Haan, ek single sheet jisme Chapter 1 se lekar Chapter 14 tak ki saari zaroori formulas hon – taaki last revision mein bhi woh kagaz haath mein pakad ke exam hall mein jaao।
UP Board Class 10 Maths All Formulas yahan ek jagah compile kiye gaye hain. Har chapter ke liye sirf woh formulas jo actually exam mein kaam aate hain – unnecessary theory nahi, sirf formulas।
Isko print karo। Bedroom ki wall par lagao। Roj ek baar dekho। Exam se ek raat pehle sab ek baar aur dekho।
UP Board Class 10 Maths All Formulas: Chapters Ka Map
UP Board Class 10 Maths mein yeh chapters hain:
Chapter 1 – Real Numbers
Chapter 2 – Polynomials
Chapter 3 – Linear Equations
Chapter 4 – Quadratic Equations
Chapter 5 – Arithmetic Progressions
Chapter 6 – Triangles
Chapter 7 – Coordinate Geometry
Chapter 8 – Trigonometry
Chapter 9 – Applications of Trigonometry
Chapter 10 – Circles
Chapter 11 – Areas Related to Circles
Chapter 12 – Surface Areas and Volumes
Chapter 13 – Statistics, Chapter 14 Probability
14 chapters, bohot saare formulas – lekin jo actually exam mein aate hain woh specific hain। Us list par focus karo.
UP Board Class 10 Maths All Formulas: Chapter 1 Real Numbers
Real Numbers chapter mein basically teen formulas kaam aate hain।
Formula 1: Euclid’s Division Lemma
a = bq + r, jahan 0 ≤ r ki value b se choti hoti hai
a is Dividend, b is Divisor, q is Quotient, r is Remainder।
Formula 2: HCF aur LCM Relation
HCF (a,b) times LCM (a,b) = a times b
Sirf do numbers ke liye kaam karta hai।
Formula 3: Prime Factorization
Har positive integer > 1 ka unique prime factorization hota hai।
HCF = Common factors ki minimum powers ka product
LCM = Sabhi factors ki maximum powers ka product
UP Board Class 10 Maths All Formulas: Chapter 2 Polynomials
Quadratic Polynomial ke liye (ax² plus bx plus c, roots α aur β):
Sum of roots: α plus β = minus b divided by a
Product of roots: α times β = c divided by a
Cubic Polynomial ke liye (ax³ plus bx² plus cx plus d, roots α, β, γ):
α plus β plus γ = minus b divided by a
(α times β) plus (β times γ) plus (γ times α) = c divided by a
α times β times γ = minus d divided by a
Quadratic banana jab roots pata ho:
x² minus (sum of roots)x plus (product of roots) = 0
UP Board Class 10 Maths All Formulas: Chapter 3 Linear Equations
Equations: a1x plus b1y plus c1 = 0 aur a2x plus b2y plus c2 = 0
Solution type identify karne ke liye:
Case 1: a1/a2 not equal to b1/b2 → Unique solution (lines intersect)
Case 2: a1/a2 = b1/b2 but not equal to c1/c2 → No solution (parallel lines)
Case 3: a1/a2 = b1/b2 = c1/c2 → Infinite solutions (coincident lines)
UP Board Class 10 Maths All Formulas: Chapter 4 Quadratic Equations
Standard form: ax² plus bx plus c = 0
Quadratic Formula:
x = {minus b plus or minus root(b² minus 4ac)} divided by 2a
Discriminant: D = b² minus 4ac
D > 0: Two distinct real roots
D = 0: Two equal real roots (root = minus b divided by 2a)
D < 0: No real roots
Sum of roots: minus b divided by a
Product of roots: c divided by a
UP Board Class 10 Maths All Formulas: Chapter 5 Arithmetic Progressions
Yeh chapter sirf do formulas par based hai – aur sab questions unsi se solve hote hain।
nth Term Formula:
aₙ = a plus (n minus 1) times d
Jahan a = first term, d = common difference, n = number of term
Sum of n Terms Formula:
Sₙ = n/2 times [2a plus (n minus 1)d]
Ya Sₙ = n/2 times (a plus l) jahan l = last term
Important Derived Formula:
aₙ = Sₙ minus S(n minus 1)
Number of terms formula: n = (l minus a)/d plus 1
📚 Yeh Posts Bhi Zaroor Padho
Formulas ke saath actual concept understanding ke liye in posts mein solved examples hain:
1. UP Board Class 10 Maths Chapter 1 Real Numbers: HCF LCM Euclid Division Solved
Euclid algorithm step by step, HCF LCM solved examples aur irrational numbers proof।2. UP Board Class 10 Maths Chapter 3 Linear Equations: Substitution Elimination Solved
Dono methods complete solved examples aur word problems ke saath।3. UP Board Class 10 Maths Trigonometry: Sin Cos Tan Table Memory Tricks Identities
Values table, memory tricks, identities complete guide।4. UP Board Class 10 Science Electricity: Ohm Law Resistance Numericals Solved
Series parallel circuits aur Ohm Law ke numericals step by step।
UP Board Class 10 Maths All Formulas: Chapter 6 Triangles
Basic Proportionality Theorem (Thales’ Theorem):
Agar DE parallel hai BC ko, toh:
AD/DB = AE/EC
Area of Similar Triangles:
Area of Triangle 1 divided by Area of Triangle 2 = (corresponding side 1)² divided by (corresponding side 2)²
Pythagoras Theorem:
AC² = AB² plus BC² (right angle C par hoga toh AB hypotenuse hai)
Wait, theek se: In right triangle with right angle at C:
AB² = BC² plus CA²
(Hypotenuse square = sum of squares of other two sides)
Converse of Pythagoras:
Agar AB² = BC² plus CA², toh angle at C = 90°
UP Board Class 10 Maths All Formulas: Chapter 7 Coordinate Geometry
Distance Formula:
d = root of [(x₂ minus x₁)² plus (y₂ minus y₁)²]
Section Formula (Internal Division):
Point dividing line AB in ratio m:n internally:
x = (m times x₂ plus n times x₁) divided by (m plus n)
y = (m times y₂ plus n times y₁) divided by (m plus n)
Midpoint Formula:
Midpoint = ((x₁ plus x₂)/2 , (y₁ plus y₂)/2)
Area of Triangle:
Area = (1/2) times |x₁(y₂ minus y₃) plus x₂(y₃ minus y₁) plus x₃(y₁ minus y₂)|
UP Board Class 10 Maths All Formulas: Chapter 8 Trigonometry
Basic Ratios (Right Triangle mein):
sin A = Perpendicular/Hypotenuse (P/H)
cos A = Base/Hypotenuse (B/H)
tan A = Perpendicular/Base (P/B)
cosec A = H/P = 1/sin A
sec A = H/B = 1/cos A
cot A = B/P = 1/tan A
Standard Values:
sin 0° = 0, sin 30° = 1/2, sin 45° = 1/root 2, sin 60° = root 3/2, sin 90° = 1
cos 0° = 1, cos 30° = root 3/2, cos 45° = 1/root 2, cos 60° = 1/2, cos 90° = 0
tan 0° = 0, tan 30° = 1/root 3, tan 45° = 1, tan 60° = root 3, tan 90° = undefined
Three Identities:
sin²A plus cos²A = 1
1 plus tan²A = sec²A
1 plus cot²A = cosec²A
Complementary Angles:
sin(90° minus A) = cos A
cos(90° minus A) = sin A
tan(90° minus A) = cot A
cot(90° minus A) = tan A
sec(90° minus A) = cosec A
cosec(90° minus A) = sec A
UP Board Class 10 Maths All Formulas: Chapter 9 Applications of Trigonometry
Height and Distance mein use:
tan θ = Height divided by Horizontal Distance
Height = Horizontal Distance times tan θ
Horizontal Distance = Height divided by tan θ
Key concept:
Angle of elevation = Angle looking upward
Angle of depression = Angle looking downward
Angle of elevation aur depression alternate angles hote hain – dono equal hote hain।
UP Board Class 10 Maths All Formulas: Chapter 10 Circles
Key Theorems (Proof nahi, statement pakka karo):
Theorem 1: Tangent is perpendicular to the radius at the point of tangency।
Theorem 2: Two tangents drawn from an external point to a circle are equal in length।
Tangent-Secant Relation:
PA times PB = PT² (jahan P external point hai, T tangent point, A aur B secant ke points)
Angle subtended at center:
Angle at center = 2 times angle at circumference (same arc par)
Angle in semicircle = 90°
UP Board Class 10 Maths All Formulas: Chapter 11 Areas Related to Circles
Basic Circle Formulas:
Area = π r²
Circumference = 2πr
Sector Formulas (angle θ in degrees):
Area of Sector = (θ/360) times π r²
Length of Arc = (θ/360) times 2πr
Segment Formula:
Area of Minor Segment = Area of Sector minus Area of Triangle
Area of Major Segment = Area of Circle minus Area of Minor Segment
Ring (annulus):
Area = π (R² minus r²) jahan R = outer radius, r = inner radius
UP Board Class 10 Maths All Formulas: Chapter 12 Surface Areas and Volumes
Yeh chapter sabse zyada formulas wala hai। Ek ek shape carefully samjho।
Chapter 12 Cube aur Cuboid Formulas
Cube (side = a):
Lateral Surface Area = 4a²
Total Surface Area = 6a²
Volume = a³
Diagonal = a times root 3
Cuboid (length l, breadth b, height h):
Lateral Surface Area = 2h(l plus b)
Total Surface Area = 2(lb plus bh plus lh)
Volume = lbh
Diagonal = root(l² plus b² plus h²)
Chapter 12 Cylinder Formulas
Cylinder (radius r, height h):
Curved Surface Area (CSA) = 2πrh
Total Surface Area (TSA) = 2πr(r plus h)
Volume = πr²h
Chapter 12 Cone Formulas
Cone (radius r, height h, slant height l):
Slant Height: l = root(r² plus h²)
Curved Surface Area = πrl
Total Surface Area = πr(r plus l)
Volume = (1/3)πr²h
Chapter 12 Sphere aur Hemisphere Formulas
Sphere (radius r):
Surface Area = 4πr²
Volume = (4/3)πr³
Hemisphere (radius r):
Curved Surface Area = 2πr²
Total Surface Area = 3πr² (curved plus flat base)
Volume = (2/3)πr³
Chapter 12 Frustum Formulas
Frustum (top radius r, bottom radius R, height h, slant height l):
Slant Height: l = root(h² plus (R minus r)²)
Curved Surface Area = π(R plus r)l
Total Surface Area = π(R plus r)l plus π(R² plus r²)
Volume = (πh/3)(R² plus r² plus Rr)
Combined Solids Ka Logic
Jab do shapes combine hoti hain:
Volume = Volume of Shape 1 plus Volume of Shape 2
Surface Area ke liye – sirf bahari surface count karo। Jo surface andar chhup jaata hai use add mat karo।
Common combinations: Cone on cylinder, hemisphere on cylinder, cone on hemisphere।
UP Board Class 10 Maths All Formulas: Chapter 13 Statistics
Mean (Direct Method):
Mean = Sigma(f times x) divided by Sigma(f)
(f = frequency, x = class mark yaani mid value)
Mean (Assumed Mean Method):
Mean = A plus [Sigma(f times d) divided by Sigma(f)]
(A = assumed mean, d = x minus A)
Mean (Step Deviation Method):
Mean = A plus h times [Sigma(f times u) divided by Sigma(f)]
(h = class size, u = (x minus A) divided by h)
Median Formula:
Median = l plus [(n/2 minus cf) divided by f] times h
Jahan:
l = lower boundary of median class
n = total frequency (Sigma f)
cf = cumulative frequency before median class
f = frequency of median class
h = class size
Mode Formula:
Mode = l plus [(f₁ minus f₀) divided by (2f₁ minus f₀ minus f₂)] times h
Jahan:
l = lower boundary of modal class
f₁ = frequency of modal class
f₀ = frequency of class before modal class
f₂ = frequency of class after modal class
h = class size
Empirical Relationship:
Mode = 3 times Median minus 2 times Mean
UP Board Class 10 Maths All Formulas: Chapter 14 Probability
Basic Probability Formula:
P(E) = Number of favorable outcomes divided by Total number of equally likely outcomes
Complementary Events:
P(E) plus P(E-bar) = 1
P(E-bar) = 1 minus P(E)
Range of Probability:
0 ≤ P(E) ≤ 1
P(impossible event) = 0
P(sure event) = 1
Addition Rule (for mutually exclusive events):
P(A or B) = P(A) plus P(B)
Saari Formulas Ek Saath: Quick Reference
Yeh alag alag chapters ki most important formulas ek nazar mein:
Chapter 1: HCF times LCM = a times b
Chapter 2: α plus β = minus b/a, αβ = c/a (quadratic)
Chapter 4: x = {minus b ± root(b² minus 4ac)} divided by 2a
Chapter 5: aₙ = a plus (n minus 1)d, Sₙ = n/2[2a plus (n minus 1)d]
Chapter 7: Distance = root[(x₂ minus x₁)² plus (y₂ minus y₁)²]
Chapter 8: sin²A plus cos²A = 1, 1 plus tan²A = sec²A, 1 plus cot²A = cosec²A
Chapter 11: Sector area = (θ/360)πr²
Chapter 12 Cone: V = (1/3)πr²h, CSA = πrl, l = root(r² plus h²)
Chapter 12 Sphere: V = (4/3)πr³, SA = 4πr²
Chapter 13 Median: l plus [(n/2 minus cf)/f] times h
Chapter 14: P(E) = favorable/total
UP Board Class 10 Maths All Formulas: Memory Tips Chapter-Wise
Sirf formulas likhna kaafi nahi – yaad bhi karna hoga।
Chapter 5 AP ke liye:
“a n d” – a (first term), n (number), d (difference) – teeno yaad hain toh sab nikaal sakte ho।
Chapter 12 ke liye:
Cone mein (1/3) factor – “cone ek teesra hai cylinder ka” yaad karo। Sphere mein (4/3) – “char tehaai”।
Chapter 13 Statistics ke liye:
Median aur Mode ki formulas visually similar hain – dono mein “l plus [fraction] times h” format hai। Pehle format yaad karo, phir andar kya jaata hai।
Trigonometry Identities ke liye:
Pehli identity central hai – sin²A plus cos²A = 1। Doosri is se: cos²A se divide karo tan²A plus 1 = sec²A milta hai। Teesri: sin²A se divide karo 1 plus cot²A = cosec²A milta hai।
Coordinate Geometry ke liye:
Distance formula = Pythagoras hi hai 2D mein। Midpoint = average। Section formula = weighted average।
UP Board Class 10 Maths All Formulas: Exam Strategy
Formulas pakki karna alag baat hai, exam mein sahi use karna alag।
Kaunse chapters highest marks dete hain:
Algebra (Chapter 3, 4, 5) milke roughly 20 marks।
Geometry aur Mensuration (Chapter 6, 11, 12) milke roughly 25 marks।
Trigonometry (Chapter 8, 9) milke roughly 15 marks।
Statistics aur Probability (Chapter 13, 14) milke roughly 15 marks।
Coordinate Geometry (Chapter 7) roughly 10 marks।
Formula bhool jaao toh kya karo:
Trigonometry mein: Identity derive karo sin²A plus cos²A = 1 se।
AP mein: First few terms likho aur pattern se nikalo।
Mensuration mein: Jo shapes hain unhe mentally khud derive karne ki koshish karo – cone ek teesra cylinder jaisi aadat lagao।
Print Karne Ka Sahi Tarika: UP Board Class 10 Maths All Formulas Sheet
Is post ko print karne ke tips:
Pehla – Desktop par kholo, landscape mode mein print karo।
Doosra – A4 paper use karo – thoda bold font better rahega।
Teesra – Color mein print karo agar possible ho – har chapter alag color mein।
Chautha – Laminate karo agar ho sake – zyada time chalta hai।
Paanchva – Bedroom ki wall par lagao – roj subah uthke dekho।
Ya phir yeh karo – khud apne haath se ek notebook mein likhna। Research confirm karti hai ki likhne se memory zyada strong hoti hai sarf padhne se।
Practice Questions: UP Board Class 10 Maths All Formulas
Khud solve karo – formula use karke:
Question 1: AP mein a = 5, d = 3. 10th term aur sum of 10 terms nikalo।
Question 2: Roots hain 3 aur minus 5. Quadratic equation banao।
Question 3: Points (2,3) aur (6,7) ke beech distance nikalo।
Question 4: Cone ka radius 7 cm, height 24 cm. Slant height aur CSA nikalo।
Question 5: Probability: Ek card deck se card draw kiya. King aane ki probability kya hai?
Answers:
Question 1:
a₁₀ = 5 plus 9 times 3 = 5 plus 27 = 32
S₁₀ = 10/2 times (2 times 5 plus 9 times 3) = 5 times (10 plus 27) = 5 times 37 = 185
Question 2:
Sum of roots = 3 plus (minus 5) = minus 2
Product of roots = 3 times (minus 5) = minus 15
Equation: x² minus (minus 2)x plus (minus 15) = 0
x² plus 2x minus 15 = 0
Question 3:
d = root[(6 minus 2)² plus (7 minus 3)²]
d = root[16 plus 16]
d = root[32]
d = 4 root 2 units
Question 4:
l = root(7² plus 24²) = root(49 plus 576) = root(625) = 25 cm
CSA = πrl = π times 7 times 25 = 175π = 550 cm² (approx)
Question 5:
Total cards = 52
Kings = 4
P(King) = 4/52 = 1/13
FAQ: UP Board Class 10 Maths All Formulas
Pehla Sawaal: UP Board Class 10 Maths All Formulas mein se sabse important kaunse hain?
Quadratic formula, AP ka nth term aur sum formula, Trigonometry ki teen identities, Surface Area Volume ke formulas (cone, sphere, cylinder), Median aur Mode ka formula, Distance aur Section formula – yeh sab highest priority hain।
Doosra Sawaal: Kya saari formulas yaad karni chahiye exam ke liye?
Haan, lekin sab ek baar mein nahi। Chapter-wise karo। Pehle jo chapters zyada marks ke hain unki formulas pakki karo। Ek hafte mein 2 chapters – 7 hafte mein sab ho jaayega।
Teesra Sawaal: Frustum ki formula yaad nahi rehti – koi trick hai?
Frustum ek cone ka cut hua part hai। Formulas mein hamesha (R plus r) aur l aate hain। Slant height formula mein R minus r aata hai (difference of radii)। Volume mein (R² plus r² plus Rr) – yeh ek specific combination hai jo yaad karni padegi।
Chautha Sawaal: Statistics mein Median aur Mode formula mein kya andar kya jaata hai – confuse hota hai?
Dono ka format same hai – l plus [fraction] times h। Median mein fraction mein: (n/2 minus cf) divided by f। Mode mein: (f₁ minus f₀) divided by (2f₁ minus f₀ minus f₂)। Median mein frequencies ka ek fraction, Mode mein modal class ki frequency se compare।
Paanchva Sawaal: Trigonometry identity derive kaise karein exam mein agar bhool gaye?
sin²A plus cos²A = 1 – yeh Pythagoras se seedha aata hai। P² plus B² = H² ko H² se divide karo। Doosri identity: pehli wali ko cos²A se divide karo – tan²A plus 1 = sec²A। Teesri: sin²A se divide karo – 1 plus cot²A = cosec²A।
Chhatva Sawaal: Coordinate Geometry ke formulas confuse hote hain Section aur Midpoint mein?
Midpoint sirf section formula ka special case hai jab m = n = 1। Midpoint = average of coordinates। Section formula mein m aur n weight hain। Pattern yaad karo: “opposite ratio times coordinate, divided by sum of ratio”।
Saatva Sawaal: AP mein n formula kaise nikalte hain?
aₙ = a plus (n minus 1)d mein se n nikalo: n = (aₙ minus a)/d plus 1। Jab last term pata ho aur n nikalna ho – yeh formula directly kaam karta hai।
Aathva Sawaal: Sphere aur Hemisphere ke formulas mein kya fark hai?
Sphere ek complete ball hai – 4πr² surface, (4/3)πr³ volume। Hemisphere aadha sphere hai – CSA 2πr² (curved surface) aur ek flat circular face πr² – isliye TSA 3πr²। Volume half of sphere = (2/3)πr³।
Nauva Sawaal: Probability mein range kya hoti hai aur kab P = 0 ya P = 1?
P ka range 0 se 1 ke beech hota hai। P = 0 jab event impossible ho (die par 7 aana)। P = 1 jab event certain ho (die par 1 to 6 mein se kuch aana)।
Dasva Sawaal: Formula sheet print karke exam mein le ja sakte hain?
Nahi – exam hall mein koi paper allowed nahi। Yeh sheet sirf revision ke liye hai – ghar par wall par lagao, roz dekho, exam se pehle sab yaad ho। Exam hall mein woh formulas apne memory mein hongi।
Conclusion
UP Board Class 10 Maths All Formulas ki ek comprehensive list yahan di gayi hai.
14 chapters, roughly 80 plus important formulas।
Ek kaam yeh karo abhi: Yeh post print karo ya ek diary mein apne haath se likhna shuru karo। Chapter 1 se 14 tak – ek ek formula।
Phir yeh routine banao: Roz ek chapter ke formulas review karo। 14 din mein poora cycle complete karo । Phir repeat karo।
Exam se ek hafte pehle – ek baar sab ek saath revision karo।
Maths formulas ghabrana nahi chahiye – yeh tools hain। Jab inke tools clearly pata hote hain, problems solve karna easy ho jaata hai।
Important Note: NCERT ki official website ncert.nic.in par Class 10 Maths ki free PDF available hai। UP Board ka syllabus NCERT ke hisaab se hai। Wahan har chapter ki exercises practice karo – formulas tab pakki hoti hain jab use hoti hain।
Disclaimer: upboard10th.com ek independent educational website hai. Yahan di gayi formulas carefully compile ki gayi hain lekin UPMSP ki official answer key aur NCERT textbook final authority hain. Kisi bhi doubt ke liye apne Maths teacher se guidance zaroor lo.
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