mathematics for class 8

7/31/2019 Mathematics for Class 8

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Model Papers Math 8th

Paper I

Find (i) A (B C) and (ii) A (B C) for the sets.

A = {a,b,c,d} B = {c,d,e} and C = {c,e,f,g}

The radius of sphere A is twice that of a sphere B. Find,(i) The ratio among their surface areas(ii) The ratio among their volumes

Evaluate 3(1 x2) 2{x3 {x3 (3 2x2)} when x = 2.

Divide x4+x2+1 by x2 x+1

Fill in the blanks by using appropriate symbols or words

(1 10=10)

1. The decimal fraction 0.6666is a non fraction.2. The product of x+1 and x+3 is .

3. In base 5 system the digits are used.

4. For a, bQ the property a+b=b+a is called .5. The equation ax+by+c = 0 is called in two variables.

6. The value of 13.70413.7 is .7. The No. whose 30% is 270 .

8. The value of

12

33

127

8

is equal to .

9. Measure of internal angle of pentagon is .

10. Solve

1 11

7 21 3

12 7

+

= .

Four choices for each item are given from which only one is correctwrite the correct choice at the space given in front of each item.

(5)

1. The complement of an angle of 45 is:

a. 135 b. 45 c. 25 d. 352. The line joins two points of a circle is:

a. Radius b. Chord c. Diameter d. Arc

3. The product of (2fm)(2fm):a. 4ffm+m2 b. 2fm+m c. f d. 2fm+m

4. If the cost of two dozen books is Rs. 500. The cost of 6 such books is:a. Rs. 125 b. Rs. 130 c. Rs. 125.50 d. Rs. 120

5. 5 men can do a piece of work in 6 days. In how many days can 3 men do the samework:

a. 12 b. 15 c. 13 d. 10

6. The greatest number which can divide 81, 161 and 254 and the remainder in each case

is 3, 5 and 7 respectively:a. 13 b. 14 c. 23 d. 15

7. Salman spent 0.7 of the total money he had. If he is left with Rs. 300 then the totalamount he had:a. Rs. 1050 b. Rs. 1000 c. Rs. 1051 d. Rs. 2000


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8. Convert 7/10 into percentage:a. 35% b. 3.5% c. 35/100% d. 0.35/100%

9. If i2 = 1 then i is equal to:

a. 1 b. 1 c. 5 d. 110. If V = U+gt, then find the value of t:

a. b. c. d.

Write T for true and F for false in front of the following statements.

(1 10=10)1. EO = N

2. NZ; where N is the set of natural numbers and Z is the set of integers.

3. (4)5 (3)5 = (22)5.4. The proportion a : b = c : d is generally written as, a : b : c : d.

5. Profit = c.p s.p.6. (a+b) (ab) = a2+b2

7. = 0.3.

8. Volume of the cylinder = 2h.

9. Pythagorus theorm was discovered by a Greek mathematician pythagorus.10.Area of the circle = 2.

Match the statements of column A with their respective statementsgiven in column B by a line.

(5)

No.

Column A Column B Column C

1. AB = B, iff, a+(b)2. A does not

belong to B

0

3. ab A : b = c : d4. ab AB5. Additive

Identityl

6. MultiplicativeIdentity

AB

7.8. Area of the

curved surface9. Slanting height

of the cone1

10. Hypotensue (a+b)

Write short answers to the following questions

(8 3=24)

1. Prove: A A/ = ; is A = {1,2,3} & U = {1,2,3,4,5}

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

2. Convert (101001)2 into equivalent number in decimal system.

Answer

_____________________________________________________________________________________________


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9. 108 10.

2. Multiple Choice Questions.1. b 2. b 3. a 4. a5. d 6. 7. b 8. d9. d 10.c

3. True False1. T 2. T 3. T 4. F5. F 6. F 7. F 8. T9. T 10.T

4. Match the columns1. A 2. aB 3. a+(b) 4. (a+b)5. 0 6. 1 7. a : b = c : d 8. l

9. ( ) ( )2 2

radius height+ 10. ( ) ( )2 2

base Altitude+

Short Question

1. L.H.S = A A/

A/ = UA = {1,2,3,4,5}{1,2,3} = {4,5}AA/ = {1,2,3}{4,5} = = R.H.SHence Proved AA/ =

2. (101001)2 = 1 25+0 24+1 23+0 22+0 21+1 20.

= 1 32+0 16+1 8+0 4+0 2+1 1.

= 32+0+8+0+0+1 = 41

Hence (101001)2 = (41)103. = 123 123

1 51 2911

512244

729243

729

4. Rebate is the amount for which tax is exempted.

5. Missing term = (29)(29) = 4a2.

6. 2x+5 = 7

2x = 75 = 22x = 2

x = 1S.S = {1}

7. hypotenouse = 98 cm2

length of sides = xx2+x2 = 98

2x2 = 98x2 = 49

x = 7 cmTherefore, length of congruent side is 7cm.

8. To write a data in the form a table in such a way that the frequency ofeach class can be observed at once is called its frequency distribution.


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Paper II

If U = {1,2,3,4,29,30} (9 4=36)C = {1,2,3,4,19,20}D = {2,4,6,8,30}

Prove the following(i) C D = C D/

(ii) D C = D C/

Find the square root of 0.204304.

Simplify x 2y [4x 6y {3x z+2(2x )}]

In a triangle ABC, right-angled at C, m=2.1cm and m=7.2cm. What isthe length of ?In the figure given prove that

a2 x2 = b2 y2

O

b

BCA y y

a c

Fill in the blanks by using appropriate symbols or words

(1 10=10)

1. Means x is a member of set A .

2. In base 5 the difference (431)5(202)5 is = ( )53. The whole part in the square root of 1.44 will be .

4. The volume of a cone where r=1 cm and h=1 cm is equal to .

5. If multiplicative inverse of a is equal to b. Then additive inverse of b is equal to.

6. If oU = vgt, then the value of g is .

7. The solution set for the equation 13x+1 = 9x+5 is .8. Given that a = 3, b = 4, c = 2 then the value of (ac)2 = .

9. (d) 7q2 7q2 = .10. What percent of 500 is 130 = .


(5)

1. a2b2 is equal to:a. a22ab+b2 b. (a+b)(ab) c. (ab)(a2+ab+b)2 d.

2. A quadrilateral in which only two sides and angles are parallel is called:a. Pentagon b. Hexagon c. Triangle d. Octagon

3. If a+b = 6 & ab = 10. Then value of a2+b2 is:a. 66 b. 64 c. 60 d. 68

4. If a rectangular field is 10.01 m by 300 m, the perimeter:


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Model Papers

a. 3003 m b. 3000 m c. 300 m d. 620 m

5. If LCM of two is 90 and HCF is 16, product of the number is:a. 1430 b. 1440 c. d. 106

6. Simplify7 1 5 7 5 14

:8 2 4 3 2 14

+

a. 3 b. c. d. None of these

7. The ratio between 5 meter and Rs. 15 is:

a. b. c. d.8. Find the square root of a22ab+b2:

a. aab+b b. ab c. Question is wrong d. (ab)9. The distance of any point on the circle from the center is called:

a. Chord b. Radius c. Arc d. Diameter

10. If the vertex of an isosceles triangle is 30, its base angles are:a. 75, 75 b. 30, 30 c. 90, 60 d. 40, 50


(1 10=10)

1. The set N (natural number) is a proper subset of the set w (whole number)

2. AOA/ = ?

3. If A and B are two sets and said to be equal then we can write them as A B.

4. 3.14159 I; where I is the set of all irrational numbers.5. O is called the additive identity element of Q.

6.5 10 1

12 3 8

=

.

7. 32a = 1a.8. 2ax2+2ax = 2ax(x+1).

9. Square root of a2+(2a+b)b is (a+b).

10.Area of curved surface of a cone = area of circle l.

Match the statements of column A with their respective statementsgiven in column B by a line.

(5)

No.


1. EUO a+b=b+a;

a,bQ2. Empty set ad = cb

3. Intersection of twosets

N

4. Commutativeproperty w.r.taddition

a2b2

5. Associative propertyw.r.t Addition

ac = bd

6. Ten numerals(digits)

7. a : b :: c : d a2+b22ab8. a : b :: d : c AB9.

(ab)2 Base (10)

10. (a2b)(a+b) (a+b)+(=a+(b+c); a,b,cQ


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Write short answers to the following questions

(8 3=24)

1. (i) If A = {a,b,c,d} and B = {a,c,f,g}find a. A B = ?

b. B A = ?

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

2. Convert 541 into binary system.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

3. Expand (2x+3y)2 by using formula.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

4. The area of a circular region is 616 sq.dm. Find its radius.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

5. Evaluate:-

(11111)5 (4444)5

Answer

_____________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________.

6. Find the square root of 1024.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

7. Write apparatus use in making regular pentagon.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.


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Model Papers

8. Define class frequency.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

Answers

Subjective type question.

1.

2. 0.452

3. 4x4y+z

Objective type Questions

1. Fill in the blanks.1. xA 2. (224)5 3. 1 4.

5. b 6. 7. 1 8. 2009. 49q4 10.26%

2. Multiple Choice Questions.1. b 2. b 3. d 4. b5. b 6. d 7. d 8. d9. b 10.a

3. True False1. T 2. T 3. F 4. T5. T 6. F 7. F 8. T9. T 10.F

4. Match the columns1. N 2. 3. AB 4. a+b = b+a a,bQ5. (a+b)+c = a+(b+c);a,b,cQ 6. base 10 7. ad = cd8. ac = bd 9. a2+b22ab 10.a2b2

Short Question

1. a. A B = {a,b,c,d} {a,c,f,g} = {b,d}

b. B A = {a,c,f,g} {a,b,c,d} = {f,g}2. 541 = (1000011101)2 2 541

2 27012 13502 6712 3312 1612 802 402 20

10

3. (2x+3y)2 = (2x)2+2(2x)(3y)+(3y)2

= 4x2+12xy+9y2

4. Area of circular region = 616 dm2

2 = 616= 616

2 = = 196


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2 = 196 = 14 dm

5. (11111)5 (4444)5Hence (11111)5(4444)5 (11111)5

= (1112)5 (4444)5(1112)5

6. = 3232

10243 9

12462124

7. Apparatus used in making regular pentagon is compass, ruler and protractor.

8. In a grouped data, the number of values falling in a particular classinterval is called the class frequency of that class.


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Model Papers

Paper III

(9 4=36)

A person got an insurance policy for his car at the rate of 3.6%. Hepaid an amount of Rs. 12,206/- as the Ist Premium of one year. Howmuch is the price of his car while he had paid Rs. 200 as service

charges?

Subtract 2x4+3x3 2 from the sum of 3x4 3x2+5x and x4 2x3+3x 5.

A rectangular field has an area of 18432 square meter. Its width is halfas long as its length. Find its perimeter.

The given figure, ABCD is of arectangle of sides 8 cm and 12cm. E and F are the mid-pointsof the sides BC and ADrespectively then by using

Pythagorus Theorem and HerosFormula. Find

(a) The area of the triangles(i) ABE (ii) FDC

(b) The area of the ParallelogramAECF

D C

F

E

A B

Fill in the blanks by using the appropriate symbols or words

(1 10=10)

1. The area of a triangle whose base is 3 cm and height (altitude) is 6 cm is equal to.

2. Every rational number has multiplicative inverse w.r.t. x except .

3. If we cannot find the exact number whose square is x then x is an number.

4.4 9

9 2 =

5. in terms of ratio is written as .

6. A polygon having six sides is called .

7. If a : b = 3 : 7 and a : c = 6 : 7 then the ratio between a : b : c is .

8. The L.C.M. of 12, 18, 24 is .

9. A = {2,4,6} B = {4, 6, 8, 10} then AB = .10. Volume of Cylinder = .


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Four choices for each item are given from which only one is correct.Write the correct choice at the space given in front of each item.

(1 10=10)

1. If length, breadth and thickness of a cuboid be 6 cm, 2 cm and 3 cm respectively, itsvolume will be:a. 36 cubic cm b. 36 square cm c. 11 cubic cm d. None

2. Equations with the same solution are called:a. Twin equations b. Direct equationsc. Equivalent d. Linear equations

3. If h is the perpendicular ehight and r is the radius of circular base, the volume ofcylinder is:

a. r2 h b. 1r2 h c. 2rh d. rh4. A square and rectangle have equal areas. If the length of the rectangle is 25m and

width 16m. What is the length of the side of the square:a. 22 m b. 21 m c. 19 m d. 20 m

5. The symbol : : stands for:a. Ratio b. Proportion c. Triangle d. Square

6. (x+2)(x1)(x1)(x+2) simplified, gives:

a. x b. x c. x2

+2 d. 07. The expression is:

a. Proportion b. Ratio c. Not proportional d. Polynomial

8. If the cost of one dozen pencils is 14.40 rupees, what will be the cost of 120 pencils?a. 440 rupees b. 400 rupees c. 140 rupees d. 144 rupees

9. 6 men complete a job in 4 days. How long would it take 3 men to complete the samejob?

a. 8 days b. 6 days c. 9 days d. 5 days

10. If 9 is added in double of a number, it gives 39. What is the number?a. 10 b. 7 c. 15 d. 16

Write T for true and F for false in front of the following statements.(1 10=10)

1. EO = .2. A = {a, b, c, c, d} ; A is a set.

3. Universal set is usually denoted by .

4. (3)+(5) = 8.

5. a+(b+c) = (a+b)+c is called commutative property w.r.t addition where a, b, cQ.6. The base 2 contain only 0 and 1 number.

7. (x) = x+y+z)8. = 0.3

9. 3(Volume of the cone) = Volume of cylinder.

10.(ab)2 = a2b2.

Match the statements of columns A with their respective statementsgiven in column B by a line.

(1 10=10)

No.


1. XX/ >2. Power set of empty

set0.3

3. 10 20 { }4. 1 0 (b+d)(a+2c)5. (a+c)(b+d)


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Model Papers

6. (a+b) x7. ab+bc+ad+cd 18. ab+2cd+2bc+ad 0.9499. (ax)(bx) 7. a4

b4

8. (a+b2)(ab)2 9. a225 10.a210a+25

Short Question

1. Insurance may be defined as a contract among two parties. Insurance is ofdifference types.

a. Life insurance

b. Vehicle and property insurance etc.

2. Surface Area of a sphere of radius = 4 2

S = ( )222

4 217

S = 5544 cm2

Therefore, surface area is 5544 cm2

3. Multiplicative inverse of is .

4. Subsets of the set {3, 5, 7} is { }, {3}, {5}, {7}, {3,5}, {3,7}, {5,7} and{3,5,7}

5. (10011)2 (1101)2 = (110)2 (10011)2(1101)2(0110)2

6. Men days

10 21 Inverse Proportion7 x=

x = = 30 days.So, the ration will be sufficient for 30 days.

7. Monthly income = 6500 Rupees

Yearly income = 6500 12 = 78,000 RupeesTax rebate = 50,000 Rupees

Taxable income = 78,00050,000= 28,000

Income tax @ 5% = = 1400 Rs.Thus, Rs. 1400 will be paid as income tax.

8. Let x1, x2, ,xn be n arithmetic quantities then their average is the value iscalled mean.

Mean =


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Model Papers

2. If x = 2, y = 3 and z = 4, find the value of x2y+y2z+z2x.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

3. Write all the subsets of the set {3,5,8}.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

4. Solve.(10110111)2+(100011)2

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

5. Net income of Faraz is Rs.98,000 per year from a small businessconcern. Calculate the amount of income tax he will have to pay at theend of the year @ 5% while the tax rebate is 40,000.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.6. Define premium.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

7. Write pythagorus theorem.

Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

8. Factorize: x2

+37x+210.Answer

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

Answers

Subjective type question.1. 1.4142 2. 35 3. 328 cm2 4. 19.5

Objective type Questions

1. Fill in the blanks.1. 510 2. 3. 2 or 01

4. 7.5 5. Commission 6. 7. 28. 3 9. 6 10.x = 8


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2. Multiple Choice Questions.1. a 2. a 3. d 4. b5. d 6. b 7. b 8. c9. c 10.c

3. True False1. F 2. T 3. T 4. T5. F 6. F 7. F 8. T9. F 10.F

4. Match the columns1. AB 2. Closure property3. Multiplicative property 4. Multiplicative inverse

5. (ab)24ab 6. (a+b)24ab 7. 2h8. 9. 2 10.(+l)

Short Question

1.4

289

=256

9= = 5

2. x2y+y2z+z2x = (2)2(3)+(3)2(4)+(4)2(2)= 12+36+32 = 80

3. Subsets of {3,5,8} is { }, {3}, {5}, {8}, {3,5}, {5,8}, {3,8}, {3,5,8}

4. (10110111)2+(100011)2 = (11011010)2 (10110111)2(100011)2

(11011010)25. Income of the year= 98,000 Rupees

Tax rebate = 40,000 Rupees

Income = 98,000 40,000 = 58,000 RupeesIncome tax payable @ 5% =

= 2900 Rupees

Therefore income tax 2900 rupees

6. The installment is to be paid is called premium.

7. Pythagoras theorem(Hypotenuse)2 = (base)2+(Altitude)2

8. x2+30x+7x+210= x(x+30)+7(x+30)= (x+7)(x+30)

Paper X

For the sets A = {1,2,3,4,5}, B = {2,4,6,8,10} and C = {2,3,5,7}

Find (i) (A B) C and (ii) (A B) C.

If x = , y = , z = , find the value of .

A solid copper sphere of radius 3cm is melted and electric wire ofdiameter 0.4 cm is made out of the copper obtained. Find the length ofthe wire.

Divide 8x3+16x2+8x+3 by 2x+3:

Fill in the blanks by using appropriate symbols or words.

(1 10=10)


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Model Papers

1.169

256= .

2. A histogram is similar to bar graph but it is constructed for a table.

3. A Polygon having all its sides and angles equal is called a .

4. Compound proportion is a relationship between two or more .

5. a(b+c) is equal to .6. Conversion of into a percentage is.

7. If the area of a circular region is 0.9856 m2 then its radius is .

8. A polygon having six sides is called .

9. 94% of is 1175.

10. 7x2>3 is a sentence.


(1 10=10)

1. 5/2 of a number is the same as 10% of 500. What is the number:a. 10 b. 100 c. 20 d. 200

2. 1/5 of the product of 25 and 15 when added to 33 is:a. 102 b. 72 c. 108 d. 75

3. Write the ratio 35 : 10 in the form of n : 1 where n is a decimal:a. 3 : 5 : 1 b. 3 : 4 : 1c. 5 : 4 : 1 d. None of these

4. All estimated the length of a room is 20m. He over estimated 25%. What is the truelength:a. 4m b. 26m c. 16m d. 15m

5. Convert 0.003 into percentage:a. 3% b. 30% c. 0.3% d. 0.03%

6. Find the value of x24x+2 if x = 1:a. 3 b. 7 c. 5 d. 0

7. The perimeter of a square whose side is 9 meter long will be:a. 36 m2 b. 36 m c. 18 m d. 25 m2

8. If a book seller sold a book for Rs. 48 at 4% loss. Then its cost price is:a. Rs. 60 b. Rs. 50c. Rs. 45 d. Rs. 60

9. If the average of 140 numbers is 20, when another is added, the average does notchange then the 141th number is:a. 21 b. 0 c. 140

10. Two shirts and Five hats together cost Rs. 285 and 2 shirts and 11 hats together costRs. 435. Then cost of 3 shirts equals to:

a. Rs. 240 b. Rs. 330 c. Rs. 150 d. Rs. 400


(1 10=10)

1. (AB)/ = A/B/.

2. (15) (1) = 15

3. (1)(15) = 144. (464)10 = (3324)10

5. If x : y = 5 : 7 and y : z = 7 : 11 then x : y : z = 5 : 7 : 11.

6. (x31) (x1) = (x21).

7. (a+b)2(ab)2 = 4ab8. = 0.05.

9. Area of total surface of a cone = (+l).


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x = = 9 eggs.Therefore 9 eggs can be bought.

5. (111)2+(10)2 = (1001)2 (111)2(10)2

(1001)2

6. (34)5 (42)5 = (3133)5 (34)5(42)5123

301 (3133)5

7. L.H.S(a+b)2 = (a+b)(a+b)= a(a+b)+b(a+b)= a2+ab+ab+b2

= a2+2ab+b2

= R.H.SHence Proved (a+b)2 = a2+2ab+b2

8. Graphic way of presenting data is by means of a histogram.

mathematics for class 8

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