hsc maths formulae for board exam
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Hsc maths formulae for board examTRANSCRIPT
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HSC IMPORTANT FORMULAE FOR BOARD EXAM REFERENCE
1 www.omtexclasses.com e-mail: [email protected]
ALGEBRAIC FORMULAE
1. π0 = 1
2. π + π 2 = π2 + 2ππ + π2
3. π β π 2 = π2 β 2ππ + π2
4. π2 β π2 = π + π (π β π)
5. π + π 3 = π3 + 3π2π + 3ππ2 + π3
6. π β π 3 = π3 β 3π2π + 3ππ2 β π3
7. π3 + π3 = π + π π2 β ππ + π2
8. π3 β π3 = π β π π2 + ππ + π2
TRIGONOMETRIC FORMULAE
1. π ππ2 π + πππ 2 π = 1
2. 1 + π‘ππ2 π = π ππ2 π
3. 1 + πππ‘2 π = πππ ππ2π
4. π‘πππ =π πππ
πππ π=
1
πππ‘π
5. πππ‘π =πππ π
π πππ=
1
π‘πππ
6. π πππ =1
πππ π
7. πππ πππ =1
π πππ
8. π ππ2π = 2π ππππππ π =2π‘πππ
(1+π‘ππ 2 π)
9. πππ 2π = πππ 2 π β π ππ2 π
= 2 πππ 2 π β 1
= 1 β 2 π ππ2 π
=1βπ‘ππ 2 π
1+π‘ππ 2 π
10. π‘ππ2π =2π‘πππ
1βπ‘ππ 2 π
11. π ππ3π = 3π πππ β 4 π ππ3 π
12. πππ 3π = 4 πππ 3 π β 3πππ π
13. π‘ππ3π =3π‘πππ βπ‘ππ 3 π
1β3 π‘ππ 2 π
14. 1 + πππ 2π = 2 πππ 2 π
15. 1 β πππ 2π = 2 π ππ2 π
16. 1 + π ππ2π = πππ π + π πππ 2
17. 1 β π ππ2π = πππ π β π πππ 2
18. π ππ π + π = π ππ π πππ π + πππ π π ππ π
19. π ππ π β π = π ππ π πππ π β πππ π π ππ π
20. πππ π + π = πππ π πππ π β π ππ π π ππ π
21. πππ π β π = πππ π πππ π + π ππ π π ππ π
1. π ππ π΄ + π ππ π΅ = 2 π ππ π΄+π΅
2 πππ
π΄βπ΅
2
2. π ππ π΄ β π ππ π΅ = 2 πππ π΄+π΅
2 π ππ
π΄βπ΅
2
3. πππ π΄ + πππ π΅ = 2 πππ π΄+π΅
2 πππ
π΄βπ΅
2
4. πππ π΄ β πππ π΅ = β2 π ππ π΄+π΅
2 π ππ
π΄βπ΅
2
5. π πππ΄ πππ π΅ =1
2 π ππ π΄ + π΅ + π ππ π΄ β π΅
6. πππ π΄ π πππ΅ =1
2 π ππ π΄ + π΅ β π ππ π΄ β π΅
7. πππ π΄ πππ π΅ =1
2 πππ π΄ + π΅ + πππ π΄ β π΅
8. π πππ΄ π πππ΅ = β1
2 πππ π΄ + π΅ β πππ π΄ β π΅
1. π‘ππ π΄ + π΅ =π‘πππ΄ +π‘πππ΅
1βπ‘πππ΄π‘πππ΅
2. π‘ππ π΄ β π΅ =π‘πππ΄ βπ‘πππ΅
1+π‘πππ΄π‘πππ΅
3. π‘ππ π
4+ π =
1+π‘πππ
1βπ‘πππ
4. π‘ππ π
4β π =
1βπ‘πππ
1+π‘πππ
5. π‘ππβ1 π₯+π¦
1βπ₯π¦ = π‘ππβ1 π₯ + π‘ππβ1 π¦
6. π‘ππβ1 π₯βπ¦
1+π₯π¦ = π‘ππβ1 π₯ β π‘ππβ1 π¦
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HSC IMPORTANT FORMULAE FOR BOARD EXAM REFERENCE
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1. πππ π + πππ π = πππ ππ
2. πππ π β πππ π = πππ π
π
3. πππ ππ = π πππ π
4. πππππ π = π
5. ππππ π = 1
6. ππππ π =πππ π
πππ π
7. πππ π = 1
8. πππ 1 = 0
1. π0 = 1
2. ππ π = ππππ
3. π
π
π
=ππ
ππ
4. ππππ = ππ+π
5. ππ
ππ = ππβπ
6. πβπ =1
ππ
7. ππ =1
πβπ
8. ππ π = πππ
9. π = π1
2
10. π3
= π1
3
11. ππ
= π1
π
1. π ππ βπ = β π ππ π
2. πππ βπ = πππ π
3. π‘ππ βπ = βπ‘ππ π
4. π ππ π
2β π = πππ π
5. πππ π
2β π = π ππ π
6. π‘ππ π
2β π = πππ‘ π
7. πππ‘ π
2β π = π‘ππ π
8. πππ ππ π
2β π = π ππ π
9. π ππ π
2β π = πππ ππ π
10. π ππ π
2+ π = πππ π
11. πππ π
2+ π = βπ ππ π
12. π ππ π + π = β π ππ π
13. πππ π + π = βπππ π
14. π ππ π β π = π ππ π
15. πππ π β π = βπππ π
DERIVATIVES FORMULAE
1. π
ππ₯π₯π = ππ₯πβ1
2. π
ππ₯π ππ π₯ = πππ π₯
3. π
ππ₯πππ π₯ = β π ππ π₯
4. π
ππ₯π‘ππ π₯ = π ππ2 π₯
5. π
ππ₯πππ‘ π₯ = βπππ ππ2π₯
6. π
ππ₯π ππ π₯ = π ππ π₯ π‘ππ π₯
7. π
ππ₯πππ ππ π₯ = βπππ ππ π₯ πππ‘ π₯
8. π
ππ₯πππ π₯ =
1
π₯
9. π
ππ₯ππ₯ = ππ₯ πππ π
10. π
ππ₯ π = 0
11. π
ππ₯ππ₯ = ππ₯
12. π
ππ₯ π₯ = 1
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HSC IMPORTANT FORMULAE FOR BOARD EXAM REFERENCE
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13. π
ππ₯ π₯ =
1
2 π₯
14. π
ππ₯π ππβ1 π₯ =
1
1βπ₯2
15. π
ππ₯πππ β1 π₯ =
β1
1βπ₯2
16. π
ππ₯π‘ππβ1 π₯ =
1
1+π₯2
17. π
ππ₯πππ‘β1 π₯ =
β1
1+π₯2
18. π
ππ₯π ππβ1 π₯ =
1
π₯ π₯2β1
19. π
ππ₯πππ ππβ1 π₯ =
β1
π₯ π₯2β1
Integration formulae
1. 0 ππ₯ = πΆ π€βπππ π ππ ππππ π‘πππ‘
2. 1 ππ₯ = π₯ + π
3. π₯πππ₯ =π₯π+1
π+1+ π
4. 1
π₯ππ₯ = 2 π₯ + π
5. 1
π₯ππ₯ = ππππ₯ + π
6. ππ₯ππ₯ = ππ₯ + π
7. ππ₯ππ₯ =ππ₯
ππππ+ π
8. π πππ₯ ππ₯ = βπππ π₯ + π
9. πππ π₯ ππ₯ = π πππ₯ + π
10. π ππ2 π₯ππ₯ = π‘πππ₯ + π
11. πππ ππ2π₯ ππ₯ = βπππ‘π₯ + π
12. π πππ₯ π‘πππ₯ ππ₯ = π πππ₯ + π
13. πππ πππ₯ πππ‘π₯ ππ₯ = βπππ πππ₯ + π
14. 1
1βπ₯2ππ₯ = π ππβ1 π₯ + π /βπππ β1 π₯ + π
15. 1
1+π₯2 ππ₯ = π‘ππβ1 π₯ + π / βπππ‘β1 π₯ + π
16. 1
π₯ π₯2β1ππ₯ = π ππβ1 π₯ + π /βπππ ππβ1π₯ + π
17. π‘πππ₯ ππ₯ = πππ π πππ₯ + π
18. πππ‘π₯ ππ₯ = πππ π ππ π₯ + π
19. π πππ₯ ππ₯ = πππ π πππ₯ + π‘πππ₯ + π
20. πππ πππ₯ ππ₯ = πππ πππ πππ₯ β πππ‘π₯ + π
21. 1
π₯2+π2ππ₯ = πππ π₯ + π₯2 + π2 + π
22. 1
π₯2βπ2ππ₯ = πππ π₯ + π₯2 β π2 + π
23. 1
π2βπ₯2ππ₯ = π ππβ1
π₯
π + π
24. 1
π₯2+π2 ππ₯ =1
ππ‘ππβ1
π₯
π + π
25. 1
π₯2βπ2 ππ₯ =1
2ππππ
π₯βπ
π₯+π + π
26. 1
π2βπ₯2 ππ₯ =1
2ππππ
π+π₯
πβπ₯ + π
27. 1
π₯ π₯2βπ2ππ₯ =
1
ππ ππβ1
π₯
π + π
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HSC IMPORTANT FORMULAE FOR BOARD EXAM REFERENCE
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π 00 00
300 π
6
450 π
4
600 π
3
900 π
2
1800 π
2700 3π
2
3600 2π
sin π 0 1
2
1
2 3
2
1 0 β1 0
cos π 1 3
2
1
2
1
2
0 β1 0 1
tan π 0 1
3
1 3 π. π·. 0 π. π·. 0
cosec π π. π·. 2 2 2
3
1 π. π·. β1 π. π·
sec π 1 2
3 2 2 π. π·. β1 π. π·. 1
cot π π. π·. 3 1 1
3
0 π. π·. 0 π. π·