Mathematics

FACTORIZATION – EXERCISE 3.2.6 – Class 9

Factorise (i) a3 – b3 – c3 – 3abc Solution: = a3 + (– b3)+(– c3) – 3a(–b) ( –c) Using x3 + y3 + z3 – 3xyz = (x + y +z) (x2 + y2 + z2 – xy – yz – xz) we get x = a y = –b c = –c… Continue reading FACTORIZATION – EXERCISE 3.2.6 – Class 9

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FACTORIZATION – EXERCISE 3.2.5 – Class 9

Factorise: (i) 8y3 – 1 Solution: = (2y)3 – 13 [∵ a3 – b3 = (a – b) (a2 + ab + b2)] = (2y – 1) [(2y)2 + 2y .1 + 12] = (2y – 1) (4y2 + 2y + 1)   (ii) 27x3 – 8 Solution: = (3x)3 – 23 [∵ a3 –… Continue reading FACTORIZATION – EXERCISE 3.2.5 – Class 9

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FACTORIZATION – EXERCISE 3.2.4 – Class 9

Resolve into factors (i) x4 + y4 – 7x2 y2 Solution: = x4 + y4 – 2x2 y2 – 2x2 y2 – 7x2 y2 = x4 + y4 + 2x2 y2 – 9x2 y2 = (x2 + y2)2 – (3xy)2 = (x2 + y2 + 3xy) (x2 + y2 – 3xy)   (ii) 4x4 +… Continue reading FACTORIZATION – EXERCISE 3.2.4 – Class 9

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Factorization – EXERCISE 3.2.3 – Class 9

Factorize (i) x2 + 9x + 18 Solution: = x2 + 6x + 3x + 18 = x (x + 6) + 3 (x + 6) = (x + 6) (x + 3)   (ii) y2 + 5y - 24 Solution: = y2 + 8y – 3y – 24 = y (y + 8) –… Continue reading Factorization – EXERCISE 3.2.3 – Class 9

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Factorization – EXERCISE 3.2.2 – Class 9

Factorize the following: (i) 9x2 – 16y2 Solution: = (3x)2 – (4y)2 Using a2 – b2 = (a + b) (a – b) = (3x + 4y) (3x – 4y)   (ii) 5x2 – 7y2 [ Hint : ( 𝟓 )2 = 5 ] Solution: ( 5 x)2 - ( 7 y)2 Using a2 – b2… Continue reading Factorization – EXERCISE 3.2.2 – Class 9

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FACTORIZATION – EXERCISE 3.2.1 – Class 9

Factorise: (i) 5x2 – 20xy Solution: = 5x(x – 4y)   (ii) 2p(x + y) – 3q(x + y) Solution: = (x + y) (2p – 3q) (iii) 4(a + b)2 – 6(a + b) Solution: = 2 (a + b) [2(a + b) – 3] = 2 (a + b) (2a + 2b –… Continue reading FACTORIZATION – EXERCISE 3.2.1 – Class 9

Mathematics

STATISTICS – EXERCISE 1.5.2 – Class 9

STATISTICS - EXERCISE 1.5.2 – Class 9 Calculate the range and coefficient of range from the following data. a) The heights of 10 children in cm: 122, 144, 154, 101, 168, 118, 155, 133, 160, 140 Solution: Heights of 10 children in cm: 122, 144, 154, 101, 168, 118, 155,133, 160,140. Range: H – L… Continue reading STATISTICS – EXERCISE 1.5.2 – Class 9

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SETS – EXERCISE 1.4.5 – Class 9

If A' = {1, 2, 3, 4}, U = {1, 2, 3, 4, 5, 6, 7, 8}, find A in U and draw Venn diagram Solution:  A' = {5, 6, 7, 8} If U = {x/x € 25, x€N}. A = {x/x € U, x ≤ 15} and B = {x/x € U, 0 <… Continue reading SETS – EXERCISE 1.4.5 – Class 9

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SURDS – EXERCISE – 1.3.4 – Class 9

Find which is larger: (i) 3∛𝟑 and 4∜𝟒 ∛(3×32)                                                        4×424 = ∛27 x ∛3                                                   = ∜256 x ∜4 = ∛81                                                             = ∜1024 = ((81)4)1/12             … Continue reading SURDS – EXERCISE – 1.3.4 – Class 9

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SURDS – EXERCISE 1.3.2 – Class 9

Simplify the following using laws of indices: (i) (16)-0.75 x (64)4/3 (16)-0.75 x (64)4/3                              [16 = 24 ] = (24)-0.75 x (24)4/3                         [64 = 26 ] = 24 x -3/4 x 26 x 4/3 = 2-3 x 28 = 25 = 32   (ii) (0.25)0.5 x (100)-1/2 (0.25)0.5 x (100)-1/2 = (0.25)1/2 x (1/100 )1/2… Continue reading SURDS – EXERCISE 1.3.2 – Class 9