Question Bank

5/26/2018 Question Bank

1/51

Question bank

ClassVI

UNDERSTANDING ELEMENTERY SHAPES

LEVELI

1. WHAT IS the measure of a right angle .

2. Define a regular polygon and draw any two .

3. Write the number of faces , vertices and edges of cuboid .

4. Draw a line PQ draw a line XY perpendicular to PQ intersecr at R and measure the angle XRQ.

5. Write the name of the following triangle :

(i)

PQR , PQ =QR=PR = 5 cm .

(ii) DEF ,E = 90.

LEVELII

6. What is the angle for the half of a revolution .

7. Whare will the hand of a clock stop if it :

(i) Start at 12 and make half of revolution clockwise.

(ii) Start at 5 and make th of revolution clockwise .

8. Draw a rough sketch of regular hexagon and shade its interior.

9. Match the following :

COLUMN I COLUMN II

1.staright angle (a) less then th of revolution .

2. right angle (b) more then half of revolution

3. acute angle ( c) half of revolution .

4. obtuse angle (d) 1/4 of revolution.

10.An angle whose measure is less than 90is :

(a) Obtuse angle

(b) Acute angle

(c) Right angle

(d) None of these .


2/51

LEVELIII

11.Which directon will you face if you start facing east and make half of revolution clockwise .

( ans . west )

12.Find the number of right angles turned through by the hour hand of a clock when it goes from

(i) 3 to 6 (ans. 1 )

(ii) 12 to 6 ( ans . 2 )

13.Right the name of triangle XYZ in which angle Y = 90, xy = yz . ( isosceles right angle)14.Draw a regular octagon .draw a rectangle by joining exactly four of the vertices of octagon.

15.Write the definition of an equilateral triangle , isosceles triangle and scalene.

CHAPTER7

FRACTION

LEVEL-I

1. Write the fraction of a shaded portion : ( ans. )

2. Write the equivalent fraction of 1/2 with denominator 8 . ( ans. 4/8)

3. Add the following :(i) 1/4+3/4 (1)

(ii) 1/8+1/8 (1/4)

4. Change 17/4 into mixed fraction. ( )5. Write as improper fraction. (11/5)

LEVELII

6. Draw a number line and locate 1/8,2/8,3/8 on it.

7. Express 27/5 into mixes fraction .

8. Find the equivalent fraction of 105/140 with denominator 4.

9. Add : 1 +3/5+1/2.

10.Simply : +

LEVEL-III

11.Savitabought 2/5 m of ribbon and lalita bought 3/4m of ribbon . what was the total

length of ribbon they bought.


3/51

12.Javed was given 5/7 of basket of oranges .what fraction of oranges was left into the

baslet. (ans. 2/7)

13.Rafiq exercised for 4/5 of an hour while rohit exercised for 3/4 of an hour .who exercised

for a longer time. (ans .rafiq)

14.Write the following in simplest form :

(i) 676/256 (ans .13/8 , 6/1 )

(ii) 1296/216

15.Write the equivalent fraction of 15/35 with numerator 135. (ans . 135/315)

CHAPTER - 8

DECIMALS

LEVEL-I

1. Write the 19.4 in the place value table.

2. Write each of the following as decimal:

(i) 5/10

(ii) 3 + 7/10

3. Express the following as cm using decimals : (i) 2mm (ii) 162 mm

4. Write each of the following decimals in words : (i) 0.03 (ii) 17.4.

5. Which is greater :

(i) 0.7 or 0.78

(ii) 03 or 3.01

LEVELII

6. Write as fractions in lowest terms : (I) 0.06 (ii)_ 0.004

7. Write each of the following as decimals. : (i) 23 +2/10 +6/1000

(iii) 7/10+ 1/5 + 6/100

8. Express as km using decimals :

(i) 8m

(ii) 8888 m

(iii) 52 km 5m

9. Rashid spent Rs 35.75 for Maths book and Rs 32.60 for Science book. Find the

totalamount spent by Rashid.

10.Subtract :(a) Rs 18.25 from Rs 20.75(b) 202.54 m from 250 m

LEVELIII11. Find the value of :

(a) 9.7566.28 (ans. 3.476 , 5.78 ,11.71 )

(b) 21.0515.27

(c) 18.56.79

12. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find


4/51

the total length of cloth bought by her .

13. Find the sum in each of the following :

(a) 0.007 + 8.5 + 30.08

(b) 27.076 + 0.55 + 0.004

14. Raju bought a book for Rs 35.65. He gave Rs 50 to the shopkeeper. How much moneydid

he get back from the shopkeeper .

15 .Show the following numbers on the number line : (a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5

CHAPTER10

MENSURATION

LEVELI

1. Find the perimeter of figure 40 cm

10cm

2. A tabletop measure 2m 25cm by 1m 50cm what is the perimeter of tabletop.

3. Find the perimeter of equilateral of side 3 m .

4. Find the area of rectangle whose length and breadth are 4 cm and 6 cm respectively.5. Find the area of square whose side is 5 m .

LEVELII

6. Find perimeter : 40cm

35cm 35cm

23cm

7. Find the perimeter of a regular hexagon whose side is 6.2 cm .

8. Find the cost of fencing a square park of side 250cm at the rate of rs.20 per m .

9. Find the area of a square plot of side 8m.

10.The area of a rectangular garden of length 50m is 300 sq .m. find the width of garden.


5/51

LEVELIII

11.Find the perimeter : 4cm 0.5cm 2.5 cm

2cm

4cm 0.5cm 2.5cm

12.Two sides of a triangle are 12cm and 14 cm .the perimeter of a triangle is 36 cm . what is the

third side .

13.Five flowers beds each of side 1.2 m are dug on a piece of land 4.8m long 4.2 m wide .what is

the area of remaining part of land.

14.A floor is 5m long 4m wide. A square carpet of side 3m is laid on the floor .find the area of the

floor that is not carpeted.

15.Sweety runs around a square park of side 75cm. Bulbul runs around a rectangular park with

length 60m and breadth 45m . who cover less distance.

CHAPTER11

ALGEBRA

LEVELI

1.IF x cm is the side of a square then what will be the perimeter.

2.Write the expression for :

(i) 7 added to p

(ii) 7 substracted from p(iii) 7 divided by p

(iv) P multiplied by p.

LEVELII

3.Write expression :

(i) 5 times y to which 3 is added.

(ii) Y is multiplied by -8 5 is added to the result.

(iii) Y is multiplies by 7 and result is substracted from 16.

4.Solve the following :(i) 3 + 5 = 12

(ii) Y2 = 19.

LEVELIII

5.Takes sarita present age to be y years : find


6/51

(i) Her age after 5 years

(ii) What will be har age 3 years back

(iii) Saritas Grandfathers is 6 times of her age , what is the grandfather age .

6.Solve the following equation .:

(i) 9u = 81

(ii) 3x2 = 12

(iii) q/3 + 2 = 7 .

7.the length of a rectangular hall is 4m less than three times the breadth of the hall . what is

length.if the breadth is b m .

CHAPTER - 12

RATIO AND PROPORTION

LEVELI

1. Give two equivalent ratio of 6:4.

2. Find the ratio of 9cm to 1.5m.

3. Find the ratio of 40 to 60 .

4. Find the ratio of 55 paise to Re. 1.

5. Are the ratios in proportion :

(i) 25g : 30g and 40kg: 48kg

LEVELII

6. Divide Rs. 60 in ratio 1:2 between kirti and kiran.

7. Find the ratio of following :

(i) 500ml to 2 lts.

(ii) 30 mins to 1.5 hrs

8. There are 102 teachers in a school of 3300 students .find the ratio of the no. of

teachers to no. of students .

9. Determine if the following are in proportion :

(i) 15, 45,40,120

(ii) 33,121,9,96

LEVELIII

10.The weight of 72 books is 9 kg . what is the weight of 40 such books .

11.If the cost of the dozen shop is rupees 153.60 . what will be the cost of 15 such shops

12.Raju purchased 10 pens for rupees 150 . and Manish buys 7 pens for rupees 84 . canyou say who got pen cheaper.

13.There are 45 persons working in a office if number of females is 25 and remaining are

males find the ratio of :

(i) No. of females to no. of males

(ii) No. of males to total persons.


7/51

CHAPTERS - 13 AND 14

SYMMETRY AND PRACTICAL GEOMETRY

LEVELI

1. List any four symmetrical objects from your home or school.

2. Draw line of symmetry :(i) H

(ii) M

(iii) X

3. Draw line of symmetry :

1.

4. Draw a circle of radius 3.2 cm.

5. Draw a line segment of length 7.3cm using rular.

LEVELII

6. write the no. of lines of symmetries of following :

(i)equilateral triangle . (3)

(ii) rectangle (2)

7. write any five alphabets having vertical line if symmetry. ( A, I ,H,T,V)

8. With the same centre O draw 2 circle of radii 4 cm and 2.5 cm.

9. Draw a line segment of length 7cm and construct its perpendicular bisector.

10.Draw the angles of following measures :

(i)60 (ii) 90.

LEVELIII

11.can u draw a triangle which has :

(i) exactly one line of symmetry .(ii) exactly 2 line of symmetry.

(iii) 3 lines of symmetry.

12.Draw the lines of symmetries in following :

(i)


8/51

(ii)

(iii)

13.Draw a circle and mark the points A , B and C such that :

(i) A is on the circle

(ii) B is interior of circle.

(iii) C is exterior of circle.

14.With PQ of length 6.1 cm as diameter draw a circle.

15.Draw an angle measure 135and bisect it.


9/51

Class: VII (TERM 2)

CONGRUENCE OF TRIANGLES

Level 1

1) ABC and PQR are congruent under the correspondence:ABCRQP .Write the parts of ABC that correspond to

2) Two line segments are congruent if ___________.

3) Among two congruent angles, one has a measure of 70; the measure of the otherangle is ___________.

4) When we write A = B, we actually mean ___________.5) If ABC and PQR are to be

congruent, name one additional

pair of corresponding parts.

What criterion did you use?

Level 2

1) In the figure, the twotriangles are congruent.

The corresponding parts

are marked. We can

write RAT?

2) Explain why


10/51

3) By applying ASA congruence rule, it is to be established that ABC QRPand it is given that BC = RP. What additional information is needed to

establish the congruence?

4) In triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR

= 5 cm and PR = 3.5 cm. Examine whether the two triangles are congruent or not. Ifyes, write the congruence relation in symbolic form. Which congruence criterion do

you use in the following?

5) If ABC FED under the correspondence ABCFED, write all thecorresponding congruent parts of the triangles.

Level 3

1) In Figure given AD = CD and AB = CB.

(i) State the three pairs of equal parts inABD and CBD.

(ii) Is ABD CBD? Why or why not?

2) In Figure, AB = AC and AD is the bisector of BAC.

(i) State three pairs of equal parts in triangles ADB and ADC.

(ii) Is ADB ADC? Give reasons.(iii) Is B = C? Give reasons.

3) In Figure, write the congruence rule and conclude that CBA DEF?

4) In Figure, DA AB, CB AB and AC = BD.State the three pairs of equal parts in ABC and DAB.


11/51

Which of the following statements is meaningful?

(i) ABC BAD (ii) ABC ABD

5) You have to show that AMP AMQ.

In the following proof, supply the missing reasons.

COMPARING QUANTITIES

Level 1

1) Find the ratio of 5km and 4 km2) Write as percent3) Express 65% as a fraction4) Express 8.1 as percent5) Convert 1:4 to percentage

Level 2

1) Are the ratios 2:3 and 3: 4 equivalent?2) Cost of an item is Rs. 50. It was sold with a profit of 12% Find its SP3) Rs. 10000 is invested at 5% interest rate per annum. Find the interest at the end of 2

Years

4) Divide Rs. 15000 in ratio of 2:3:55) The population of a city decreased from 25000 to 24500 . Find the percentage

decrease

Level 3

1) The strength of the school increased from 550 to 605. What is the increase percent inthe strength?

2) The cost of an item is Rs. 1200. If the shopkeeper sells it at a loss of 10% . Find theprice at which it is sold.

3) In how many years Rs. 1200 becomes Rs. 1632 at 12% p.a. simple interest.4) In an examination, 96% of the candidates passed and 54 failed. How many

candidates appeared in the examination?


12/51

5) What percent of one hour is 36 seconds

RATIONAL NUMBERS

Level 1

1) Write a rational number between -3 and -4.

2) Fill in the box 3) Write the standard form of

4) Draw on the number line5) Find the reciprocal of 7/9

Level 2

1) Write five rational number between and

.

2) Which is greater ?3) Add

4) Subtract

5)

Level 3

1)

in ascending order

2)

3) 4)

by their difference

5)

PERIMETER AND AREA

Level 1

1) Write the formula for the perimeter of a rectangle2) Write the formula for the area of a square.3) The side of a square is 5 cm . Find its perimeter4) Find the area of a parallelogram if its base is 15 cm and corresponding height is 4.5

cm

5) Find the circumference of a circle having radius 7 cm

Level 2

1) Find the area of a square park whose perimeter 320 m


13/51

2) Find the length of a rectangle whose breadth is 10 m and area is 250 m2

3) Find the area of a triangle if its base is 5cm and corresponding height is 3.2 cm4) If the area of a circular sheet is 154 cm

2. Find its radius.

5) The circumference of a circle is 12.56 cm find its diameter ( Level 3

1) Convert 2 hectare in m2.

2) What is the area of the shaded region ifthe outer and inner radii are 10.5cm and 7 cm respectively.

3) The diameter of the wheel of a car is 70 cm. How many revolutions will it make totravel 110m

4) A wire is in the shape of a square of side 8 cm . If the wire is re-bent into rectangleof length 9 cm, the find the breadth of the rectangle.

5) Find the altitude of a triangle if its area is 30 cm2and base is 20 cm

ALGEBRAIC EXPRESSIONS

Level 1

1) Write an algebraic expression for Product of numbers y and z subtracted from 10.

2) Identify the numerical coefficients of each terms of the expression: 3) Show the terms by factor tree of the expression : 4) What is the value of -5x

2at x= -1.

5) Add 3x + 11 and 7x5

Level 2

1) Add -7mn+5,12mn+2,9mn8, -2mn32) Collect like terms and simplify the expression: 12m29m + 5m4m27m + 103) Subtract 24ab10b18a from 30ab + 12b + 14a

4) Subtract a (b5) from b (5a)5) Find the value of the expression n3+ 5n2+ 5n2 at n= - 2

Level 3

1) What should be the value of a if the value of 2x2+ xa equals to 5, when x = 02) Simplify the expression and find its value when a = 5 and b =3.

2(a2

+ ab) + 3ab

3) From the sum of 4 + 3x and 54x + 2x2, subtract the sum of 3x

25x and

x2

+ 2x + 5.

4) What should be taken away from 3x2

4y2

+ 5xy + 20 to obtain

x2

y2

+ 6xy + 20?

5) Add: 14x + 10y12xy13, 187x10y + 8xy, 4xy

EXPONENTS AND POWERS

Level 1


14/51

1) Express 256 as a power of 2.2) Which one is greater 2

3or 3

2

3) Express 432 as a product of prime factors.4) Express in standard form34300000005) Write 279404 in expanded form

Level 2

1) Simplify : (

)

2) Evaluate 3) Find 4) Express 108 192 as product of prime factors in exponential form5) Find the number from expanded form

Level 3

1) Compare 2.71012and 1.5108.

2) Simplify:

3) Express in exponential form after simplifying: [ ]

4) Write in simplest form:

5) Simplify:

SYMMETRY

Level 1

1) Copy the figures with punched holes and find the axes of symmetry for thefollowing:

2) Given the line(s) of symmetry, find the other hole(s):


15/51

3) Using dotted line as mirror line complete the symmetric figures:

4) State the number of lines of symmetry for the following:

(a)An equilateral triangle (b) An isosceles triangle (c) A scalene triangle (d) Asquare

(e) A rectangle (f) A rhombus (g) A parallelogram (h) A

quadrilateral

(i) A regular hexagon (g) a circle

5) What letters of the English alphabet have reflection symmetry.

Level 2

1) Which of the following figures have rotational symmetry of order more than 1:

2) Write the order of rotational symmetry:


16/51

3) Name any two figures that have both line symmetry and rotational symmetry.4) Name the quadrilaterals which have both line and rotational symmetry of order

more

than 1.

5) Can we have a rotational symmetry of order more than 1 whose angle of rotation is(i) 45? (ii) 17?

Visualising Solid Shapes

Level 1

1) Draw a net for a cube.2) Match the nets with appropriate solids:3) The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric

sketches of this cuboid.

4) Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketchan oblique or isometric sketch of this cuboid.

5) Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:

(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)

(b) A cube with an edge 4 cm long.

Level 2

1) If two cubes of dimensions 2 cm by 2cm by 2cm areplaced side by side, what would the dimensions of the

resulting cuboid be?

2) What cross-sections do you get when you give a

(i) vertical cut (ii) horizontal cut

to the following solids?

(a) A brick (b) A round apple (c) A die

(d) A circular pipe (e) An ice cream cone


17/51

ANSWERS

Congruence of Triangles

Level1:(1) (i)C (ii) B (iii) AC (2)they have equal length(3) 70(4)they arecongruent(5)BC=QR,ASA

Level2: (1)WON(2)AAS(3)B=R ,C=P(4)Yes,ABC RPQ.(5)Ref. NCERT Ex-7.1Q3

Level3: Refer NCERT (1)Example3(2)Example5(3)ASA(4)Example9(5)Ex-7.2 Q3

Comparing Quantities

Level1: (1)5:4(2)75%(3)13/20(4)810%(5)25%

Level2: (1)No(2)Rs.56(3)Rs.1000(4)Rs.3000,Rs.4500,Rs.7500(5)2%

Level3: (1)10%(2)Rs.1080(3)3 years(4)1350(5)1%

Rational Numbers

Level1:(1)-31/10(2)20(3)2/5(4)draw yourself(5)9/7

Level2: (1)any five between 30/60 and 40/60(2)-5/6(3)-4/3(4)-1(5)7/12

Level3: (1)-9/10,-5/6,-2/5(2)20(3)-17/36(4)27/13(5)-4/15

Perimeters and Areas

Level1: (1)2(+b) (2) (side)2(3)20cm(4)67.5cm2(5)44cm

Level2: (1)6400cm2(2)25(3)8cm

2(4)7cm(5)2cm

Level3: (1)20000m2(2)192.5cm

2(3)50(4)7cm(5)3cm

Algebraic Expression

Level1: (1)10-yz(2)1,2,-3(3)do yourself(4)-5(5)4x+6

Level2: (1)12mn-4(2)8m2-16m+10(3)6ab+22b+32a(4)-5a+5b-2ab(5)0

Level3: (1)-5(2)38(3)Refer NCERT Ex-12.2Q6part-b(4)Q5of Ex-12.2(5)Q2part-v of Ex-12.2

Exponents and Power

Level1: (1)28(2)3

2(3)2

43

3(4)3.43109(5)NCERT Ex-13.3Q1

Level2; (1)310

(2)36(3)2(4)2

83

3(5)86045

Level3: (1) 2.71012is greater(2)162(3)53(4)a3b(5)5t4/8


18/51

CLASS - VIII

FACTORIZATION

Level 1

1) Factorize +xy+8x+8y

2) Factorize +14a

3) Factorize -36

4) Find and correct the error in these expressions

5y+2y+y-7y=o

5) Work out the following divisions

(10x-25) (2x-5)

Level-2

1) Factorize the following expressions

-10q+21

2) Factorize -

3) Divide z (-80) by 5z (z+4)

4) Divide 5(2x+1) (5x+5) (2x-5)

5) Factorize the expression and divide then as directed (-25p+20) (p-1)

Level-3

1) Factorize

2) Factorize the expression

3) Divide as directed

52pqr (p+q) (q+r) (r+p) 104pq (q+r) (r+p)

44 by 11x(x-8)


19/51

5) Find and correct the error in the following mathematical statement

DIRECT AND INVERSE PROPORTIONS

1) A train travels 60km in 1 hour. How long will it take to go 150km?

2) The rent of 7 Hectares is Rs 875, what is the rent of 16 Hectares?

3) If x=ky and when y=4, x=8 then k=?

4)10 men can dig a tent in 15 days, how long will 3 men take?

5) The time taken for a fixed journey and the speed of the vehicle is an example of inverse or

direct variation

Level II

1) There are 100 students in a hostel; food provision for them is for 20 days. How long will

these provisions last, if 25 more students join the group?

2) Two persons could fit new window in a house in 3 days. How many persons would be

needed to fit the window in one day?

3) 6 pipes are required to fill a tank in 1hour 20 minutes. How long will it take if only 5 pipes

of the same types are used?

4) If 15 workers can build a wall in 48 hours, how many workers will be required to do the

same work in 30 hours?

5) A machine in a soft drink factory fills 840 bottles in 6 hours. How many bottles will it fill in

five hours?

Level III

1) Suppose 2 kg of sugar contains 9crystals. How many sugar crystals are there in-

i) 5 kg of sugar?

ii)1.2 kg of sugar?

Algebraic Expressions and identities

Level 1

Q1 Identify the terms, their coefficient for each of the following expressions


20/51

i)

ii)

iii)

iv)

Q2 Classify the following polynomials as monomials, binomials, trinomials andpolynomials

Q3 Add

Q4 Find the product

Q5 Evaluate the following product

Level 2

Q1 Add

Q2 what must be subtracted from to get Q3 multiply

Q4 simplify and find its value for

Q5 Use suitable identity to find the product

Level 3

Q1 Find the product

Q2 Simplify


21/51

Q3 Simplify for

Q4 Find the product using suitable identity

Q5 Subtract from

Comparing quantities

Level 1

Q1 find the ratio of 12kg to 60gm

Q2 A washing machine marked at Rs 15,000 is available for Rs 14,000. Find the

discount given and discount percent

Q3 Find S.P if a profit of 5% is made on a cycle of Rs 3000

Q4 Find C.I on Rs 12,000 for 2 years at 10% p.a. compounded annually

Q5 Find C.I on Rs 10,000 for 1 year 6 months at 20% p.a. compounded half

annually

Level 2

Q1 Convert each part of ratio to percentage

Q2 The price of an L.C.D was Rs 35,000 last year. It has increased by 10% thisyear. Find the price this year

Q3 If 8% VAT is included in the prices, find the original price of a refrigerator

bought for Rs 13,500

Q4 Find C.I on a sum of Rs 8,000 for 2 years at 5% p.a. compounded annually

Q5 The cost of a washing machine worth Rs 10,000 depreciated by 5%. Find its

value after one year

Level 3

Q1 Find S.P if a profit of is made on a mixer grinder bought for Rs 650 and

expenses of Rs 50 made on ots repairs

Q2 Renu bought two fans for Rs 1200 each. She sold one at a loss of 5% and

other at a profit of 10%. Find the selling price of each. Also find out total

profit or loss


22/51

Q3 In what time the compound interest on Rs 800 at 20% per annum will amount

to Rs 1152, if compounded annually

Q4 If the cost price of 10 chairs is equal to S.P of 16 chairs. Find the gain or loss

percentage

Q5 A defective briefcase costing Rs 800 is being sold at a loss of 8%. If the price

is further reduced by 5%. Find the selling prize.

VISUALISING SOLID SHAPES

Level 1

Q1 Draw a figure to show top, front, side view of a dice

Q2 Draw a map of your class room

Q3 Write Eulers formula. Verify it for faces, vertices, and edges of a cube

Q4 Write down the no. of faces in a triangular prism

Q5 Write no. of faces, vertices, and edges of a prism with square base

Level 2

Q1 Write the no. of faces, vertices, and edges of a pyramid with square base

Q2 Draw a map of your school

Q3 Is a square prism same as a cube? Explain

Q4 Differentiate between a prism and pyramid by drawing figures

Q5 Verify Eulers formula for a pyramid with square base

Level 3

Q1 Show the front, top and side views of a matchbox drawing suitable figures

Q2 Draw the map of your school compound using proper scale and symbols forvarious features like gardens, main building, playgrounds

Q3 Can a polyhedron have 10 faces, 20 edges, and 15 vertices?

Q4 Write the no. of faces, edges and vertices of a triangular pyramid and verify

Eulers formula.


23/51

Q5 Draw figures of three solids which are not polyhedrons

EXPONENTS AND POWERS

Level 1

Q1 Find the value of

Q2 Infind the base and exponent

Q3 If

Q4 Evaluate


Level 2

Q1 Find the value of 0.0016 in exponential form


Q3 Write the result in power notation simplifying

Q4 Evaluate

[

]

Q5 Find the value of [ ]

Level 3

Q1 Write 150000000 in standard form

Q2 Write the value of

Q3 Evaluate

Q4 Find the value of m for which

Q5 Evaluate

MENSURATION


24/51

Level 1

Q1 Write the perimeter of

a) Square of side 4cm

b) Triangle of sides 9, 11, 14 cm

Q2 The diagonals of a rhombus are 7.5 cm and 12cm. Find its area.

Q3 Find the total surface area of cuboid of dimensions

Q4 Find the side of a cube whose surface area is

Q5 What shape will it take if the height of a cuboid becomes zero

Level 2

Q1 A square of side 6cm and a rectangle of length 80m have same perimeters. Which of the

two has larger area?

Q2 Find the area of a rhombus whose side is 6cm and one altitude is 4cm. If one diagonal is

8cm, find the other diagonal

Q3 Find the total surface area of a cuboid of dimensions

Q4 Find the volume of a room of height 4cm and floor is in a shape of a square whose side

6cm

Q5 The base radius and height of a right circular cylinder are 5cm and 10cm. find its surfacearea.

Level 3

Q1 A flooring tile has a square shape with side 10 cm. How many such tiles are required to

cover an area 1080 m2?

Q2 Find the total surface area and the lateral surface area of a cube of side 10 cm?

Q3 The heights of two circular cylinders are same, their volumes are respectively 16 m3and

81 m3. Find the ratio of base radii.

Q4 A classroom is 11m long, 8m wide and 5 m high, find the sum of areas of its floor and the

four walls.

Q5 Find the length of the longest pole that can be put in a room of dimensions


25/51

INTRODUCTION TO GRAPHS

Level 1

Q1 What is the abscissa of a point (-3,-2)

Q2 In which quadrant does (3,-6) lie?

Q3 Where p(x,0) lies?

Q4 What are the quadrants of origin?

Q5 What is Ordinate?

Level 2

Q1 Where is x coordinate of a point zero?

Q2 What is the name of point where both axes meet?

Q3 The adjoining graph shows the movement of an object across a playground. Answer the

following questions

a) For how much time object was stationary?

b) Find the time taken to reach the distance of 75m?

c) At what time the object became stationary?

Q4 Draw a graph for the following


26/51

No. of articles 5 10 20 15 8

Cost of articles(in Rs) 25 50 100 75 40

Q5 Plot the points and verify if they lie on a line

Level 3

Q1 The following table gives displacement is of a moving particle at various time

Time(in sec) 0 2 4 6 8 10

Displacement(in m) 3 8 13 18 23 28

Draw displacement-time graph for the above data. Find

a) Displacement at 7 seconds

b) Is it a linear graph?

Q2 Ajit can ride a scooter constantly at a speed of30 km/h. Draw the distance time graph for

this situation. Use it to find

i) The time taken by Ajit to ride 75km.

ii) The distance covered by Ajit in 3

hours.


27/51

CLASS -IXSurface Areas and Volumes

LEVEL I

1. If the volume of a cube is 125 cm3

, then its surface area isa) 25 cm2.

b) 100 cm2.

c) 150 cm2.

d) 300 cm2. [Ans.:

c) ]

2. If an edge of a cube is 20 cm, then the number of cubes of 5 cm edge that can be formed from this

cube is

a) 256

b) 64c) 16

d) 4 [Ans.: b) ]

3. If the radius of a cylinder is 3 cm and height is 4 cm, then its total surface area is

a) 24 cm2

b) 33 cm2

c) 42 cm2

d) 56 cm2 [Ans.: c) ]

4. If two cylinders of same lateral surface have their radii in the ratio 4:9, then the ratio of theirheights is

a) 2:3

b) 3:2

c) 4:9

d) 9:4 [Ans.: d) ]

5. If the volume of a right circular cylinder with height 14 cm is 1584 cm3, then its diameter is

a) 3 cm

b) 6 cm

c) 12 cm

d) 24 cm [Ans.: c) ]

LEVEL II


28/51

1. A plastic box is 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is open at the top.

Ignoring the thickness of the plastic sheet, determine:

(i) The area of the sheet required for making the box.

(ii) The cost of sheet for it, if a sheet measuring 1m2costs Rs. 20.

[Ans.: (i) 5.45 m2 (ii) Rs.

109]

2. The slant height and base of a colonial tomb are 25 m and 14 m respectively. Find the cost of

white washing its curved surface area at the rate of Rs. 210 per 100 m2.

[Ans.: Rs. 1155]

3. A jokers cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. find the

area of the cloth required to make 10 such caps.

[Ans.: 5500

cm2]

4. A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

[Ans.: 38.5

kilolitres]

5. The volume of a right circular cone is 9856cm3. If the diameter of the base is 28 cm, find

(i) Height of the cone

(ii) Slant height of the cone

(iii)Curved surface area of the cone.

[Ans.: (i) 48 cm (ii) 50 cm (iii) 2200

cm2]

6. The inner diameter of a circular well is 3.5 m. it is 10 m deep. Find

(i) Its inner curved surface area

(ii) The cost of plastering this curved surface area at the rate of Rs. 40 per m2.

[Ans.: (i) 110 m2 (ii) Rs.

4400]

7. A hemisphere brass bowl has inner-diameter 10.5 cm. Find the cost of tin-planting it on the inside

at the rate of Rs. 16 per 100 cm2.

[Ans.: Rs.

27.72]

8. The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio

of their surface areas.

[Ans.:

1:16]


29/51

LEVEL III

1. A 10 m long wall is to be built across an open ground. The height of the wall is 4 m and the

thickness of the wall is 24 cm. If this wall is to be built with bricks whose dimensions are 24 cm

X 12 cm X 8 cm, how many bricks would be required?

[Ans.: 4167

bricks]

2. A cylindrical metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm and the

outer one is 4.4 cm. Find its

(i) Inner curved surface area

(ii) Outer curved surface area

(iii)Total surface area

[Ans.: (i) 968 cm2 (ii) 1064.8 cm2 (iii) 2038.08

cm2]

3. It costs Rs. 2200 to paint the inner curved surface of a cylindrical tank of height 10 m deep. If

the rate of painting is Rs. 20 per m2, find

(i) The inner curved surface area of the tank

(ii) The radius of the base

(iii)Capacity of the tank

[Ans.: (i) 110 m2 (ii) 1.75 m (iii) 96.25

kilolitres]

4. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the

interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the

length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

[Ans.: Volume of wood=5.28 cm3; Volume of

graphite=0.11cm3]

5. A hemispheric bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find

the outer curved surface area of the bowl.

[Ans.: 173.25 cm2]

6. A hemispheric dome of a building needs to be painted. If the circumference of the base of the

dome is 17.6 m, find the cost of painting it at the rate of Rs. 5 per 100 cm2.

[Ans.: Rs.

24640]

7. A right circular cylinder just encloses a sphere of radius r. Find

(i) Surface area of the sphere

(ii) Curved surface area of the cylinder

(iii)Ratios of the areas obtained in (i) and (ii).


30/51

*Ans.: (i) 4r2 (ii) 4r2 (iii)

1:1]

CHAPTER CONSTRUCTIONS

Level 1

Q1.Construct an angle of 450

at the initial point of a given ray and justify the construction.

Q.2Construct an angle of 450at the initial point of a given ray and justify the construction.

Q.3Construct the following angles and verify by measuring them by a protractor:

(i) 75 (ii) 105 (iii) 135

Q.4 Draw any line segment and its perpendicular bisector .

Q.5 draw any angle and construct its bisector .

Level 2

Q.6Construct a triangle ABC in which BC = 7cm, B = 75 and AB + AC = 13 cm.

Q.7 Construct a triangle ABC in which BC = 8cm, B = 45 and ABAC = 3.5 cm.

Q.8 construct an equilateral triangle given its side and justify your construction

Level 3

Q9Construct a triangle PQR in which QR = 6cm, Q = 60 and PRPQ = 2cm.

Q10. Construct a triangle XYZ in which Y = 30, Z = 90 and XY + YZ + ZX = 11 cm.

Q11. Construct a right triangle whose base is 12cm and sum of its hypotenuse and other

Q.12 Construct a triangle ABC, in which B = 60, C = 45 and AB + BC

+ CA = 11 cm.

Chapter Area of Parallelogram and circles

Level1

Q.1 If a triangle and a parallelogram are on the same base and between the same parallels ,then theratio of the area of the triangle to the area of parallelogram is

(a) 1:4

(b) 1:2

( c) 1:3


31/51

(d) 2:1 Ans b

Q.2 The area of a rhombus is 10 cm2.If one of the diagonal is 4 cm , then the other diagonal is

(a) 2.5 cm

(b) 5 cm

(c) 6 cm

(d) 8 cm Ans b

Q.3PQRS is a quadrilateral whose diagonal PR divides it into two parts ,equal in area , then PQRS

IS

(A) always rhombus

(b)is a rectangle

(c ) is a parallelogram Ans c

(d) none of these

Q.4ABC and BDE are two equilateral triangles such that D is the mid point of BC .Then ar( BDE

)=1/4 ar( ABC). Write true or false and justify your answer

Q.5The diagonal of square of is 10 cm .its area is

(A) 20cm2

(b)25cm2

(c ) 50cm2

(d) 100cm2

Level2

Q.6 Show that a median of a triangle divides it into two triangles of equal areas.

Q.7 E is any point on median AD of a ABC. Show that ar (ABE) = ar (ACE).

Q.8In Fig.ABCD is a quadrilateral and BE || AC and also BE meets DC produced at E.

Show that area of ADE is equal to the area of the quadrilateral ABCD.


32/51

Q.9 ABCD is a trapezium with AB parallel to CD .A line parallel to AC intersect AB at X and BC at

Y. Proe that ar ( ABX ) = (ACY)

Q.10. If a triangle and a parallelogram are on the same base and between the same

parallels, then prove that the area of the triangle is equal to half the area of the

parallelogram.

Level 3

Q.11 A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat ofthe village decided to take over some portion of his plot from one of the corners to construct

a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given

equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain

how this proposal will be implemented.

Q.12 Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas.

Show that the arallelogram is greater than that of the rectangle.

Q.13 P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the

mid-point of AP, show that

(i) ar (PRQ) =1/2 ar (ARC) (ii) ar (RQC) = 3/8 ar (ABC)

(iii) ar (PBQ) = ar (ARC)

Q.14 Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that

ar (APB) ar (CPD) = ar (APD) ar (BPC).

Q.15 D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar

(AEC).

CHAPTER 10 CIRCLES

Level 1

Q.1 How many circles can be drawn passing through

(a) one point

(b) two Point

(C) three collinear points

Q.2 Prove that if chords of congruent cicrles subtend equal angles at their centre,then chords

are equal.

Q.3 In the adjoining fig P,Q and R are points on the circle with centre O .If PQR=1000

then find OPR.


33/51

Q.4 Given an arc of circle give a construction to find its centre.

Q.5A chord of circle is equal to the radius of the circle .Find the angle subtended by the chord

at a point on the major arc and also a point on the minor arc.

LEVEL 2

Q.6 ABCD is a cyclic quadrilateral whose diagonal intersect at E . IF DBC = 700and BAC = 30

0,

Fin BCD .Further, if AB =BC ,find angle ECD .

Q7- Prove that circle described on any one of the equal sides of an isosceles triangle as

diameter bisects the base .

Q.8 Prove that the cyclic parallelogram is rectangle.

Q.9 If non parallel sides of a trapezium are equal , Prove that it is a cyclic.

Q.10 Two congruent circles intersect each other at point A and B .Through A ,any line

segment PAQ is drawn so that P,Q lie on the two circles .Prove that PB=BQ.

LEVEL 3

Q.11 If a pair of opposite sides of a cyclic quadrilateral is equal , prove that its diagonal are

also equal.

Q12 If ABC and ADC are two right triangles with common hypotenuse AC , Prove that

angle CAD= angle CBD.

Q.13Prove that circle drawn with any side of a rhombus as diameter , Passes through the

points of intersection of its diagonals.

Q.14 If a line intersects two concentric circles with centre O at A ,B,C and D .Then prove that

AB=CD.

A C C D

Q.15 If the medians BE and CF of triangle ABC intersects at G,then prove that area of GBC=

area of quad.AFGE.

CB

O


34/51

Linear Equation in Two Variables

Level 1

Question 1: If point (3,0) lies on graph of equation 2x + 3y = k, then find the value of k.

Answer 1: k = 6.

Question 2: What is the equation of x axis ?

Answer 2: y = 0.

Question 3: Draw the graph of y = x.

Answer 3:

Question 4: Express y in terms of x given that 2x5y = 7. Check whether point (-3,-2) is on the

line?

Answer 4: y = 2x7 / 5 ; No.

Question 5: Write co-ordinate of any two points which lie on line x + y = 8. How many such

points are there?

Answer 5: (2,6),(5,3) ; Infinite.

Level 2

Question 1: Find three solutions of the equation 3 = 2x + y.

Answer 1: (0,3) , (1,1) , (2,-1)

Question 2: If point (3,4) lies on the graph of 3y = ax 7, then find the value of a.

Answer 2: a = 5/3.

Question 3: Give geometric representation of 3x +12 = 0 as an equation in (1) One variable ;

(2) Two variable.

Answer 3:

Question 4: The cost of pen is 5 times the cost of pencil. Write a linear equation in two

variables to represent the statement.


35/51

Answer 4: Let cost of pencil = x, cost of pen = y. So, linear equation would be : y = 5x.

Question 5: Draw the graph of x 2y = 4. Find the co-ordinates of point where it meets x-axis

and y-axis.

Answer 5: Meets x-axis at (4,0) , y-axis at (0,-2).

Level 3

Question 1: Draw the graph of equation 2x + 3y - 6 = 0.

a) Using graph paper determine whether x=3, y=0 is a solution.

b) Find value of y if x = -3.

c) Find value of x if y = 2 from the graph.

Answer 1:

a) Yes.b) y = 4.

c) X =4.

Question 2: Find m if point (7,-3) lies on the equation (y3/7) = m (x2/7).

Answer 2: m = - 24/27.

Question 3: Draw the lines x=4 , y=2 and x=y on same graph paper and identify what type of

figure obtained. Also, write the point of vertices of the figure formed.

Answer 3:

Question 4: The cost of petrol in a city is Rs 40 per litre. Write an equation with x as number

of litres and y total cost.

Answer 4: y = 4x.

Question 5: Draw the graph of linear equation y = mx + c for m = , c= 3/2. Read from the

graph value of x when y=4.5.

Answer 5: x=6.

Quadrilateral.

Question 1: The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of theAnswer 1: 360,600,1080,1560


36/51

Question 2: Two angles of quadrilateral are 50` and 80`. Other two angles are in ratio of

8:15. Then find the remaining two angles.

Answer 2: 80` , 150`.

Question 3: What is the name of quadrilateral whose diagonals bisect each other at right

angles?

Answer 3: Square of Rhombus.

Question 4: Show that the diagonals of a rhombus are perpendicular to each other.

Question 5: Diagonal AC of a parallelogram ABCD bisects angle A . Show that it bisects angle Calso,

Level 2

Question 1: In a parallelogram, show that angle bisections of two adjacent angles

intersect at right angles.

Question 2: ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CDand DA respectively. Show that the quadrilateral PQRS is a rectangle.

Question 3:ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB

and parallel to BC intersects AC at DShow that

(i) D is the mid-point of AC (ii) MD AC(iii) CM = MA =1/2AB

Question 4: Show that the quadrilateral formed by joining the midpoint of consecutive

sides of a rhombus is a rectangle.

Question 5: If non parallel sides of a trapezium are equal then prove it is cyclic.

Level 3

Question 1: Prove that in a triangle, the line segment joining the mid points of any two

sides are parallel to third side and half of it.

Question 2: ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the

angles of the rhombus.


37/51

Question 3: ABCD is a quadrilateral in which AB || DC, AD = BC. Prove that angle A =

angle B and angle C = angle D.

Question 4: ABCD is a rectangle in which diagonal AC bisects angle C and angle C.

Prove that ABCD is a square

Question5: State and prove mid point theorem.

CLASSX

QUADRATIC EQUATIONS

Level-1

1. Check whether the following are quadratic equations:

2. Find the roots of the following quadratic equations by factorisation:

3. Find the roots of the following quadratic equations, if they exist, by applying the quadratic

formula.


38/51

4. Find the nature of the roots of the following quadratic equations.

If the real roots exist, find them;

(I) 2x2

3x + 5 = 0 (II) (III) 2x2

6x + 3 = 0

5.

Find the values of kfor each of the following quadratic equations, so that they have two

equal roots.

(I) 2x2

+ kx + 3 = 0 (II) kx(x 2) 6 = 0

Level-2

1. Find two numbers whose sum is 27 and product is 182.

2. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the

other two sides.

3. The sum of the reciprocals of Rehmans ages, (in years) 3 years ago and 5 years from now is

. Find his present age.

4. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have

taken 1 hour less for the same journey. Find the speed of the train.

5. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the

area is 800 m2? If so, find its length and breadth.

Level-3

1. The difference of squares of two numbers is 180. The square of the smaller number is 8 times

the larger number. Find the two numbers.

2. Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours

less than the smaller one to fill the tank separately. Find the time in which each tap can

separately fill the tank.

3. Solve for x:

=+

+

, x 0, a 0, b 0, x - (a + b)

4. A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters

in such a way that the differences of its distances from two diametrically opposite fixed gates

A and B on the boundary is 7 meters. Is it possible to do so? If yes, at what distances from the

two gates should the pole be erected?5. A two-digit number is such that product of its digits is 18. When 63 is subtracted from the

number, the digits interchange their places. Find the number.

ARITHMETIC PROGRESSION

Level-1


39/51

1. Which of the following are APs? If they form an A.P. find the common difference dand write

three more terms.

(i) 2, 4, 8, 16 (ii) (iii) 1.2, 3.2, 5.2, 7.2 (iv)

10, 6, 2, 2 (v)

2. Which term of the A.P. 3, 8, 13, 18, is 78?

3. How many three digit numbers are divisible by 7.4. Find the 20thterm from the last term of the A.P. 3, 8, 13, , 253.

5. In an AP

(i) Given a= 5, d= 3, an= 50, find nand Sn.

(ii) Given a= 7, a13= 35, find dand S13.

(iii) Given a12= 37, d= 3, find aand S12.

(iv) Given a3= 15, S10= 125, find dand a10.

(v) Given d= 5, S9= 75, find aand a9.

Level-2

1. Check whether 150 is a term of the A.P. 11, 8, 5, 2,

2. Find the 31stterm of an A.P. whose 11thterm is 38 and the 16thterm is 73.

3. If the 3rdand the 9thterms of an A.P. are 4 and 8 respectively. Which term of this A.P. is

zero.

4. Which term of the A.P. 3, 15, 27, 39, will be 132 more than its 54thterm?

5. The sum of 4thand 8thterms of an A.P. is 24 and the sum of the 6thand 10thterms is 44. Find

the first three terms of the A.P.

6. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18

respectively.

7. Show that a1, a2 ,an, form an AP where anis defined as below

(i) an= 3 + 4n (ii) an= 9 5n

Also find the sum of the first 15 terms in each case.

8. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of

first nterms.

Level-3

1. If the pth, qth& rthterm of an AP are x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) =0.

2. If the sum of the first nterms of an AP is 4nn2, what is the first term (that is S1)? What is thesum of first two terms? What is the second term? Similarly find the 3

rd, the10

thand

the nth

terms.


40/51

3. A spiral is made up of successive semicircles, with centres alternately at A and B, starting withcentre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, as shown in figure. What is the total

length of such a spiral made up of thirteen consecutive semicircles?

4. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row,18 in the row next to it and so on. In how many rows are the 200 logs placed and how many

logs are in the top row?

5. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potatoand other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.

A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in

the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she

continues in the same way until all the potatoes are in the bucket. What is the total distance

the competitor has to run?

6. The ratio of the sum of first n terms of two APs is 7n1:4n27. Find the ratio of their 11 th

terms.

7. If the pth term of an AP is q and the qthterm is p. Prove that its n thterm is (p + q - n).

8. Find the sum of all natural nos. between 101 & 304 which are divisible by 3 or 5.

COORDINATE GEOMETRY

Level-1

1. Find the distance between the following pairs of points:


41/51

(i) (2, 3), (4, 1) (ii) (5, 7), (1, 3) (iii) (a, b), (a, b)

2. Check whether (5, 2), (6, 4) and (7, 2) are the vertices of an isosceles triangle.

3. Find the coordinates of the point which divides the join of ( 1, 7) and (4, 3) in the ratio 2:3.

4. Find the ratio in which the line segment joining the points ( 3, 10) and (6, 8) is divided by (

1, 6).

5. Find the area of the triangle whose vertices are:

(i) (2, 3), ( 1, 0), (2, 4) (ii) ( 5, 1), (3, 5), (5, 2)Level-2

1. Name the type of quadrilateral formed, if any, by the following points, and give reasons for

your answer:

(i) ( 1, 2), (1, 0), ( 1, 2), ( 3, 0) (ii) ( 3, 5), (3, 1), (0, 3), ( 1, 4)

2. Find the point on thex-axis which is equidistant from (2, 5) and ( 2, 9).

3. If Q (0, 1) is equidistant from P (5, 3) and R (x, 6), find the values ofx. Also find the distance

QR and PR.

4. Find the coordinates of the points of trisection of the line segment joining (4, 1) and ( 2,

3).

5. Find the ratio in which the line segment joining A (1, 5) and B ( 4, 5) is divided by thex-axis.

Also find the coordinates of the point of division.

6. Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, 3)

and B is (1, 4)

7. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, findxand y.

8. AB is the diameter of a circle whose centre is (2, -3). If the co-ordinates of B are (1 ,4) then

find the co-ordinates of A.

9. In each of the following find the value of k, for which the points are collinear.

(i) (7, 2), (5, 1), (3, k) (ii) (8, 1), (k, 4), (2, 5)

10.Find the area of the quadrilateral whose vertices, taken in order, are ( 4, 2), ( 3, 5), (3,

2) and (2, 3).

Level-3

1. If A and B are ( 2, 2) and (2, 4), respectively, find the coordinates of P such

that and P lies on the line segment AB.2. Find the area of the triangle formed by joining the mid-points of the sides of the triangle

whose vertices are (0, 1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given

triangle.

3. Find the coordinates of the centroid of the triangle ABC whose vertices are A(6, -6), B(3, -7)

and C(3, 4).


42/51

4. Determine the ratio in which the line 2x+ y4 = 0 divides the line segment joining the points

A(2, 2) and B(3, 7)

5. Find the centre of a circle passing through the points (6, 6), (3, 7) and (3, 3).

SOME APPLICATIONS OF TRIGONOMETRY

Level-1

1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of

a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with

the ground level is 30 .

2. The height of a tower is 10 m. Find the Suns altitude when the length of its shadow is 103

m.

3. A contractor plans to install two slides for the children to play in a park. For the children

below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is

inclined at an angle of 30 to the ground, where as for the elder children she wants to have a

steep side at a height of 3 m, and inclined at an angle of 60 to the ground. What should be

the length of the slide in each case?

4. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away

from the foot of the tower is 30. Find the height of the tower.

5. A kite is flying at a height of 60 m above the ground. The string attached to the kite istemporarily tied to a point on the ground. The inclination of the string with the ground is 60.

Find the length of the string, assuming that there is no slack in the string.

Level-2

1. A tree breaks due to storm and the broken part bends so that the top of the tree touches the

ground making an angle 30 with it. The distance between the foot of the tree to the point

where the top touches the ground is 8 m. Find the height of the tree.

2. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation

from his eyes to the top of the building increases from 30 to 60 as he walks towards the

building. Find the distance he walked towards the building.

3. From a point on the ground, the angles of elevation of the bottom and the top of a

transmission tower fixed at the top of a 20 m high building are 45 and 60 respectively. Find

the height of the tower.


43/51

4. The angle of elevation of the top of a building from the foot of the tower is 30 and the angle

of elevation of the top of the tower from the foot of the building is 60. If the tower is 50 m

high, find the height of the building.

5. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60

and the angle of depression of its foot is 45. Determine the height of the tower.

Level-3

1. As observed from the top of a 75 m high lighthouse from the sea-level, the angles of

depression of two ships are 30 and 45. If one ship is exactly behind the other on the same

side of the lighthouse, find the distance between the two ships.

2. A straight highway leads to the foot of a tower. A man standing at the top of the tower

observes a car as an angle of depression of 30, which is approaching the foot of the tower

with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60.

Find the time taken by the car to reach the foot of the tower from this point.

3. The angles of elevation of the top of a tower from two points at a distance ofaand bfrom

the base of the tower and in the same straight line with it are complementary. Prove that the

height of the tower isab.4. The angles of depression of the top and the bottom of an 8m tall building from the top of a

multi-storied building are 30 and 45, respectively. Find the height of the multi-storied

building and the distance between the two buildings.

5. The angle of elevation of a cloud from a point 60 m above the lake is 30 and the angle of

depression of the reflection of the cloud in the lake is 60. Find the height of the cloud.

CIRCLES

Level-1

1. How many tangents can a circle have?

2. Fill in the blanks:

(i) A tangent to a circle intersects it in _______ point (s).

(ii) A line intersecting a circle in two points is called a __________.

(iii) A circle can have __________ parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called ____.

3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a

point Q so that OQ = 12 cm. Length PQ is :

(A) 12 cm. (B) 13 cm (C) 8.5 cm (D) cm

4. In the given figure, if TP and TQ are the two tangents to a circle with centre O so that POQ =

110 , then PTQ is equal to

(A) 60 (B) 70 (C) 80 (D) 90


44/51

5. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the

centre is 25 cm. The radius of the circle is

(A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

Level-2

1. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.2. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger

circle which touches the smaller circle.

3. A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD =AD + BC

4. Prove that the angle between the two tangents drawn from an external point to a circle issupplementary to the angle subtended by the line-segment joining the points of contact at

the centre.

5. If tangents PA and PB from a point P to a circle with centre O are inclined to each other anangle of 80 , then find the value of POA.

Level-3

1. Prove that the perpendicular at the point of contact to the tangent to a circle passes through

the centre.

2. Prove that the parallelogram circumscribing a circle is a rhombus.

3. In the given figure, XY and XY are two parallel tangents to a circle with centre O and anothertangent AB with point of contact C intersecting XY at A and XY at B. Prove that AOB=90 .


45/51

4. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary

angles at the centre of the circle.

5. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and

DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm

respectively (see given figure). Find the sides AB and AC.

GEOMETRICAL CONSTRUCTIONS

Level-1

1. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.

2. Draw a circle of radius 5 cm. Take a point P on it. Construct a tangent to the circle at point P.

3. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair oftangents to the circle and measure their lengths.

Level-2

1. Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides

are of the corresponding sides of the first triangle.

2. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides

are of the corresponding sides of the first triangle.3. Draw a triangle ABC with side BC = 7 cm, B = 45, A = 105. Then, construct a triangle

whose sides are times the corresponding side of ABC. Give the justification of the

construction.

4. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at

a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.


46/51

5. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle

of 60.

Level-3

1. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and B = 90. BD is the

perpendicular from B on AC. The circle through B, C, and D is drawn. Construct the tangents

from A to this circle. Give the justification of the construction.

2. Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of

tangents from this point to the circles. Give the justification of the construction.

AREAS RELATED TO CIRCLES

Unless stated otherwise

Level-1

1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which

has circumference equal to the sum of the circumferences of the two circles.

2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having

area equal to the sum of the areas of the two circles.

3. Tick the correct answer in the following and justify your choice: If the perimeter and the area

of a circle are numerically equal, then the radius of the circle is

(A) 2 units (B) units (C) 4 units (D)7 units

4. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60.

5. In a circle of radius 21 cm, an arc subtends an angle of 60 at the centre. Find:(i) The length of the arc

(ii) Area of the sector formed by the arc

(iii) Area of the segment forced by the corresponding chord

Level-2

1. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each

wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

2. Find the area of a quadrant of a circle whose circumference is 22 cm.

3. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in

5 minutes.

4. A chord of a circle of radius 12 cm subtends an angle of 120 at the centre. Find the area of

the corresponding segment of the circle.

*Use = 3.14 and ]

5. Find the area of the shaded region in the given figure, if radii of the two concentric circles

with centre O are 7 cm and 14 cm respectively and AOC = 40.


47/51

Level-3

1. Find the area of the shaded region in the given figure, if PQ = 24 cm, PR = 7 cm and O is the

centre of the circle.

2. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also

a circle of diameter 2 cm is cut as shown in the given figure. Find the area of the remaining

portion of the square.

3. The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as

centre, a circle is drawn with radius equal to half the length of the side of the triangle (See

the given figure). Find the area of shaded region. *Use = 3.14 and ]


48/51

4. Calculate the area of the designed region in the given figure common between the two

quadrants of circles of radius 8 cm each.

5. In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with

BC as diameter. Find the area of the shaded region.

SURFACE AREAS AND VOLUMES

Unless stated otherwise

Level-1

1. 2 cubes each of volume 64 cm3are joined end to end. Find the surface area of the resultingcuboids.

2. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of

.

3. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6cm. Find the height of the cylinder.

4. Metallic spheres of radii 6 cm, 8 cm, and 10 cm, respectively, are melted to form a single solidsphere. Find the radius of the resulting sphere.

5. A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of itstwo circular ends are 4 cm and 2 cm. Find the capacity of the glass.

Level-2


49/51

1. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The

total height of the toy is 15.5 cm. Find the total surface area of the toy.

2. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter

the hemisphere can have? Find the surface area of the solid.

3. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder,

as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm,

find the total surface area of the article.

4. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full

of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm,having a hemispherical shape on the top. Find the number of such cones which can be filled

with ice cream.

5. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all

around it in the shape of a circular ring of width 4 m to form an embankment. Find the height

of the embankment.

Level-3

1. A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how

much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two

hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure).

2. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is

open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a

sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find

the number of lead shots dropped in the vessel.

3. A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which issurmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole,

given that 1 cm3of iron has approximately 8 g mass. *Use = 3.14+

4. A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a

hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that

it touches the bottom. Find the volume of water left in the cylinder, if the radius of the

cylinder is 60 cm and its height is 180 cm.


50/51

5. A metallic right circular cone 20 cm high and whose vertical angle is 60 is cut into two parts

at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn

into a wire of diameter cm, find the length of the wire.

6.

PROBABILITY

Level-1

1. Complete the following statements:

(i) Probability of an event E Probability of the event not E = _______.

(ii) The probability of an event that cannot happen is _________. Such as event is called

_________.

(iii) The probability of an event that is certain to happen is _________. Such as event is called

________.

(iv) The sum of the probabilities of all the elementary events of an experiment is _________.

(v) The probability of an event is greater than or equal to _______ and less than or equal to

_______.

2. Which of the following cannot be the probability of an event?

3. A die is thrown once. Find the probability of getting

(i) a prime number;

(ii) a number lying between 2 and 6;

(iii) an odd number.

4. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into

the bag. What is the probability that she takes out

(i) an orange flavoured candy? (ii) a lemon flavoured candy?

5. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is

the probability that the ball drawn is (i) red? (ii) not red?

Level-2

1. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out

of the box at random. What is the probability that the marble taken out will be (i) red? (ii)

white? (iii) not green?

2. A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5coins. If it is equally likely that one of the coins will fall out when the bank is turned upside

down, what is the probability that the coin

(i) Will be a 50 p coin? (ii) Will not be a Rs.5 coin?

3. A die is thrown twice. What is the probability that

(i) 5 will not come up either time? (ii) 5 will come up at least once?

4. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting


51/51

(i) a king of red colour (ii) a face card (iii) a red face card

(iv) the jack of hearts (v) a spade (vi) the queen of diamonds

5. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif

wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise.

Calculate the probability that Hanif will lose the game.

Level-3

1. Five cardsthe ten, jack, queen, king and ace of diamonds, are well -shuffled with their face

downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up

is (a) an ace? (b) a queen?

2. (i)A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What

is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn

at random from the rest. What is the probability that this bulb is not defective?

3. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random

from the box, find the probability that it bears

(i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.

4. Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the following table:

Event:

Sum of two dice2 3 4 5 6 7 8 9 10 11 12

Probability

(ii) A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

Therefore, each of them has a probability . Do you agree with this argument?

5. Find the probability of 53 Sundays in (i) an ordinary year (ii) a leap year

Question Bank

Documents