![LOGARITHMS Synopsis and Formulae logx N 0>0,1>0,1#1 a = a = xN ; logm logm logm 2 (ab) b a+ S ()= logm] logm logm bl 0 logb logb 111 m a Q ಕ 1 logb logb" | b >0,b#1, 5 0 m 0>0, i # 0 ) m logb" logb 0 n loga 0 1 ೆಕ logb 8 b = 1 PRAVINDRA LOGARITHMS Synopsis and Formulae logx N 0>0,1>0,1#1 a = a = xN ; logm logm logm 2 (ab) b a+ S ()= logm] logm logm bl 0 logb logb 111 m a Q ಕ 1 logb logb" | b >0,b#1, 5 0 m 0>0, i # 0 ) m logb" logb 0 n loga 0 1 ೆಕ logb 8 b = 1 PRAVINDRA](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_569656_1324445d_1785001568444_sc.jpg?tenant=sc&referrer=pwa-sharechat-v2&f=444_sc.jpg)
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🌺 padmavathi 🌿#📖ఎడ్యుకేషన్✍ #🧪10th సైన్స్ #📘ఇంటర్ సైన్స్ & మ్యాథ్స్
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call_me_joy❤️#✌️నేటి నా స్టేటస్ #🏆పోటీ పరీక్షల స్పెషల్ #🤔టిప్స్ & ట్రిక్స్ విత్ ఫన్👨🏫 #➗10th గణితం #💼TSPSC/ APPSC ప్రత్యేకం
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P RAVINDRA#➗10th గణితం #📖ఎడ్యుకేషన్✍ #🏆పోటీ పరీక్షల స్పెషల్ #👩💻టెట్/DSC ప్రత్యేకం #🎓జాబ్ ప్రిపరేషన్📚![ARITHMETIC PROCRESSION is called Arithmetic Progression (A.P), A series of the form here "a is first term and "d" is a, a + d, a + 2d, a + 3d, common difference Common difference, Znd term st term Or *d is found by Znd term or any two consecutive terms 3rd term th term of an AP 1)d (n an = a + Example The series is clearly in A.P -1, 3, 7, 11, with common difference d = 3 - (-1) = 4/ Sum of first n terms 2) [2a (2)[a + !] 1)d] (n - + Or of the AP is = where | = last term in the given A.P ದ If a, b, C are three consecutive numbers, Condition for three they are in AP if and only if then consecutive numbers | to be in A.P 2b = a + c Let total number of terms be N. term from the end nth Then nth term from the end [ _ (n - 1)d of an A.P a + (N - n)d KEY POINTS IMPORTANT FORMULAE an = ೩ + (n - 1)d A.P is increasing If d > 0 = decreasing [ = a + (n - 1)d Ifd < 0 AP is > Sn = (2) [2a (n 1)d] If d = 0 All terms are equal > (?) [a + [] Number of terms from a to Sn = (Ida ) +1 (1da ) +1 is n n = Understand the concept; Practice PRAVINDRA makes Practice regularly, Perfect! Score excellently! ARITHMETIC PROCRESSION is called Arithmetic Progression (A.P), A series of the form here "a is first term and "d" is a, a + d, a + 2d, a + 3d, common difference Common difference, Znd term st term Or *d is found by Znd term or any two consecutive terms 3rd term th term of an AP 1)d (n an = a + Example The series is clearly in A.P -1, 3, 7, 11, with common difference d = 3 - (-1) = 4/ Sum of first n terms 2) [2a (2)[a + !] 1)d] (n - + Or of the AP is = where | = last term in the given A.P ದ If a, b, C are three consecutive numbers, Condition for three they are in AP if and only if then consecutive numbers | to be in A.P 2b = a + c Let total number of terms be N. term from the end nth Then nth term from the end [ _ (n - 1)d of an A.P a + (N - n)d KEY POINTS IMPORTANT FORMULAE an = ೩ + (n - 1)d A.P is increasing If d > 0 = decreasing [ = a + (n - 1)d Ifd < 0 AP is > Sn = (2) [2a (n 1)d] If d = 0 All terms are equal > (?) [a + [] Number of terms from a to Sn = (Ida ) +1 (1da ) +1 is n n = Understand the concept; Practice PRAVINDRA makes Practice regularly, Perfect! Score excellently!](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_317670_9a4e052_1785149294267_sc.jpg?tenant=sc&referrer=feed-service&f=267_sc.jpg)
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![MATHS TUITIONS 1th MATHS WARASIGUDA, SECUNDERABAD MENSURATION SYNOPSIS CUBOID Lateral Surface Area of the Cuboid (L.S.A) = 2h(l + b) here [ = length Total Surface Area of the Cuboid (T.S.A) २(Ib + bh + hl) b = breadth h = height V = Ibh Volume of the Cuboid 2) CUBE : 4$2 Lateral Surface Area of the Cube (L.S.A) here side or) edge 6$2 Total Surface Area of the Cube (T.S.A) of the cube $3 Volume of the Cube V 3) REGULAR CIRCULAR CYLINDER : Curved Surface Area of the Cylinder (C.S.A) = 2nrh here 1 radius of the base Total Surface Area of the Cylinder (TSA) = Zir(h + r) h = height TT2h Volume of the Cylinder; V SPHERE 4TT2 Surface Area of the Sphere; A= here ٣ = radius 3 Volume of the Sphere, V T1*3 5) HEMISPHERE Hemisphere (C.S.A) 2112' Curved Surface Area of the hereT = rudius 31T2 Total Surface Area of the Hemisphere (T S.A) = 2 Volume of the Hemisphere, V Tr3 3 6) RIGHt CIRCULAR CONE here r = radius Curved Surface Area of the Cone (C.S.A) = nrl of the base Total Surface Area of the Cone (T.S.A) = nr(r + 4) height h = TT2h Volume of the Cone, V = slant height] 3 Also [2 = 12 + h2 Practice Today, Success Tomorrow! PRAVINDRA, MSc Dedicated to Your Success in MATHS MATHS TUITIONS 1th MATHS WARASIGUDA, SECUNDERABAD MENSURATION SYNOPSIS CUBOID Lateral Surface Area of the Cuboid (L.S.A) = 2h(l + b) here [ = length Total Surface Area of the Cuboid (T.S.A) २(Ib + bh + hl) b = breadth h = height V = Ibh Volume of the Cuboid 2) CUBE : 4$2 Lateral Surface Area of the Cube (L.S.A) here side or) edge 6$2 Total Surface Area of the Cube (T.S.A) of the cube $3 Volume of the Cube V 3) REGULAR CIRCULAR CYLINDER : Curved Surface Area of the Cylinder (C.S.A) = 2nrh here 1 radius of the base Total Surface Area of the Cylinder (TSA) = Zir(h + r) h = height TT2h Volume of the Cylinder; V SPHERE 4TT2 Surface Area of the Sphere; A= here ٣ = radius 3 Volume of the Sphere, V T1*3 5) HEMISPHERE Hemisphere (C.S.A) 2112' Curved Surface Area of the hereT = rudius 31T2 Total Surface Area of the Hemisphere (T S.A) = 2 Volume of the Hemisphere, V Tr3 3 6) RIGHt CIRCULAR CONE here r = radius Curved Surface Area of the Cone (C.S.A) = nrl of the base Total Surface Area of the Cone (T.S.A) = nr(r + 4) height h = TT2h Volume of the Cone, V = slant height] 3 Also [2 = 12 + h2 Practice Today, Success Tomorrow! PRAVINDRA, MSc Dedicated to Your Success in MATHS](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_391106_b3181a5_1785168389873_sc.jpg?tenant=sc&referrer=feed-service&f=873_sc.jpg)
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