 and 4.

SECTION- D Q.21. Akash bought vegetable weighing 10 kg. Out of this 3 kg 500 g is onion, 2 kg 75 g is tomato and the rest is potato. What is the weight of potato?

Q.22. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of

6x – 4y – 4z and 2x + 4y –7.

Q.23. A mathematics teacher wants to see whether the new technique of teaching she applied after half yearly exam was effective or not. She take the score of 5 weakest children in the half yearly exam (out of 25) and in the annual exam (out of 25).

(i) Draw a double bar graph choosing an appropriate scale.

(ii) Which student showed maximum improvement?

Students Divya Anil Ashish Rita Sandeep

Half yearly exam

10 15 12 20 9

Annual exam 15 18 16 21 15

1 3

15 25

4 10

–5 12

2 5



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Q.24. Find the mean, mode median and range of the following data.

7, 11, 12, 11, 12, 9, 8, 11, 18

Q.25. In quadrilateral ABCD. Prove that

AB + BC +CD +DA > AC + BD

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



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SOLUTIONS SECTION-A

Q.1 (i)(b) 60 (ii)(c) 45 (iii)(c) –2 y2 (iv)(d) 25 52 (v(c) –108

(vi)(c) –7+10=3 (vii)(d) Subtraction is commutative for integers. (viii)(b) 1

SECTION-B

Q.2 x+45= 115 (exterior angle of a triangle is equal to sum of opposite interior angles) x =115– 45 =70

Q.3 x2 – 2x+120 for x=–10 (–10)2 – 2 (–10)+ 120 100 + 20 +120=240

Q.4 Ascending order 9, 10, 13, 15, 16, 19, 20, 20, 20, 23, 24, 25, 25 Number of observations = 13

therefore 13 1 14

2 2

= 7th observation is the median.

therefore median = 20

Q.5 (i) 56 – 93 (ii) –43 + 6 or any other option

Q.6 Terms –xy2 , 2x2 , –3y3 Factors by tree diagram

Q.7 2 256

2 128 2 64 2 32 2 16 2 8 2 4 2 2

1 256= 22222222 = 28

–1 x y y 2 x x –1 3 yyy



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Q.8 Since AC=AB Therefore B=C (isosceles Δ property] Also CAD=B+C (Exterior property) Let B=C= x 110 = x+ x 110 = 2x 110

2 x

55= x Q.9 Rectangle L= 14

1 29

2 2m m

B= 111 23

2 2m m

P= 2 (L+B)

P= 2 29 23

2 2

= 2 29 23

2

= 2

52

2m

= 52m

Q.10 In ΔABC A+B+C=180 (by angle sum property) Let A=80 B=C= x Therefore 80+ x+ x=180 2 x=100 x= 50 (Therefore Equal angles are 50)

Q.11 44.5 8000

44.5 44.5 5.5625

8000 8 1000 1000

=.0055625 =.0055625

5.5625

844.5 40 45 40 50 48 20 16 40 40



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Q.12 (i) 39087.8= 3.90878 104

(ii) 3006194 = 3 106 + 6 103 + 1 102 +9 101+ 4 100

SECTION-C

Q.13 Temperature at 12 noon= + 10C Drop in temperature in 1 hour=2C Required temperature = –8C Therefore total drop in temperature= 10–(–8)= 10 + 8=18C 18C will drop in 18 2=9 hours i.e at 9. p.m Drop in temperature till midnight = 12 2=24 C Therefore temperature at midnight = 10 – 24=–14C

Q.14 (–7)m = –343 (–7)m = (–7)3 Comparing powers as base is

same m=3

Q.15 4 (2x – 1) + 3x + 11 8x – 4 + 3x + 11 11x +7 If x = 2 11(2)+7 22+ 7=29

Q.16 40 + x +25 = 180 (sum of all angles on straight line is 180°) 65 + x= 180 x= 115 y = x+ 25 = 115 + 25=140 (Vertically opposite angles) z = 40 (Vertically opposite angles)

Q.17 4 3 2 2 2 3 2

3 2 3 3 2 3

2 9 4 [2 ] [3 ] 2

6 8 27 [2 3] [2 ] 3

4 6 6 4 2 6 6 6

3 3 6 3 3 6 3 3 9 6

2 3 2 2 3 2 3

2 3 2 3 2 3 2 3



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50

=3

1 1

2 8

Q.18 In ΔABM

AB+BM>AM

In ΔACM

AC+CM>AM

Adding (i) & (ii)

AB+BM+AC+CM >2AM

AB+BC+AC >2AM (Since BM=MC given)

Q.19

(i) 10 15 10 25 50 5

53 25 3 15 9 9

(ii) 4 5 2

10 12 5

=1 1 1 1

5 3 1 15

Q.20 1= 108 (given)

3 = 108 (corresponding angles)

1+ 2 = 180 (Linear pair)

108 + 2= 180 2 = 72 4 = 2 = 72 (alternate exterior angles)

SECTION-D

Q.21 Total vegetables bought= 10 kg

Weight of Onion = 3.500 kg

Weight of tomato = 2.075 kg

Therefore Potato bought = 10 kg – (3.500 kg + 2.075 kg)

= 10 kg – 5.575 kg= 4.425 kg

In equality property



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Q.22 6 4 4 2 4 7 13 4 7 6 6 3x y z x y x y z z x y

6 2 4 4 4 7 13 6 4 3 7 6x x y y z x x y y z z

8 4 7 19x z x y z

8 19 4 7

11 5 7

x x z z y

x z y

Q.23

Sandeep shows maximum improvement

Q.24

Mean =

7 11 12 11 12 9 8 11 18

9

9911

9

Median= 7, 8, 9, 11, 11, 11, 12, 12, 18

9 1 10

2 2

= 5th observation= 11 is the median

15

SC

AL

E O

F M

AR

KS

SCALE 1 UNIT = 5 marks

35

30

25

20

10

5

Divya Anil Ashish Rita 0 Sandeep



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Mode= Maximum number of times an observation occurred = 11

Q.25 To prove AB + BC +CD +DA > AC +BD

Proof: In Δ ABC AB + BC > AC eq-1 In Δ BCD BC + CD > BD eq-2 In Δ ADC AD + DC > AC eq-3 In Δ BAD AB + AD > BD eq-4

Adding equations 1, 2, 3 and 4

2(AB+ BC + CD + DA)> 2(AC + BD)

AB + BC + CD + DA > AC + BD Hence Proved

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

Inequality Property

A B

C D



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MODEL TEST PAPER

Summative Assessment-I [Unsolved]

Time: 2 hr 30 min. Max Marks: 80



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

SECTION A

Q.1 (i) Integer which is its own additive inverse is.

(a) 1 (b) –1

(c) 0 (d) None of this

(ii) In power notation (– ) × (– ) × (– ) × (– ) can be expressed as.

(a) – 4

(b) – –4

(c) (–5)4

(d) – 4

(iii) Which of following statement is true?

(a) Two acute angles form a linear pair. (b) A linear pair is a pair of adjacent angles which do not have common arms. (c) Adjacent angles are always complementary. (d) Adjacent supplementary angles form a linear pair.

(iv) Which of the following pair of terms are like terms

(a) 5x2y, 6xy2 (b) xyz, xy

(c) –5xy, 7xy (d) –7x2, –7y2

(v) In the Figure l || m and p is transversal then its pair of corresponding

angles are.

(a) (3 + 2) and (4 + 6) (b) (1 + 2) and 5 (c) (2 + 3) and 4 (d) None of above

1 5

1 5

1 5

1 5

1 5

1 5

1 5

• 2

3

6

1

4 5

l

m

p

t



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(vi) Which of the following is not equal to 2?

(a) 3º + 2 º

(b) 2 × 5 º

(c)

(d)

(vii) The perpendicular line segment from a vertex of a triangle to its opposite

side is called __________ of a triangle.

(a) Altitude

(b) Median

(c) Base

(d) Hypotenuse

(viii) If two parallel lines are intersected by a transversal than a pair of consecutive interior angles are

(i) Supplementary

(ii) Equal

(iii) Complementary

(iv) None of these

SECTION B

Q.2 Paras studies for 6 hrs. He devoted 3 hrs of time for Mathematics.

How much time he devoted for other subjects.

Q.3 Find the value of x and y in given figure

Q.4 A two wheeler covers a distance of 55.03 km in 1 litre of petrol. How much distance will it cover in 10 litre of petrol?

Q.5 Show terms and factors of expression –3ab + 2b2 – 5 by a tree diagram?

Q.6 Find the product 395 × (–35) + (–395) × 65 by using suitable property?

Q.7 Find the range of data 5, –5, 4, –4, –3, 0, –1, 1

10 5 4º 2º

40º 70º

x

y



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Q.8 (i) Distance between Earth and Moon is 384000000 m. Express it in the standard

form.

(ii)Write product form of ( –2)5 m3.

SECTION C

Q.9 Answer the following questions according to given figure:

(i) Name the pair of obtuse vertically opposite angles?

(ii) Name the pair of supplementary angles.

(iii) If 1 = 2, then AB||CD. State this property.

Q.10 Subtract the quotient of (–57) 19 from the product of (–18) × (–5) × (–4)?

Q.11 Express 312 × 975 as product of prime factors in exponential form?

Q.12 From the sum of 4 – 3x and 5 –4x + 2x2 subtract –3x2 – 5x + 1?

Q.13 Calculate value of A according to given figure. Q.14 Simplify the expression by using laws of exponents. Q.15 The scores of mathematics test (out of 45) of 11 students is as follows:

43, 45, 42, 43, 38, 40, 43, 35, 38, 43, 42

Find the median and mode of the given data.

35 × 105 × 25 57 × 65

2

B 1

A

C • E

F

• G 4

D

3

• J K •

A

B C x

2x

60º

D•

E •



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Q.16 Calculate perimeter of the following figure.

12 cm

4 cm

5 cm 6 cm

Q.17 According to the given figure, find the value of x, y and z, if AB||CD and AE||FC.

SECTION D

Q.18 Simplify the given expression and then find the value for m = –2

10m2 – 9m – (5m – 4 m2) – 7 m + 10

Q.19 (i) Is it possible to have triangle with the sides 6cm, 3cm and 2cm? Give reasons. (ii)Draw a sketch of ∆PQR where QD is a median.

(i) Is PD = RD. State Yes or No. (ii) How many medians can a triangle have?

Q.20 Do as directed: - (i) Find 76.5 0.01 (ii) Write expanded form of 20.03? (iii) Express 5 cm in m. (iv) What is reciprocal of –13

(v) Evaluate: 2

1

3

1

Q.21 ABCD is a quadrilateral. Show that

AB + BC + CD + DA > AC + BD.

2 7

1 8

3 5

3 4

1 2

A B

E

D

C

A •

E •

• B

120º

z

• D

x C

y

• F

50º

• G

A B

D C



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Q.22 The performance of a student in half yearly and final examination is given below:

Draw a double bar graph choosing appropriate scale. In which subject there is maximum improvement of marks?

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

SUBJECT Eng Hindi Maths Sc. S.St

Half yearly 80 78 74 85 60

Final 83 65 64 90 55



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58

MODEL TEST PAPER-2

Summative Assessment-I [Unsolved]




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

SECTION: A

Q.1. (i) The successor of (–1) is _________.

(ii) Write the coefficient of „y‟ in the given expression 4x – 2yx2.

(iii) Find the range of first ten whole numbers.

(iv) Express in standard form 38705.6

(v) Evaluate (–9)3.

(vi) Evaluate 3

2 of 27.

(vii) Find the supplement of 47º.

(viii) Which is greater 0.25 or 0.205?

SECTION: B

Q.2. (i) Write a pair of integers whose sum gives a negative integer.

(ii) Write a pair of integers whose difference gives a negative integer.

Q.3. Solve: 72

1 ÷ 3

2

1.

Q.4. The ages of a group of teachers in a school are as follows.

33 40 38 23 35

28 59 32 40 26

Find the mean age of these teachers.



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Q.5. Find an angle which is 3

2 of its complement.

Q.6. Subtract 22 354 pqpq from pqqp 22 35 .

Q.7. Simplify using laws of exponents

852

852

Q.8. Find x in the given figure:

Q.9. Subtract (– 53 + 58) from (100).

Q.10. Find median and mode of the data

87, 36, 68, 92, 54, 95, 87

Q.11. Find product using a suitable property

125 ×(– 34) × 8 × 20

SECTION: C

Q.12. If P=3x2 –7x –8, Q= x2 + 8x – 3, R = –5x2 – 3x +2, find P – Q + R.

Q.13. Simplify using laws of exponents. (Give the answer in exponential form)

6623 532

Q.14. Given n||m and t is the transversal, find x and y in given figure. t

2x+5 y –5

1

n

m

25˚

2

A B

x

D

40˚ 70˚

C

O



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Q.15. The marks in a Math test (out of 50) of 21 students are as follow:

43 40 38 29 43 48 38 40 50 43 38 45 49 38 43 42 29 50 44 45 40

(i) Make a frequency table for the data. (ii) Find the mode of the data.

Q.16. (i) Divide 44.5 by 8000.

(ii)Convert 32 cm in km.

Q.17. Solve using properties and name the property used

28945 × 99 – (– 28945)

Q.18. In the following figure EF||GH, EAB=60˚ and ACH=105˚. Determine CAF

& BAC.

Q.19 Simplify and then find value for m= –2

10m2 – 9m – (5m – 4m2)

Q.20 Find the perimeter of a rectangle whose length is 69.03 cm and breadth is 21.97 cm.

SECTION: D

Q.21 The performance of students in 1st term and 2nd term is given below. Draw a double bar graph choosing appropriate scale and answer the following questions.

Subject English Hindi Math Science S.Science

1st term 70 60 88 81 73

2nd term 67 72 95 85 75

A

B C

F

60˚

105˚

E

G H



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(i) In which subject has the child improved his performance the most?

(ii) In which subject has his performance gone down?

Q.22 Simplify using laws of exponents.

57

55

65

25103

Q.23 Subtract the sum of 1 – 2x + 3yx + 4xyz and 3x – 2xy + 4xyz –1 from the sum of

3x – 4y + 5xy – 6xyz and 2x – 3xy.

Q.24 Find x, y and z if AB||CD & AE||CF

Q.25 In a test (+5) marks are given for every correct answer and (–2) marks are given for every incorrect answer. Rahul answered all the questions and scored 40 marks though he got 16 correct answers. How many incorrect answers had he attempted? ============================================

A

120˚

B

F

50˚

E

z

D

C x

y

G



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62

MODEL TEST PAPER

Summative Assessment-II (Solved)




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

SECTION-A Tick the correct answer. Q.1. (i)Angle included between the side DE and EF of the Δ DEF is

(a) D (b) E

(c) F (d) None of these

(ii) A piece of wire is 40 cm long. It is bent in the form of a square then its side is

(a) 10 cm (b) 20 cm

(c) 4 cm (d) 8 cm

(iii) To find – we multiply – by

(a) –

(b) –

(c) –

(d) None of these

(iv) 0.75 is equal to (a) 75 percent

(b) percent

(c) 7.5 percent

(d) None of these

(v) Δ LMN can be constructed, when LM=4 cm, MN= 5.5 cm and M=50 using criterion

(a) SAS (b) SSS

(c) AAA (d) ASS

(vi) 7 less than the thrice of the sum of x & y is

5 7

1 2

1 2

7 5

57 2

12 2 7

5 2



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(a) 3(x+y)–7 (b) 7–3(x+y)

(c) 7–3x+y (d) None of these

(ii) A rhombus has ____________ number of lines of symmetry (a) 1 (b) 2

(c) 4 (d) No line of symmetry

(vii) The product of a rational number and its multiplicative inverse is (a) 0 (b) 1

(c) Number itself (d) None of these

SECTION-B

Q.2. What % of 400 is 300 marks.

Q.3. Convert 3.5 into fractions & then into percents.

Q.4. Find –

Q.5. Form the equation for the following statements: Half of a number is 18 less than twice the number.

Q.6. Is it possible to construct a Δ PQR in which PQ=7 cm. QR= 13 cm and RP= 5 cm. Give reasons.

Q.7. The radius of a car’s tyre is 35 cm. Find the distance covered by it in 1 round.

Q.8. A shop has 400 parts out of which 8, are defective. What percent are defective?

Q.9. Solve the equation: = 2x.

Q.10. Write the angle of rotation and order of rotation of square.

Q.11. State true or false. (i) Squares having same perimeter are congruent. (ii) Squares having same area are congruent.

SECTION-C

Q.12. Anita borrowed Rs. 5000 from the bank in the year 2001. She paid Rs. 450 as interest in the year 2003. Find the amount paid to the bank.

Q.13. Find the area of an equilateral triangle, with perimeter equal to 18 cm and altitude measuring 4 cm.

13 5

8 5

11 15

12x – 8 4



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B

M

L P

O A

Q.14. Solve equation & find the value of x

+7=

Q.15. What will be the decrease in the percentage if a number is decreased from 200 to 175?

Q.16. How many times 132 cm long wire can be wrapped around a circle with radius 7 cm.

Q.17. A man sold a cooler for Rs. 4500 at a loss of 25%. Find the cost price of the cooler?

Q.18. In the given figure PL OB and PM OA such that PL=PM

(i) Is Δ PLO Δ PMO?

(ii) State the conditions of congruency.

Q.19. Harpreet thinks of a number and then he doubles it. He adds 20 to it. He gets an answer equal to 6 times the number. What is the number?

Q.20. Δ ABC and Δ DEF are congruent triangles by S.S.S congruence condition. Find the value of x & y.

SECTION-D

Q.21. Construct the Δ PQR where PQ=4 cm, QR=6 cm, LQ=110.

x – 3 5

2x +1 3

A

x – 5 27 B C

D

E F x +5 45

A D

C B

O



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Q.22. AB & CD are two diameters of the given circle with centre O.

(i) Is Δ AOC Δ BOD. State the conditions of congruency.

(ii) Is AC = BD.

Q.23. A rectangular field is 120 m long and 48 m wide. How many triangular flower beds with side 18 m & height as 8 m can be laid in this field?

Q.24. Construct an isosceles right angled triangle XYZ where X=90 and

XY=YZ=4 cm.

Q.25. Rakhi’s brother is 8 years older than four- fifth of her age. If her brother is 32 years old. What is Rakhi’s age?

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



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SOLUTIONS

SECTION-A

Q.1 (i) (b) E (ii) (a) 10cm

(iii) (b) 5

7

(iv) (a) 75 percent (v) (a) SAS (vi) (a) 3(x+y)-7 (vii) (b) 2 (viii) (b) 1

SECTION-B

Q.2 %75100400

300

Q.3.

Fraction

Q.4

8 11 13

5 15 5

24 11 13

15 5

13 13 13 5 1

15 5 15 13 3

Q. 5 Let the no. be x

1822

xx

Q.6 No because sum of two sides i.e. PQ + RP < QR ( third side)



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Q.7 Radius of Car’s tyre = 35 cm Circumference of circle = 2πr

22

2 357

220cm

Therefore , distance covered in one round = 220 cm.

Q.8 Total parts = 400 Defective = 8

Percentage of defective parts =8

400×100 = 2

Q.9 12 8

4

x = 2x

12x-8 = 8x 12x-8x = 8 4x = 8 x = 2.

Q.10 Angle of rotation of a square = 90°

order of rotation of a square = 4.

Q.11 (a) T (b) T

SECTION-C

Q.12 Amount borrowed by Anita = 5000 Rs

Interest paid by her = 450 Rs

Amount paid by Anita = 5000 + 450 = 5450. Rs

Q.13 Perimeter = 18 cm

Perimeter of Equilateral triangle is = 3 × side 18 = 3side

18

3side

6cm = side

Area of triangle =1

2× base × height



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= 1

2× 6 × 4

= 12 cm. Q.14.

3 2 17

5 3

3 35 2 1

5 3

3 3 35 5(2 1)

3 9 105 10 5

9 105 5 10 3

100 9 7

9113

7

x x

x x

x x

x x

x x

x

x

Q.15 decrease in % = × 100

Original amount = 200 Change in amount = 200-175 = 25

= 25

100200

= 25

12.5%2

Q.16 Radius = 7cm

Circumference = 2πr = 2 ×22

7× 7 = 44cm.

Total distance in 1 round = 44cm

No. of rounds = = 132

44 = 3cm.

Q.17 S.P.= Rs. 4500 Loss = 25%

C.P.of cooler = 100

.100 %

S PLoss

.



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= 100

100 25 ×4500

= 100

75 × 4500

= Rs. 6000. Q.18 (i) Yes ∆ PLO ∆ PMO (ii) In Δ PLO & Δ PMO PL=PM (given) PLO = PMO =90 (given) OP=OP (common) ∆ PLO ∆ PMO

Q.19. Let the number be x

A.T.Q 2x + 20 =6x 6x – 2x = 20 4x = 20 x= 5

Q.20. As the triangles are congruent

B = E (CPCT) x – 5 = 45 x = 45 + 5 = 50 C = y + 5 27 = y + 5 (27– 5) = y y = 22

SECTION-D

Q.21.

P Q

R

110 4 cm

6 cm



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Q.22. (i) Yes

In Δ AOC and Δ BOD

OA = OB (Radii of the circle)

AOC = BOD (V.O.A)

OB= OD (Radii of the circle)

(ii) AC = BD (CPCT)

Q.23. Length of rectangular field = 120 m

Breadth of rectangular field = 48 m

Area = l b

= 120 48 = 5760 m2

Area of flower bed= l b

=18 8 = 144 m2

Number of beds = Area of rectangle Area of flower bed = 5760 = 40 144

Q.24. Q.25. A.T.Q Let Rakhi age be x years According to the question

X Y

Z

4 cm

4 cm



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48 32

5

4 4032

5

4 40 160

4 160 40

4 120

30

x

x

x

x

x

x

Hence, Rakhi’s age = 30 years =============================================



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72

MODEL TEST PAPER-1

Summative Assessment- II (Unsolved)



Read the question paper well before answering. Each part of Q1 carries 1 mark. Q9 to Q19 carries 2 marks each. Q20 to Q29 carried 3 marks each. Q30 to Q34 carries 4 marks each.

Section- A

Q1. (i)Solve x=12. The value of x is :

(a) 18 (b) –18

(c) 36 (d) None of these

(ii) Angle of rotation in rectangle is :

(a) 900 (b) 1800


(iii) Circumference of a circle is 88cm. Its radius is :

(a) 7 cm (b) 3.5 cm

(c) 14 cm (d) None of these

(iv) In PQR, if PQ = QR & Q=300, then R will be :

(a) 300 (b) 700


(v) If the price of a pair of jeans increase from Rs 1000 to Rs 1200, the

increase percent is :

(a) 12% (b) 200%

(c) 20% (d) None of these

(vi) Divide p by 4 and then add 13. If the result is 11, what is the value of p?

(a) 8 (b) –2

(c) –8 (d) None of these

–2 3



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(vii) 64 chairs can be purchased for Rs 2560. The cost of 90 chairs will be : (a) Rs 3600 (b) Rs 360

(c) Rs 1400 (d) None of these

(viii) ABC is an equilateral triangle and AD BC. ABD is congruent to:

(a) ACD (b) ADC

(c) ABC (d) None of these

Section- B

Q2. Find the ratio of Rs 30 to 900p. Q3. In the adjacent figure, show that

POQ ROS mentioning the congruency of criteria used.

Q4. Cost of an item is Rs 50. It was sold with a profit of 12%. Find the selling

price. Q5. Divide 80 into 2 parts such that the greater part is 4 times the smaller

part. Q6. What happened to the perimeter of the square if its side is doubled?

Q7. State the order and angle of rotation in : (i) Rhombus (ii) Regular hexagon

Q8. Can the triangle with following measures be constructed? If not, why (i) AB = 8 cm, BC = 4 cm, AC = 3 cm (ii) P = 900, Q = 950, QR = 4 cm

Q9. What percent of 2 hours is 30 minutes?

Q10. The quotient of twice a number and 3 is 4. Find the number.

Q11. Express as a rational number :

(i) with denominator 77 (ii) with numerator –12

2 7



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Section- C Q12. Frame the equation for the following statements :

(i) In an isosceles triangle, both the base angles are twice the vertex angle. (ii) Rahul’s father is 2 years less than 4 times Rahul’s age. Age of Rahul’s father is

46 years. Q13. An article was sold for Rs 630 with a profit of 5%. What was its cost

price? Q14. Find the area of unshaded portion. Q15. The length of a park is 4 times its breadth. Find the breadth of the park if

the perimeter is 420m.

Q16. In how many years will Rs 7,500 amount to Rs 11,700 @7% p.a. simple interest.

Q17. The sum of 3 rational numbers is . If 2 of the numbers are

and , find the third rational number.

Q18. Construct ABC, right angled at B, given that AC = 5cm and BC = 3 cm. Write the measure of third side.

Q19. In the given figure, AD = BC and AD||BC. Prove that AB = DC.

Q.20 Solve 3(y – ) = 2 (2y–6)

–6 5 –9

15

3 10

1 3



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Section- D

Q.21 Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70m and breadth 45m and parallel to its sides. Find the area of the roads.

Q.22 In a triangle, the ratio of 3 angles is 4:6:8. Find the measure of each angle. Also find the percentage of each angle. Q.23. In the given figure :

(i) Is ABD CBD. Give reasons

mentioning the congruence criteria used.

(ii) Does BD bisects ABC. Give reasons.

(iii) Can the congruency be proved by

any other criteria? If yes, mention it.

Q.24 Solve and verify :

= Q.25 The 2 sides of a parallelogram PQRS are 6cm & 4cm. The height corresponding to the base RS is 3cm. Find.

(ii) Area of parallelogram. (iii) The height corresponding to the base PS

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

4m + 2 4m + 10

1 2



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76

MODEL TEST PAPER-2

Summative Assessment- II (Unsolved)

GENERAL INSTRUCTIONS.

Attempt all the questions neatly with formulae & figures properly labelled wherever required.

Section-A (Q1): Each part carries 1 mark. Section-B (Q2- Q 11): Each question carries 2 marks. Section-C (Q 12-Q 20): Each question carries 3 marks. Section-D (Q21- Q 25): Each question carries 5 marks.

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

SECTION A (1 × 8= 8) Q.1. Fill in the blanks:

(i) 9

7 and

9

7

both are positive rational numbers. State (True/ False)

(ii) Two circles are congruent if they have same ____________.

(iii) Can we construct a right angled triangle ABC where mA= 100°, BC= 4.5

cm and AC= 3 cm (Yes/ No) ___________.

(iv) Product of rational number 4

3and its multiplicative inverse is ___________.

(v) Side included between the angles P and Q of PQR is ____________.

(vi) 1m2 = ____________ cm2.

(vii) x= 9 satisfies the equation x – 9= 1 (Correct/ Incorrect)_____________.

(viii) 9

2

7

4 = _____________

SECTION B (2 × 10= 20)

Q.2. Price of a shirt decreases from Rs 800 to Rs 600. Find the percent decrease.

Q.3. Find BC, if the area of a triangle ABC is 36 cm2 and the height AD is 3 cm.

A

B C D



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Q.4. Express 7

2as a rational number with

(i) denominator – 77 (ii) numerator 26

Q.5. Given that AB = AC and BD = CD.

(i) What additional information is needed to prove that ABD ACD by SSS congruence rule, giving reason.

(ii) Is B= C ? Why?

Q.6. Do as directed: (i) Translate the given statement into an equation. “Twice of a number m subtracted from 23 gives –5.”

(ii) Express the given equation in statement form.

862

p

Q.7. Are the ratios 1 : 2 and 2 : 3 equivalent? Show the working.

Q.8. Find the area of a circular table top of diameter 1.4 m.

Q.9. Find any two rational numbers between 7

3 and

5

4?

Q.10. If XD is bisector of YXZ, fill in the given blanks according to the figure.

(i) XY = XZ (Given) (ii) XD = XD (Common) (iii) YXD = __________ (Reason) ____________ (iv) XDY __________ by ___________ congruence criterion.

Q.11. Solve for k:

–5 = 6 (k – 11) + 7

SECTION C (3 × 9= 27)

Q.12. The area of a square and a rectangle are equal. If the side of the square is 40 cm and breadth of the rectangle is 25 cm, find the length of the rectangle.

Q.13. (i)Simplify and write the result in standard form.

6

72

35

9

5



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(ii)Write the additive inverse of the result

Q.14. Construct a LMN right angled at M, given that LM = 5 cm and MN = 3 cm.

Q.15. Aryan borrowed Rs 3500 at 7% p.a. rate of interest. Find the amount to be paid back at the end of the second year.

Q.16. In a class of 25 students, the number of girls is 5

2 of the boys. Find the number of

boys in the class. Q.17. In the given figure, prove that DEO PRO using congruence rule.

Q.18. DL and BM are the heights on the sides AB and AD respectively of parallelogram ABCD. If the area of parallelogram is 1470 cm2, AB = 49 cm and AD = 35 cm.

(i) Find the length of DL. (ii) What is the perimeter of parallelogram ABCD.

Q.19. What should be subtracted from

3

1

2

1 to get –

5

1?

Q.20. The cost of the box is Rs 120. If the shopkeeper sells it at a loss of 10%. Find the price at which it is sold.

SECTION D (5 × 5= 25)

Q.21. A rectangular park is 90 m long and 75 m broad. A path 5 m wide is constructed outside the park. Find the area of the path. Also find the cost of cementing it at the rate of Rs 40 per m2. [Figure is must]

Q.22. Answer the following questions: (i) Express profit when SP > CP. [Formula]



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(ii) Varsha saves Rs 4000 from her salary. If this is 10% of her salary. What is her salary?

(iii) Convert 0.65 to percent.

Q.23. Draw a line PQ. Draw perpendicular to PQ at any point on it. On this perpendicular choose a point X, 3.8 cm away from PQ. Through X, draw a line AB parallel to PQ.

Q.24. DA AB, CB AB and AC = BD in the given figure:

(i) State three pairs of equal parts in ABC and DAB with reason.

(ii) Which of the following statement is meaningful: (a) ABC BAD (b) ABC BAD

(iii) State the congruence rule used.

Q.25. (i) People of Sundaram village planted trees of mangoes and apples in the village garden. The number of apple trees were two more than three times the number

of mango trees. If number of apple trees were 77, what was the number of mango trees?

(ii) Tushar thinks of a numbers. If he adds 19 to it and divide the sum by 5, he will get 8. Find the number.

*************

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Practice Assignment for Summative Assessment-I

Revision module- 1 Integer

Q.1 Fill in the blanks:

(i) Natural numbers, Zero and opposite of natural numbers together are called _____________.

(ii) A positive integer is _____________ than its opposite.

(iii) Zero is greater than every _____________ integer.

(iv) Zero is less than every _____________ integer.

(v) The opposite of 27 is _____________.

(vi) The opposite of – 160 is _____________.

(vii) The greater the number, the _____________ is its opposite.

Q.2 Indicate the following using integers:-

(i) 50m above sea level

(ii) 80 C below zero.

(iii) The temperature has fallen further by 50 C.

Q.3 Insert the symbol > or < in each blank:-

(i) – 52 ______ 25 (ii) 17 ______ – 34 (iii) –7 ______ – 16 (iv) – 6 ______ 0 (v) 8 ______ 0 (vi) –15 ______ 2

Q.4 Verify

19 × {7 + (– 3)} = 19 × 7 + 19 × (– 3)

Q.5 Fill in the blanks: -

(i) (–7) + (–11)+9 = _______________

(ii) (–8) + 17 = _______________

(iii) 15 + (–19) = _______________

(iv) 28 + 84 = _______________



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(v) –6 + ___________ = 0

(vi) 0 + ____________ = – 5

(vii) –1368 + _____________ = 0

(viii) ____________ + (-27) = 0

Q.6 Find the product using suitable properties:-

(i) 1487 × 327 + (– 487) × 327 (ii) 4 × (– 25) × 166

(iii) 8 × 291 × 125 (iv) 28945 × 99 – (– 28945)

Q.7 Find the Value of: -

(i) 32475 ÷ 1 (ii) 694 – (725 ÷ 725)

(iii) 0 ÷ 719 (iv) (1465 ÷ 1465) – (1465 ÷ 1465)

Q.8 Fill in the blanks: -

(i) – 20 + = – 30

(ii) 70 + = – 20

(iii) 46 – (– 56) =

(iv) – 78 + (– 217) =

Q.9 A tank is full of 2000 litres of water. Due to a leakage the quantity changes

by – 4 litres every hour. How long will it take to get empty?

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

Revision module- 2 Fractions and decimals

Q.1 Evaluate:

(i) 0.08 0.13

(ii) 3 7.42

(iii) 2 1

(iv)

1 26

6 13

4 18

35 20

9 14



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(v) 2 + 1

(vi) –

Q.2 Arrange , , in descending order.

Q.3 Mintoo cuts a strip of length 6cm into smaller strips of length cm. How many

strips will she get?

Q.4 litre of oil costs Rs20. What is the cost of 5 litres of oil?

Q.5 Which is greater

of or of

Q.6 Which is greater 0.02 or 0.2 and by how much?

Q.7 What decimal fraction of a rupee is 25 paise?

Q.8 Convert: (i) 75m to cm (ii) Rs 7.25 to paise (iii) 55km to m (iv) 17562 g to kg

Q.9 The side of an equilateral triangle is 1.5cm. Find its perimeter

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

Revision module- 3 Lines and Angles

Q.1 Find the unknown angles:

(i) Given: l|| m

1 3

4 9

5 12

1 3

1 2

1 2

1 4

3 2

3 7

1 6

3 5

2 3

1 4

1 2

y

x l

m 130



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(ii) Given : a || b

Q.2 Fill the table using the figure below: -

SL.No Name of all the Angles

1

2

3

4

5

6

7

Interior angles

Exterior angles

Pairs of corresponding angles

Pairs of alternate interior angles

Pairs of alternate exterior angles

Pairs of interior angles on the same

side of the transversal

Pairs of exterior angles on the same

side of the transversal

4

1 3

2

6

7

5

8

l

m

n

y

a

b

x

80



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Q.3 Think and answer the following- Draw a rough sketch if possible.

(i) Can two adjacent angles be supplementary? (ii) Can an acute angle be adjacent to an obtuse angle? (iii) Can you find the complement of an obtuse angle? (iv) Can the supplementary of a right angle be an acute angle?

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

Revision module- 4 The triangle and its properties

Q.1. Is it possible to have a triangle with the following sides? Give reasons to support your answer. 5cm, 12cm, 13cm Q.2. Find the value of the unknown angles x and y.

(i) (ii)

Q.3. The angles of a triangles are in the ratio of 3:4:1. Find the measure of each angle of the triangle.

Q.4. One of the exterior angles of a triangle is 100˚ and its interior opposite angles are equal to each other. What is the measure of each of these two angles?

Q.5. Find the missing sides of the following triangles:

15

A

12

B D x C y

50˚

x +20˚ x y



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Q.6. Find x, in the figures given below.

(i) (ii)

(iii) (iv)

Q.7. One of acute angles of a right triangle is 53˚. Find the other acute angle.

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

Revision module- 5 ALGEBRAIC EXPRESSIONS

Q.1 Write each of the following statement as an algebraic expression: -

(i) 8 times a number equals 40

(ii) A number decreased by 11 is 15

(iii) 9 subtracted from one third of twice a number

(iv) Twice a number subtracted from square of number.

(v) Three less than 5 times a number.

(vi) Five times a number is 8 more than the number

(vii) Square of number k added to thrice of number b

(viii) Twice the number subtracted from one fifth of a number

Q.2 Write coefficient of ‘q’ in the terms of following expressions: - –7pq, 3p – 2q, 4 –p + q, a + bp, 18pqr

Q.3 Subtract-

(i) 4a + 3b from 2a + 2b –4

x

120˚

x 20˚

x 90˚



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(ii) 10a2 –5a from –10a –6a2

(iii) 6x3 –7x2 + 5x –3 from 4 –5x + 6x2 –8x3

(iv) 6x3 –8x2 + 4x – 2 from 5 – 4x + 6 x2 – 8x3

(v) 1 – x2 – y2 from xy + y2 – x2 + 1

(vi) 4a –7ab +3b + 12 from 12a – 9ab + 5b –3

(vii) 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Q.4 If A = 3x2 –7x –8, B = x2 + 8x –3, C = –5x2 –3x +2. Find:

(i) A + B – C (ii) B + C –A

(iii) A – B + C (iv) A – B – C

Q.5 What should be added to x2 + 4 to get x2 – 4?

Q.6 What should be subtracted from 2x2 – 3x + 6 to get 4x2 – x + 21?

Q.7 How much is x2 –2xy + 3y2 less than 2x2 – 2xy + xy?

Q.8 How much does 9x2 + 7x – 2 exceed 2 x3 + 4 x2 + 3x + 1?

Q.9 From the sum of 4x2 –6x + 3 and –4x2 –7x + 5, subtract 3x2 –8x + 6?

Q.10 If n = –7 find value of – 3x2 (n + 10)?

Q.11 From sum of x2 – 3y2 – 6xy, 2x2 – y2 + 8xy, y2 + 8 and x2 – 3xy

subtract – 3x + 4y2 – xy + x – y + 3 Q.12 Fill in the blanks: -

(i) A symbol having a fixed numerical value is called ________.

(ii) A symbol which takes various numerical values is called ________.

(iii) Constant term of 7 x2 – 9 = ________.

Q.13 What should be value of ‘p’ if value of –3x2 + x + p equals to 4 when x = 2?

Q.14 Add the following: -

(i) 10 x2 – 15x – 12, – 15 x2 + 14x + 16, 16 x2 – 5x + 25



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(ii) 6 m2n + 3mn – 2n2, n2– mn – m2n, mn – 3 n2 – 4m2 n

Q.15 Simplify these expressions and find values if x = –2, y = 1, z = 0.

(i) 9 + 5 (x + 7) – z – 2(x +z)

(ii) 7 (x + y) + 3xyz + 2 (x + y + z)

Q.16 From p3 – 4 + 3p2 take away 5p2– 3p3 + p – 6

Q.17 (A) Find the values of each of the following expression for a = 1, b = 2 and c = –1.

(i) a3 + b3 + c3 – 3abc

(ii) a2 + b2 + c2 – ab – bc – ca

(B) If x = 0 and y = 2 then evaluate-

(i) x2 – y + 3

(ii) 8 y2 – 2 x3

(iii) x2 – 2 y2 – 7

(iv) x3 y – 7 y3 –5x

(v) x + y

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

1 3

1 4



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Revision module- 6 EXPONENTS AND POWER

Q.1. Do as directed:

(i) Write in exponential form.

(a) 4 × 4 × a × a × b × b ×b (b) – 125 (c) 512

(ii) Write in expanded form. Also write their base and exponent.

(iii) Express as single power xa × ya

(iv) Convert into power notation –

(v) Express 4985.5 in the standard form.

(vi) Express 0.0000732 in the standard form.

(vii) Express in expanded form.

7, 644 × 10–5

(viii) Express in the usual form.

4 × 105 + 3 × 102 + 2 × 10 + 10˚

(ix) Express 256 as the power of 2

Q.2. Which is greater: 25 or 42

Q.3. Simplify using laws of exponents:

(i)

(ii) (29˚ – 23˚) × 16˚

(iii)

(iv)

Q.4. Find the value of (8x)3 if x = –

1 64

58 × b7 (25)3 × b4

(33) 2× 52 92 × 5

( )3 × ( )3

( )2 × ( )4

3 5

1 7

3 5

1 7

1 8



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Q.5. By what number 610 should be divided to obtain 216.

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

Revision module- 7 DATA HANDLING

Q.1 Find the mean of all factors of 8.

Q.2 Twelve students were given a maths test and the time (in minutes) taken by them to complete the test is listed below. Find the mean and range of these times. 10, 9, 12, 11, 8, 15, 9, 7, 8, 6, 12, 10

Q.3 The minimum and maximum temperatures of different cities on a particular day are given below:

Temperature Cities

Ambala Chennai Banglore Delhi Jaipur Jammu Bhopal Minimum 26C 27C 24C 28C 29C 26C 25C

Maximum 37C 36C 28C 38C 39C 41C 35C

Construct a vertical double bar graph. Also answer the following questions on the basis of the bar graph:

(i) Which city has the greatest difference in the minimum and maximum temperature on the given day?

(ii) Which is the hottest city and which is the coldest city? (iii) Name the city, which has the least difference between the minimum and

maximum temperatures. (iv) Name the two cities where the maximum temperature of one was less than the

minimum temperature of the other.

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

Practice Assignment for Summative Assessment-II

Revision module- 1 RATIONAL NUMBERS

Q.1. Simplify and express the result as a rational number in the standard form: -

(i) ×

(ii) ÷

15 28

–119 9

–8 15

–16 3



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(iii) Subtract from

(iv) + +

Q.2. Express the following rational numbers in their lowest form and standard form.

Rational form Lowest form Standard form

(i)

(ii)

Q.3. Which of the following pairs of rational numbers are equivalent:

(i) ,

(ii) ,

Q.4. What should be added to ( + + ) to get 3?

Q.5. The product of two rational numbers is . If one of the number is , find the other.

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

Revision module- 2 CONGRUENCE OF TRIANGLES

Q.1. In the given figure, triangles ABC and DCB are right angled at A and D respectively

and AC = DB. Prove that ∆ABC ∆DCB.

Q.2. In the given figure, PL OA

and PM OB such that PL = PM.

14 –32

–32 42

7 –8

– 7 8

6 5

12 8

11 15

–13 20

–12 5

31 10

12 –15

–7 –20

1 2

1 3

1 5

– 28 81

14 27



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Is ∆PLO ∆PMO. Give reasons.

Q.3. In the given figure, prove the pair of triangle is congruent. Give reasons.

Q.4. In the given figure, BD and CE are altitudes of ∆ABC and BD = CE. (i) Is ∆BCD ∆CBE. (ii) State the 3 pairs of matching parts used in answer (i).

Q.5. In the given figure, conclude that the ∆AOC ∆BOD. Q.6. In the given figure, AB||DC and AB = DC.

(i) Is ∆ACD ∆CAB?

(ii) State the three pairs of matching part used to prove congruency.

(iii) Which angle is equal to CAD. (iv) Is AD||BC.

Q.7. In the following figure, prove that (i) AC = EF (ii) DF || BC

6cm 6cm 4cm

2cm 2cm

A

C D

B

A

E D

B C

A D

C B

O 70˚

70˚ 3cm 3cm

A B

C

D

F

E

A

B C

D



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Q.8. In the given figure, AD is a median of Δ ABC and BL and CM are perpendiculars

from B and C respectively on AD and DM. Prove that;

(i) ∆DBL ∆DCM

(ii) BL = CM

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

Revision module - 3 SIMPLE EQUATIONS

Q.1. Write the equation for the following statements:

(i) If you subtract 5 from one fourth of x, you get 39.

(ii) A number plus is equal to 4

(iii) 3 less than 5 times a number is 75. (iv) 23 is equal to seven times a number added to 7. (v) 5 more than twice a number is 45.

Q.2. Match the following- EQUATION SOLUTION

(i) 2(x + 1) =4 (ii) 3x = 0 (iii) 2(y – 1) = 12 (iv) 5z = 50 (v) 2(x +1) = 14

(a) 7 (b) 1 (c) 6 (d) 0 (e) 10

1 2

1 2



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Q.3. Write the following equation in statement form-

(i) 5x – 2=8

(ii) Y + = 5

(iii) 5q – 7 = 18

(iv) = 10

(v) 2x + 9 = 11

Q.4. Solve the following equation by trial and error method- (i) 4y + 3 = 11 (ii) 4x – 8 = 12

Q.5. Solve the following equations-

(i) 9a – 7 = 14 + 2a

(ii) + 4 = –

(iii) – = – 2

(iv) 3(2x – 1) + 2(1 – 5x) = 9 + x

(v) a + = 5 – 6a

Q.6. Setup equations and solve them: (i) Which number is 4 more than the product of 6 and 2

(ii) Find a number x that is 5 times the difference between 16 and 4

(iii) A is 15 years older than B now. Ten years ago A was four times B’s age. What are their ages now?

(iv) A number is divided into two parts. One part is 10 more than the other. The sum of the parts is 40. What are two parts? What is the number?

(v) The sum of four consecutive numbers is 46. find the numbers.

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

1 3

5x 7

2a 5

a 3

1 5

x 8

1 2

x 6

3 2



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Revision Module - 4 COMPARING QUANTITIES

Q.1. Fill in the blanks: -

(i) A ____________ is formed when two quantities are compared by division (i.e)

a : b or

(ii) To convert a percentage into a fraction or a decimal, divide it by __________.

(iii) Ratio of 500 to 50 is ___________.

(iv) The ratio of 5 hours to ___________ minutes = 6:1.

(v) is written as ___________ %

(vi) is written as ___________ %.

(vii) 64% as a fraction in lowest terms is ____________.

(viii) as a percent = ____________.

(ix) 5.05 as a percent = ____________.

(x) 90% as a decimal = ____________.

(xi) 50% of 250 = ____________.

(xii) 750 marks out of 1000 is ___________ % marks.

(xiii) To compare two quantities, the ___________ must be the same.

Q.2. Mrs. Shah gets Rs. 30,000 as her monthly income. She spends 25% of it on grocery items and 20% of it on house rent. How much does she spend on both?

Q.3. Convert into percentage and find out which is more 20 marks out of 25 (or) 35 marks out of 40.

Q.4. Sakshi has to type 176 pages. She has completed 25% of her work. How many pages has she typed?

Q.5. Find x if 8% of x is 96.

Q.6. Mr. Verma saves 23% of his salary. He receives Rs. 24,500 as salary every month. What is his monthly expenditure?

a b

24 10 3.4 100

3 4



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Q.7. A dealer purchased an old cycle for Rs. 500, spent Rs. 150 on repairs and sold it for Rs. 663. What is his gain or loss%?

Q.8. Mohan purchased a machine for Rs. 800. He sold it at a profit of 10%. What was the selling price of the machine?

Q.9. A table costing Rs. 500 is sold at a loss of 13%. What is the selling price of this table?

Q.10. Mr. Verma borrowed Rs. 32,000 from a bank at 8% per annum. He cleared the loan after 3 years. What sum did he pay to clear the loan?

Q.11. Mohita borrowed Rs 7000 from a money lender at certain rate. She cleared the loan after 3 years by paying Rs. 8050. At what rate per annum was the interest charged?

Q.12. A fruit vendor buys a basket of 100 oranges for Rs 300. He sells the oranges at Rs 70 a score. Find his gain or loss percent.

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

Revision Module- 5 PRACTICAL GEOMETRY

Q.1. Draw a line PQ. Take any point R outside PQ. Through R, draw a line RS parallel to PQ with scale and Compass.

Q.2. Construct ∆PQR in which Q = 45˚, PQ = 5.5cm and QR = 6.5cm. Find the length of third side.

Q.3. Construct an equilateral triangle having its perimeter 16.5cm.

Q.4. Construct a ∆ABC in which AB = 5cm, B = 45˚, C = 40˚. Q.5. Construct a triangle in which one side is 6cm and sum of two equal sides is 9cm.

Q.6. Draw a line, and mark points X and Y on it, such that XY = 6cm. Mark a point A above XY and another point B below XY. Draw perpendiculars from A and B to XY. Check to see if the perpendiculars are parallel to each other.

Q.7. Construct a triangle AOB given that OA = 5cm, OB = 4.5cm and AOB = 50˚. Q.8. Construct triangle ABC given that AB = 4.8cm, BC = 5.2cm and perimeter of triangle is 14.6cm.

Q.9. Draw a line AB = 6cm, mark a point P above AB and Q below AB. Draw two lines parallel to AB through P & Q.

Q.10. Draw a line segment PQ = 5.5cm. At Q draw another line segment QR equal to 5.5cm at an angle of 60˚ with QP. Join PR. What kind of a triangle will this be? Why?



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Q.11. Draw a line segment AB equal to 5cm. At A and B, construct perpendicular segments, each equal to 5cm. Mark these AD and BC. Join CD. What is the measure of CD? What kind of figure is ABCD?

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

Revision Module- 6

TOPIC– PERIMETER & AREA

Q.1. Find the area of a rectangular plot one side of which is 36 cm and its diagonal is 48 cm.

Q.2. The length of a rectangle is twice its breadth. If its perimeter is 120m, find its area.

Q.3. How many stamps can be cut off from a rectangular sheet of size 125cm×85cm if each stamp has a size 25cm×17cm?

Q.4. The side of a square flower bed is 1m 80cm long. It is enlarged by digging a strip 20cm wide all round it. Find the area of the enlarged flower bed and also the increase in the area of the flower bed.

Q.5. A school auditorium is 50m long and 30m wide. This auditorium is surrounded by a verandah 5m wide on the outside of it. Find the area of the verandah. If tiles of 50cm×50cm are fixed on the verandah, how many tiles will be required.

Q.6. The area of triangle is equal to that of a square whose each side measures 70m. find

the base of the triangle when the height is 98m.

G

E F

H

B A

D C

P Q

S R

Auditorium

Verandah



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Q.7. The lengths of the base and the height of a triangle are in the ratio 4:5. If the area of the triangle is 40 sq m, find the length of its base and height.

Q.8. A floral design on the floor of a building consist of 280 tiles. Each tile is in the shape of a parallelogram of height 3cm and base 5cm. find the cost of polishing the design at Rs 1.20 per square centimeter.

Q.9. How many square metres of glass will be required for a window which has 12 panes, each pane measuring 25cm by 16cm?

Q.10. The ratio of the radii of two circles is 2:5. What is the ratio of their circumferences?

Q.11. The inner circumference of a circular track is 220m. The track is 7m wide everywhere. Calculate the cost of putting up a fence along the outer circle at rate of Rs 2 per meter.

Q.12. A race track is in the form of a ring whose inner circumference is 352m, and the outer circumference is 396m. Find the width of the track.

Q.13. A piece of wire is bent in the shape of an equilateral triangle of each side 6.6cm. It is rebent to form a circular ring. What is the diameter of the ring?

Q.14. A bicycle wheel makes 5,000 revolutions in moving 11km. Find the diameter of the wheel.

Q.15. A water sprinkler in a lawn sprays water as far as 7m in all directions. Find the length of the outer edge of wet grass.

Q.16. A rectangular field is measuring 260m by 180m. How long will it take for a girl to go four times round the field, if she walks at the rate of 3.8m/ sec.

Q.17. The diameter of a circular garden is 98m. A circular path of width 7m is laid outside the garden. Find the area of the path.

Q.18. A circular carpet of radius 2.1m is spread in a room of length 6m and breadth 5m. Find the area of the floor of the room not covered by the carpet.

Q.19. The length of the minute- hand of a clock is 8.4cm. Find the area swept by it in 1 hour.

Q.20. The diameter of the wheel of a car is 77cm. How many revolutions will it make to travel 121km.?

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FORMATIVE ASSESSMENT-I [50 Marks] MCQ HOLIDAY …...Chapter: Visualising solid shapes (Maths Lab...

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Transcript of FORMATIVE ASSESSMENT-I [50 Marks] MCQ HOLIDAY …...Chapter: Visualising solid shapes (Maths Lab...