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1 Key book 8 Keybooks are freely available at our website PROGRESS PUBLISHERS KRISHNA NAGAR, DELHI - 00 FAX : 0-099; progress.india@vsnl.com

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3 Chapter Rational Numbers Exercise.. (a) False (b) True (c) True (d) False. (a) Negative (b) Positive (c) Positive (d) Positive (e) Negative. (a) (b) (c) (d). (a),, 8 8 (d) 0,, 0. (a) = 9 = 8 8 (e) 9 (b), 9, 8 (e), 8, (c) 0, 0, 0 8 (b) = 0 = 8 (c) 8 = 8 = 8. (a) > (b) 8 < (c) 9 <. (a) 0 < < 0 < 0 (b) < < < (c) 0 < < 0 8. (a) 8 9 > 0 > (b) > 8 9 > > (c) > 8 > 9 Exercise.. (a) True (b) True (c) False (d) False. (a) (b) 9, (c) (d). (a) 9 0 (b) (c) 0 (d) (e) (f) (a) 9 0. Exercise.. (a) False (b) False (c) True (d) False (e) True (f) False. (a) (b) (c) (d) 8. (a) 8 (b) (c) (d)

4 Exercise.. (a) (b) (c) (d) (e) (f) (g) (h) (a) (b). (a) 0, 0, (b) 0 0, 0, 0. (a) 00, 00, 00, 00, 00, 00 (c), 0, 9, 8,,. (a) 0, 80, 0 (c) 9 0, 9 0, 0 Exercise.. 000, 0 by bus, by bicycle (c), (d),,, (c),, (b) 9 0, 9 0, 9 0, 9 0, 9 0, 9 0 (b) 0, 9 0, 0. m kg 0. `, 0. 9 cm 0. days MCQ Sum 0.. none of these 8. 0

5 Revision Exercise. (a) False (b) False (c) False (d) False. (a) 8, (b) 9 (c) Closure (d). (a) 0 (b) 0 (c) 0 (d) 0. 0, 0, 0, 0, 0, 0, 0, 8 0, 9 0, (a),,, 0 (c) 0 9, 8, 9, (a) 0 (b) (b) 80, 0, 80, 89 0 (c) km. 88 ml Chapter Exponents and Powers Exercise.. (a) ( ) (b). (a) Base = b l (c) b l (d) e o, Power = (b) Base =, Power = 9 (c) Base =, Power = 0 (d) Base =, Power =. (a) b l (b). (a) 9 b l (b). (a) 8. (a) (b) b l (c) b l (c) (b). (a) 9 (b) b l (d) b l (d) b l 8 8 b l (c) (d) 80 (c) (c) (d) (d) 9

6 Exercise.. (a) (b) (c) (d) (f) (g) (h) (e) 8 (i) (b) (c) (a) (a) 9 (b) (c) b l. (). (a) 800 (b) (c) 8 Exercise.. (a).8 0 (b).89 0 (c). 0 (d).8 0. (a).0000 (b) 0.8 (c) (d) (a) m (b).9 0 kg (c) m (d). 0 g. (a). 0 (b) (a). 0 >. 0 (b). 0 >. 0. times (approx) : 8. (a).0 0 (b). 0 (c) (a) 8. 0 (b) (c).80 0 MCQ - I Revision Exercise. (a) False (b) True (c) True (d) True. (a) (b) (c) e o (d) (a) Base =, Power = (b) Base =, Power = (c) Base =, Power = (d) Base = 8, Power =

7 . (a) n (b) (c) (d) (a) (b) (c) (d) (a) (b).09 0 kg (c). 0 (d). 0. (a) (b) kg (c) (d) kg. (a).8 0 (b) (a). 0 (b) (approx). (approx) Chapter Squares and Square Roots Exercise.. (a) perfect (b) odd (c) n (d) n (e) odd (f) 0 (g) 8 (h) (i). (a) True (b) False (c) False (d) False (e) True. (a) (b) 9 (c) (d) (e) 9 (f) (g) (h) 9 (i) (j) 0., 9. They end with digits,, or 8 or have an odd number of zeros.. (a) (9) = 80 (b) (0) = 899 (c) () = 0 (d) (8) = 0 (e) () = 808. (a) + = (b) 8 + = (c) = 99 (d) = 99 (e) = 9 8. (a), (b), 0 (c), 9. (a) () = (b) (0) = 00 (c) () = 0. (a) 8 = (b) = (a) (9) = (b) () = + (c) () = + (d) () = + (e) () = Exercise.. (a) 8 (b) 0 (c) (d) 88 (e) (f) 9. (a) (b) 8 (c) 0 (d) 980 (e) (f) 0

8 8. (a) Yes (b) No (c) No (d) Yes. (a), 8, 0 (b),, (c), 8, 0 (d) 8,, (e), 8, 0 (f), 0,. (a) Yes (b) No (c) Yes (d) No. (a) (b) 9 (c) 89 9 (d). (e). (f) Exercise.. (a) 8 (b) 0 (c) (d) 9. (a) (b) (c) (d) 8 (e) 90 (f) (g) (h) (i) 9 (j) 80. (a), (b), (), 98 (d), 0. (a), (b), 8 (c), (d), 0. (a) (b) (c) (d) (e) 89 (f) (g) 8 (h) (i) 0 (j). 0089,. 9998, 8., 8 9., 0. (a) (b) Exercise.. (a). (b) 0.8 (c) 0. (d).. (a). (b) 0. (c). (d).. (a) (b) (c) (d) 0.. cm Exercise m. 0 m , 9. 8 cm MCQ - II ,, Revision Exercise. (a) 9 (b) (c) 89.,,, 89 (d). (a) 9 (b) 89 (c) 88 (d) 909

9 . (a) (b) 0 (c) (d). (a) (b) (c) 9 (d). (a) (b) 98 (c) (d). (a) (b) (c).0 (d) , 80. 9, 9.. cm. cm, cm. 99,,. 800 Chapter Cubes and Cube Roots Exercise.. (a) True (b) True (c) False (d) False. (a) 9 (b). (c) (d) 8 (e). (a) 8 (b) 89 (c) 000. (a) 9 (b) (c) (d) (e) (f) (g) 8 (h) (i) (j). (a) 0 (b) 8 (c) (d) (e). (a) (b) (c) (d) 9 (e). (a) = ( ) = (0) = 00 (b) = ( ) = () = (c) = ( ) = () = (d) = ( ) = () = 0 Exercise.. (a) (b) (c) 8 (d) 0.,.,., 9, 8., 088,. (a) (b) (c) (d) 9. (a) 0.8 (b). (c) 0.09 (d). 8.,. Exercise.. (a) (b) 0 (c) 9 (d). (a) (b) 9 (c) 8 (d).. cm. 90. cm. 8. cm. ` 9.0. cm

10 MCQ - IV cm 0. Revision Exercise. (a) True (b) False (c) True (d) False (e) True. (a) 0 (b) 00.9 (c).8 (d) 9 (e) (a) 8 (b) (c) 0 (d) (e) (f) 8 (g) 0 (h) (i) 0 (j) 00. (a) (b) (c) (d) (e) 9. (a) 0. (b) 0. (c) 0. (d). (e).., 0 8., 9. 8 cm 0. 0., 8. 8, 88 Chapter Exercise. Playing with Numbers. (a) Divisible by and (b) Divisible by, and 0 (c) Divisible by and (d) Divisible by,, and 0 (e) Not divisible by,, or 0. (a) Divisible by and (b) Divisible by none of,, or 9 (c) Divisible by none of, or 9 (d) Divisible by, and 9 (e) Divisible by none of, or 9. (a) Divisible by and (b) Divisible by and (c) Divisible by (d) Not divisible by or (e) Divisible by and. (a) Divisible by (b) Divisible by and 8 (c) Divisible by (d) Divisible by none of or 8 (e) Divisible by

11 (a) 0 or or or 9 (b) 0 or or or 9 (c) or 9 (d) 8. (a) A =, B = 9, D = (b) A =, B =, C = (c) A =, B = (d) A = 8 (e) A =, B = Exercise.. (a) (b) 99. (a) 0 (b) (c) 0. (a) The number in general form is : a 00 + b 0 + (a+) = 0a + 0b + The reversed number is (a+) 00 + b 0 + a = 0a + 0b + 00 The difference = 98 Reverse of difference = = 089 (b) Subtract from the final answer and divide the remainder by 00 to get the original number.. (a), (b), 9 (c), (d) 9, (e), 89., Exercise.. (a) 9 (b) 8 (c) (c). (a) (b) b l. 0 [(x x) = 0]

12 Chapter Algebraic Expressions Exercise.. (a) x, y, ;,, (b) x y, xy, xy ;,, (c) xyz, xy, yz ;,, (d), 8x, y, x y ;, 8,, (e) x, x, ;,, (f) x, y ;,. (a) Binomial (b) Monomial (c) Polynomial (d) Binomial (e) Trinomial (f) Polynomial. (a) xy + x y 8xy, (b) x + x + x + x, (c) + x x + x9, 9 (d) x + 8x x + x +, 9 x9 (e) x +, (f) x y + xy 8xy + x,. (a) x + x (b) x y xy + 9x y 8xy. (a) x x + 0x x 8 (b) x + y x y. x + x + x +. x + x x 0x x + x + x x 0 9. x + x + 0x x x + 8x Exercise.. (a) x y (b) 8 9 xy (c) x y z. 8x y. (a) m n (b) a b (c) x + xy 8y. (a) xy x y + 8x y xy (b) x y + xy x + 8y 8 (c) x 0y + xy (d) x x + x x + 8 (e) x y xy (f) x 8x + x +. (a) x x + x (b) 9 x 9 x + x 8 (c) x + 0xy x y + (d) 0x + x 8x 0x x + (e) 0x 89 x + 0 x 9 x + 8. (a) (b) 9 (c) (a) 0x + x y xy y (b) x y z (c) 8x + x y xy y 8. x + x + x + 9. x y + xy 8y + 0x + 9x y 0xy x y + xy 0. x + 8x x 0. x + x 8x +. x + x 0x + x

13 Exercise.. (a) xy (b) (e) 0 ab (f) xy (c) xyz (d) xy z. (a) 8 x y + y 9x y (b) a + 8b 9 (c) 0 mn + n 8 m (d) x + 0 y. (a) x x +, remainder = 0 (b) x x, remainder = (c) x + x +, remainder = x (d) x + x, remainder = 0. (a) No (b) Yes (c) No (d) Yes. x x. a = 0, b = Exercise.. (a) x + x + (b) y + y (c) x + x (d) x x (e) a x + 0 (f) x + x y y. (a) x + 80xy + y (b) 9x xy + 9y (c) x 0x + (d) x xy + y (e) 0.0x + 0.xy + 0.y (f) 9 x + x y + (g) x (h) 9 x 9 9 y. (a) x + y + 9z 0xy y + 0zx (b) 9 8 x 8x y + xy y (c) x + 00x y + 0xy + y (d) 9 x + y + z + 9 xy yz zx (e) x x y + xy y (f) x + 8x y + 88xy + y (g) x + x x + (h) x + 9y + z xy + 0yz - 80zx y. (a) 80xy (b) 0xy zx (c) 0x + 8xy (d) xy. (a) 90 (b) (c) 9 (d) (e) 80 (f) 000 (g) 8 (h) (a) 808 (b) 90 (c) 008 (d) (a) (b) 0

14 Exercise. MCQ - V (a) x x + x = x (add coeff. of x) (b) ( y ) = y 8 (laws of exponent) (c) x y = x y (divide each term) (d) (z + 0) = z + 0z + 00 (use identity) (e) (x + ) = 8x + 8 (multiply each term) (f) x + 9 = x + (divide each term) (g) x + x = x (addition of like terms) (h) (y ) = y y + y (use identity). y. x y, 8x y. x x + 8x 0. xy. 9. x + x 8. x Revision Exercise. (a) x x (b) x a (c) x x y + xy y (d) (e) y. (a) False (b) False (c) True (d) True. x x +. (a) x, x, ;,, (b) x y, 8xy, xy ;, 8, (c) 9ab, a b, a b ; 9,,. (a) x + x + 9x + (b) 9 x + x + x 9 x +. (a) 0x + x + 9 x (b) x x x 8. (a) x y (b) 8x x (c) x + x x + x (d) x 8x + x x + x x + 8. (a) x x (b) x 8x + 9x + x 9. x + 9x 0x + ; 0. (a) Q = x + x, R = 0 (b) Q = x + x, R = x 8. (a) Yes (b) No. (a) x + 8x (b) x xy + 9y (c) 9x + x + (d) x 9y

15 (e) x x + (f) x x y + xy 8y (g) x + 0x y + 0xy + y (h) x + y + z xy 0yz + 80zx. (a) 9 (b) (c) 89 (d) 000 (e) 88 (f) 09. (a) x (x x) = x x (multiply each term) (b) (x ) (x + ) = x x (check sign while operating brackets) (c) x = x (divide each term) (d) (x ) = x 0x + (use identity) Chapter Factorisation Exercise.. (a) y (b) x x x y y (c) regrouping (d) factors. (a) x y = x y = x y = x xy = x y = y x = x y = x xy = y x (b) -x y = -x y = - x y = - x y = -x y = -y x = x -y = y -x = -xy xy = xy -xy = -x y y = x y -y = -xy x = xy -x = - x x y y (c) x y = x y = x y = x xy = x x y (d) -xy = - xy = -xy = - xy = -xy = -x y = x -y = -y x = y -x = - x x y = -x y = x -y = -x y = x -y. (a) xy (b) xy (c) ab (d). (a) 9x y = 9x y = 9 x y = 9x y = 9y x = 9x xy = x 9xy = y 9x y = 9y x y = 9xy xy = x y = xy xy = xy xy = x xy = y x y = x y (b) abc = abc = abc = a b c = a bc = b ac = c ab = ab c = bc a = ac b (c) x y = x y = x y = x y = y x = xy x = x xy = x x y = x xy = y x = x y = xy x (d) -yz = yz = yz = yz = yz = y z = y z = z yz = z yz = y z z = yz z = yz z = z y = z y. (a) x x (x y) (b) y (x + y)

16 (c) x x x y y y y (d) - x y (x + y). (a) 0xy z (xz + x yz) (b) (ab bc + a c ) (c) pr (q + 9r 8p q r) (d) m n (m mn + n). (a) (-x + y) (b) (a + b) ( ab ) (c) (x y) (x + ) (d) (x ) (xy 9z + 0x yz ) 8. (a) (x y + 9z) (b) xy (x y + z) (c) 9x ( x + x ) (d) m n (m + n ) Exercise.. (a) 0xy (xy ) (b) m n (m n 8m ) (c) pq (q + p) (d) abc (c ac + ab ). (a) (x 8y)(x + 8y) (b) b u vlb u+ vl 8 8 (c) (x )(x + ) (d) (9q + r )(q r)(q + r) (e) ( m)( + m)( + m ) (f) (a )(a + ). (a) (x )(x ) (b) (y + ) (y + ) (c) 8(m )(m ) (d) (8x + )(8x + ) 9 9 (e) b p lb p l (f) e y zoe y zo 9 9. (a) (x )(x ) (b) (m + )(m ) (c) (x + 9)(x + ) (d) (x 8)(x + ) (e) (z + )(z ) (f) (y )(y + ). (a) (a 8)(a + ) (b) (y 9)(y 8) (c) (m + )(m ) (d) (z + )(z + ) (e) (x )(x ) (f) (p + )(p ). (a) xy (x + y + x) (b) (9m n ) (c) ( y)( y) (d) (a b)(a b) (e) (y + 0)(y + ) (f) (x )(x + ) (g) (x + 0)(x + ) (h) (x )(x ) (i) (x + y )(x y)(x + y) (j) (b )(b + )(b ) (k) (x )(x ) (l) (y 9x)(y + 9x) Exercise.. (a) xy y + x (b) 8x y y 9 x y (c) x (d) y( xy). (a) x (b) x (c) (x + y)(9x + y ) (d) (x + y)(x y). (a) x y (b) x (c) y (d) (y )

17 MCQ - VI. xy z. x y. (x )(x + ). (x )(x )(x + ). (x + y). p + q = a, pq = b. (x y)(x + y)(x + y ) 8. (x 9) 9. (y ) 0. (x )(x + ) Revision Exercise. (a) HCF of constants HCF of variables (b) 9 x x y y y (c) x (x ) (y xz) (d). (a) 0x (y ) (b) xy(x y) (c) x(x y)( + y) (d) 0a b (0a ). (a) 0x(8x + x 9) (b) xy ( xy + x ) (c) x(x )(x + ) (d) y z (y z ). (a) b(a )(a b) (b) (m + n)(m + 9n) (c) (x y)(y + ) (d) m( + n)(m n). (a) (a )(a + )(a + ) (b) x(x y)(x + y)(x + y ) 9 9 (c) e x yzoe x+ yzo 8 8 (d) xy z (xy z)(xy + z) (e) (8ab cd)(8ab + cd) (f) ( y)( + y) (g) x (x ) (h) x ( x + ) (i) n(m n). (a) x (x x ) (b) (8a + )(8a + ) (c) (y + )(y + ) (d) e z yoe z yo (e) y(y 0)(y 0) (f) (x y)(x y) (g) (x 0)(x 0) (h) (x + 8)(x + ) (i) (x )(x + ). (a) (x 0)(x 8) (b) (x + )(x ) (c) (x + )(x ) (d) (x + )(x + ) (e) (x )(x ) (f) (x + 0)(x 9) (g) (x + )(x + ) (h) (x + )(x ) (i) (x )(x + ) 8. (a) (x )(x + ) (b) x (x )(x + ) (c) (a + b)(a + b ) (d) (9x y)(9x + y) (e) (x )(x + )(x + ) (f) (x y)(x + y)(x + y ) Chapter 8 Exercise 8.. (a), (c) and (f) Linear Equations in One Variable. (a) LHS = x y, RHS = 0 (b) LHS = x + y, RHS = (c) LHS = x +, RHS = x (d) LHS = x + y, RHS = (e) LHS = x y RHS = - (f) LHS = y, RHS = x 0

18 8. (a) x = is not a solution (b) y = is a solution (c) x = 8 is a solution (d) x = is a solution but x = is not a solution. (a), (d) and (f) Exercise 8.. (a) (b) 8 (c) 8 (d) 8. (a) (b) (c) 9 0 (d) 8 (e) (f). (a) (b) (c) (d) (e) (f). (a) (b) (c) (d) 9 (e) (f) 88 (g) 9 9 (h) Exercise 8.. 9,.,,. Geeta s age = yrs, Father s age = yrs..,,., 0,. 8. L = cm, B = cm km/hr. Sonu s age = yr, Sonali s age = 9 yr.,. 0, 0, 0. cm. hr. Cost of one ball point pen = ` 8, cost of one fountain pen = `. Length = 00 m, breadth = 0 m 8. Number of ` 0 notes =, number of ` 0 notes = 8 MCQ - VII. x 8 = 0 x ,. 08,, 0., years 0. m, m Revision Exercise. (a) and (c). (a) y = is not a solution (b) x = 0 is a solution but x = 0 is not (c) x = is a solution but x = is not. (a) (b) (c) (d) (e) (f) (g) (h) 0. (a) 8 (b) (c) (d) 0 9 (e) (f) A = ` 00, B = ` 00, C = ` , 9.. 8, 8, 8. 8 years l = cm, b = cm. 00 l

19 Chapter 9 Comparing Quantities Exercise 9.. (a) 8% (b) % (c) % (d) 8 % (e) % (f) %. (a) 80% (b) 0.% (c) 8 % (d).8 % (e) 0 % (f) %. (a) 9 % (b) % (c) 9% (d) 0 % (e) % (f) 9 %. (a) (b) (c) (d) (e) (f) (a) (b) 0.00 (c) 0. (d) 0.00 (e) 0. (f) 0.0 Exercise 9.. (a).8 (b) kg (c) 0 inches (d) ` 8.. (a) 0% (b) % (c) % (d) %. 0000, 00, %. %. % 8. English 9. 8% decrease 0. 0% Exercise 9.. (a) Profit 9 % (b) Profit % (c) Loss.% (d) Loss %. (a) SP = ` 8 (b) CP = ` 00 (c) CP = ` (d) SP = `.0. Profit %. Loss = 0%. %. ` 0 9. ` CP = ` 00, Profit = ` Loss % 0. ` 00. CP = ` 800, SP = ` 89. SP of first = ` 0, SP of second = ` 90 Exercise 9.. (a) ` 0 (b) ` 8. (a) Discount = ` 0, 0% (b) Discount = ` 0, 8%. ` 800. Total discount = ` 9.0, Amount returned = `.0. ` 000. ` 000. `. 8. ` 0 9..% 0. %. `.0. `.0 MCQ - VIII..%... 0%. 8 %. %. ` % 9. % 0. `.0 9

20 Revision Exercise. (a) 00 (b). %. %. 00. old price = `, new price = ` 0. B. Laxmi = ` 0000, Rajeev = ` 000, Sunil = ` Profit % 9. % Profit 0. Loss %. ` %. ` 0.0. ` 8 Chapter 0 Interest Exercise (a) ` 0, ` 0 (b) ` 000, ` 000 (c) ` 800, ` 8000 (d) ` 88.0, ` years. % or %. ` 0000, ` 800. ` 000, ` ` ` 000,.% 8. ` ` 000, 9% 0. ` 0000, ` 0000 Exercise 0.. (a) `, ` (b) ` 80, ` 80 (c) ` 9., ` 9. (d) ` 90, ` 0. ` 0., ` 0.. `.80. ` ` % p.a.. 8 years 8. ` (a) ` 0, ` 0 (b) ` 008, ` 08 (c) ` 8., ` ` 0. 0% p.a.. ` 000, ` 000. ` ` 000, 0% p.a.. years Exercise 0... m. ` tons. 90. (a) 000 (b) MCQ - IX. P + P R T 00. ` 0. 0.%. ` 0. 8%. years. % % 0. Scheme

21 Revision Exercise. (a) ` 0.0, ` (b) ` 80, ` 80. ` 000. years. ` 000. ` 00. ` 000. ` 000, % p.a. 8. ` % p.a. 0. ` ` ` 8. ` 90. % p.a. Chapter Direct and Inverse Variations Exercise.. (a), (b), (c), (d). (a) Yes (b) No (c) Yes. (a) x (b) a (a) 8 (b) m. ` (a). m (b) 9 m 0. (a) ` 00 (b) ` 00. (a) days (b) 0 km. (a) 9 days (b) ` 00 Exercise.. (a), (b) and (c). (a) (b) x 8 8. (a) Yes (b) No (c) Yes. 8.. kg. days 8. (a) 0 hr (b) 0 km/hr 9. (a) 0 (b) 0. ` 00 Exercise.. days. 9 days. days. days. days. 8. hr 8. days 9. 0 min 0. days Exercise.. 0 km/hr. (a) km/hr (b) hr. km. km/hr 9. 9 s. s. m 8. 8 km/hr 9. 8 km/hr 0. 0 km/hr MCQ - X y 9 8 y 9 b 0 a 00 0 b days... hr. seconds 8. 0 minutes 9. 0 m 0. 0

22 Revision Exercise. (a) Direct (b) Inverse (c) Direct (d) Inverse. (a) Inverse (b) Direct x 8 0 y x y 0 0. (a). (a) 0 (b) (a) (b) days 9. days 0. days, X = 8 days, Y = 8 days, Z = days. hrs. days. seconds. 8 km/hr. 9 hrs Chapter Visualising Shapes EXERCISE.. D D D D D D D. (a) Cylinder, Cone, Hemisphere (b) Prism, Cuboid (c) Sphere, Cylinder (d) Cube, Pyramid, Cuboid, Cylinder. Front Side Top (a) (b) (c) (d)

23 . Front Side Top (a) (b) (c) EXERCISE.. F E V (a) Cube (b) Triangular Prism (c) Square Pyramid (d) Pentagonal Prism Chapter Exercise. Understanding Quadrilaterals. (a) Heptagon (b) Quadrilateral (c) Nonagon (d) Triangle. (a) 0 (b) 9 (c) Polygon (d) Regular. (a) False (b) False (c) True (d) True. (a) Concave (b) Convex (c) Concave (d) Concave. (a) Sides - AB, BC, CA Diagonals - None

24 (b) Sides - AB, BC, CD, DE, EF, FA Diagonals - AC, AD, AE, BD, BE, BF, CE, CF, DF (c) Sides - JK, KL, LM, MN, NO, OP, PQ, QJ Diagonals - JL JM, JN, JU, JP, KM, KO, LP, MO, MP, MQ, NP, NQ, OQ (d) Sides - WX, XY, YZ, ZW Diagonals - WX, XZ. (a) 080 (b) 800 (c) 0 (d) (a) (b) 80 (c) 0 (d) 0 Exercise.. (a) PQ, RS and QR, SP (b) SP, PQ and QR, RS (c) PR, QS (d) ùpqr, ùqrs and ùrsp, ùspq , 8, 8,. They are also supplementary.. 00, 00, 00, 0. ùp =, ùq = 0, ùr =, ùs = 0 8. (a) 0 (b) (c) Exercise.. MNQP, MNFE, MNCB, PQFE, PQCB, EFCB. ùa =, ùb = 8, ùc =, ùd = 8., 0,, (a) JM = ML and JK = KL (b) ùmjk = ùmlk (c) MK (d) Right Angle (90 ). ùcdb =, ùadb =. x =, y = 0 8. ùw = 0, ùx = 0, ùy = 0, ùz = 0 9. cm 0. JK = cm, KL= 0 cm, LM = cm, MJ =0 cm Exercise.. (a) Rectangle / Square (b) Rectangle / Square (c) Rhombus / Square (d) Perpendicular, bisect. (a) Rectangle / Square (b) Parallelogram (c) Isosceles Trapezium.. 8 cm. cm (d) Rhombus / Square.,,,. x =, Perimeter = cm MCQ - XI. kite. bisect each other. Rectangle. 0. Rectangle.,,. 8 cm 8. 8, 9. Rhombus 0.

25 Revision Exercise. (a) True (b) False (c) True. (a) Perpendicular (b) Rectangle / Square (c) 90. (a) (b). (a).. 0, 0,, 0. (a) 0 (b) 0 (c) 8. Rectangle or square 9., 0,, 0 0.,,,. x = 0, y =. Sides are 8 cm, cm, diagonal is 0 cm. cm. (a) 0 (b) 0 (c) 8. ùabo =, ùodc =, ùacb =, ùcbd = 0 Chapter Mensuration Exercise.. cm. 80 m, 0 m. 0 cm. m. ` 08. cm. cm 8. Perimeter = cm, Area = cm 9. ` m, ` 0 Exercise.. cm. 0 cm, 80 cm. 0 cm, 8 cm. 8 m. 0 cm. cm, cm. 80 cm cm 9. (a) 0 cm (b) cm 0. (a) 00 m (b) 00 m Exercise.. (a) LSA = 0 cm, TSA =0 cm (b) LSA = 8. cm, TSA = 98. cm. L = cm, B= 9 cm, H = cm. cm. cm. Area = 88 m, cost = ` 0. LSA =.8 cm, TSA =. cm. 000 cm 8. (a) CSA = 0 cm, TSA = 09 cm (b) CSA = 0 cm, TSA = 000 cm 9. LSA = 990 cm, TSA =. cm 0. :. 0. `.8. ` cm Exercise... 8 cm. ` m.. kg. 0 cm. 0 cm g 9. Ratio of CSA = :, Ratio of volume = : 9

26 0. cm. cm. LSA = cm TSA =.8 cm (approx). 0.. cm (approx). cm MCQ - XII. 0 cm Òr + Òrh. cm cm. 9 cm 8. 9 cm cm Revision Exercise. cm (approx). 8 cm. 9. cm. Area of Path = 0 m, Cost = ` 90. ` 0. Cost of levelling = ` 9, Cost of fencing = ` 0. 0 m 8. cm 9. m 0. cm. 0.9 cm. length = m, area = m. length = m, area = 0 cm l Chapter Data Handling & Representation Exercise.. (a) Frequency (b) Inclusive (c) (d) Range. Heights (in cm) Tally Marks Frequency Total 0. (a) 99 (b) 0 (c). (a) Class Interval Tally Marks Frequency Class Interval Tally Marks Frequency Total Total 0 (b) Maximum plants attain a height of 9 cm

27 . Class Interval Tally Marks Frequency Total 0 8. Class Tally Frequency Cummulative Interval Marks frequency Total 0 Exercise. Class Frequency Cummulative Interval frequency (a).8 (approx) (b).8. Monthly Number of Cummulative Expend. (in `) Families frequency Total (a) (b) ` 000 ` 0000 (c) 9.. cm..9.. (a) 9 (b) 0. kg (approx) (c). 8. (a).0 (approx) (b).8 (approx) Exercise.. Hotel Name A B C D Number of bottles = 0 bottles

28 . Expenditure (`) Number of students Rent Food Transport Bills Clothes Misc Head Marks. 0 Number of persons Weight (in kg)

29 . Number of workers Weekly wages (in `). Cartoon show Sector angle Chhota Bheem º Ben 0 º Tom and Jerry 08º Jungle Book º Mr Bean º Ben 0 Tom and Jerry Chhota Bheem 0 º º º º 08º 80 0 Mr Bean Jungle Book. Stream Sector angle Medical Science 00º Non-medical Science 90º Humanities º Commerce º Vocational Studies 0º Non-medical science Humanities º º Medical science º 0º º 00 0 Vocational studies Commerce 8. Cause Sector angle Floods 0º Drought 0º Low supply of fertilizers º Poor monsoon 0º Crop diseases º 9. (a) Hindi (b) 0 (c) Yes Drought Low supply of fertilizers 0º º Floods 0º º 0º 8 Crop diseases Poor monsoon 9

30 0. Temperature (Cº) (Sat, 0.) (Tue, 9.) (Thu, 8.) (Fri, 8.8) (Wed,.) (Sun,.) (Mon,.). 00 Mon Tue Wed Thu Fri Sat Sun Day (IV, 9) (I, 8) (V, 8) 0 (VI, 8) (X, ) Runs scored (II, ) (VII, 8) (VIII, ) 0 0 (III, 0) 0 IX, ) I II III IV V VI VII VIII IX X Inning Exercise.. (a) 0, (b) (c) (d) equal. (a) 9 (b) (c) 9 (d).. (a) (b) (a) 9 (b) (c) MCQ - XIII : Histogram 0. 0

31 Revision Exercise Ḃlood group Tally Marks Frequency. Class Interval Tally Marks Frequency A B AB 0-0 O Total 0 Total Frequency Class interval Number of entries Long jump Language Hindi 80º English º Malayalam º Tamil 8º Marathi º French 8º 9. Sector angle Zone East West South North Central English Number of teachers High jump Cycling Gymnastics Swimming Track Sport Events Hindi 0 80º 8º = 0 teachers 8º º º French 0 º 0 Marathi 0 Malayalam Tamil Judo

32 . (a) ` 000 (b) ` 000 (c) ` 8000 (d) ` Rainfall (cm ) 0 0 Rainfall (cm ) Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Month (Jan, ) (Feb, ) (Mar, 0) (Apr, 0) (June, ) (May, ) (July, ) (Aug, 0) (Sep, 0) (Oct, 8) (Nov, ) (Dec, ) Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Month. (a). (a). (a) 9 0 Chapter (b) (b) (b) 9 00 (c) (c) 0 (d) 9 (d) (c) 0 (d) 9 0 Cartesian System and Coordinates Exercise.. (a) (b), (c) (d)

33 . Y (, ) (, ) (0, ) (, 0) X o 8 X (, ) (, ) (, ) (, ). A (, ) B (, ) C (, ) D (, ) E (, ) F (, 0) G (0, ) H (, ) Y. Trapezium Y (, ) (, ) (, ) (, ) X o 8 X. (a) (b) x 0 y Y Y x 0 y 0 Y (, ) (, ) (, ) X o X Y (0, ) x + y = (, ) (, 0) X o X Y (0, ) x + y = (, )

34 (c) (d) x 0 y Y x 0 y 0 Y (, ) X o X (, ) (0, ) (, ). x 0 y 0 Y x y = (, ) X (, 0) (, ) o (0, ) X (, ) (, 0) X o X (0, ) (, ) (, 8) 8 Y x y = (, ) Y x y = Exercise.. x y (a) km/hr (b) 0 Km (c) 90 Km Cost of Production Y Y (8, 800) (, 0) 00 (, 00) 00 (, 0) X o X Y Number of Units

35 Revision Exercise. (a), (b) line (c) III (d) Y axis. Pentagon Y (, ) (, ) (, ) X o 8 X (, ) (, ) (fig.). (, ) x + y = 0 x y = 0 Y. A (, ), B (, ), C (, ), D (, ) E (0, ), F (, 0), G (, ) H (, ) Chapter 8 x 0 y 0 x 0 y Y (, ) (0, ) (, ) (, ) (, 0) X o X (, ) (, ) (0, ) x + y = 0 Y x y = 0 Formulae & Equations Exercise 8.. (a) y = x +, Where Rajeev's age = x, Rohit's age = y (b) x = 8, Where salary = x, Saving = y y (c) E= mv, Where Energy = E, Mass = m, Velocity = v (d) SP = MP y + x = (x + y) +, Where ten's digits = y, unit's digits = x. 0y + x 8 = 0x + y, where ten's digits = y, unit's digits = x. A = 00y + 0 (x y), A = amount (A P) 00. (a) 00 (b) T = PR, 8

36 Exercise 8.. (a) x =, y = (b) x =, y = (c) x =, y = (d) x =, y =. (a) x =, y = (b) x =, y = (c) x =, y = (d) x =, y =. (a). ` 0. l = cm, b = cm. º and 8º. l = m, b = 0 m 8., 9. 0 and Starting salary = ` 000, Increment = ` 000 Exercise 8.. (a), (b) and (c). (a) x = is a solution but x = is not (b) x = 9 & x = are solution. (a), (b), (c), (d) 9,. and. Kumble =, Kapil =.. and and 8 0. Base = cm, altitude = cm. and. and 9 CHAPTER 9 Exercise 9. Set Theory. (a) {0, 0, 0, 0, 0, 80} (b) {0, 08,,, 9,,, 0,,,, 8, 8, 9, 99} (c) {M, I, S, P} (d) {January, June, July}. (a) {x : x Î N, x 0} (b) {x : x Î z, - x } x (c) {x : x is a vowel in English alphabet} (d) & x : x N +!, x 0. Subsets of A =, {}, {}, {}, {}, {, }, {, }, {, }, {, }, {, }, {, }, {,, }, {,, }, {,, }, {,, }, {,,, }. (a) A È B = {,,,, } (b) B Ç C = {} (c) A È (B Ç C) = {,,, } (d) (A Ç B) È C = {,,,, } (e) A' Ç B' = {, } (f) A Ç (B È C)' = {} (g) A' È (B Ç C)' = {,,,,, } (h) A B = {, } (i) C A = {, } (j) (B - A) È (A - C) = {,, }. (a) B A (b) (A Ç B)' A B A B

37 (c) A È B, A Ì B (d) A' Ç B (e) A Ç B, B Ì A B A B A B. (a) (b) (c). (a) 0 (b) 0 Exercise 9.. x =, y = 8 (b) x =, y =. (a) A B = {(m, ), (m, ), (m, ), (m, ), (n, ), (n, ), (n, ), (n, ), (p, ), (p, ), (p, ), (p, )} (b) B A = {(, m), (, n), (, p), (, m), (, n), (, p) (, m), (, n), (, p), (, m), (, n), (, p)}. (a) R = {(, ), (, ), (, ), (, ), (, ), (, 8)} (b) Domain of R = {,,,,, } Codomain of R = {,,,,,,, 8, 9, 0} Range of R = {,,,,, 8}. (a) R = {(, ), (, ), (, ), (9, )} = {(a, b) : a Î A, b Î B, a = b + } (b) A B (c) Domain of R = {,,, 9} Range of R = {,,, }. Domain of f = set of all natural numbers Range of f = set of all even natural numbers. (a) (b) (c) (d) 9

38 CHAPTER 0 More on Geometry Exercise 0.. cm. (a) x = 0, y = 90 (b) x =, y = (c) x = 0, y = 0, z = 0. (a) AB, CD (b) BOA (c) AXB. (a) m (minor AB) = 80º (b) m ABC = 0º (c) m (major AB) = 80º. (a) (, ) (b) (, ) (c) (, -) (d) (-, ). A (, ), B ( 8, ), C (, ), D (, ), E (, ) SAMPLE PAPER SA Section A. (b). (a). (d). (c). (a). (a). (d) 8. (c) 9. (d) 0. (b). (x + y) (x y). (a) (b) Section B 0 0. We can't cancel in numerator with in denominator (x ) + = x + = x. Mass of proton approx. 8 times more than that of electron cm Section C.,. (a) 909 (b) 8. 8, 9, 8 8

39 9. (a) or 0 (b) (c) (d) 0 (e) or 0. (x + y ) (x + y + ).,. 80, multiplicative inverse = 80. x + x + x 8x x , x Section D 9. Quotient = x x +, remainder = x 0. (a) (x 9) (x + ) (b) (x ) (x + ) (x + ). (a) 88. (b) (b).. (a) 80 (b) 08x y + y SAMPLE PAPER SA I Section A. (b). (a). (b). (d). (b). (d). (d) 8. (b) 9. (b) 0. (c) Section B. 0, 0, 0 and 0. 0%. km/hr. cm. 80. Loss % 8. Section C Font Side Top 9

40 9. Train º Bus 9º 0º Auto 0º 0º Others On foot 0. ` %. y =. Days. Area = 8 cm, perimeter = 80 cm.. years. 00 cm Section D 8. 0 m 9. ` (a) 0 (b) 0 (c) 0 (d). Height Tally Frequency (cm) Marks Total. ` 9090., ` 0.. (a) cm (b) cm No. of Employees Y Mental Ability Test Height (cm) X , 0, 8.,, 9.,, 0.. HDIYRZGG. Mother. Daughter. Brother-in-law. Three. East. D is third to the left of E