Samacheer Kalvi Class 10 Maths formula sheet for relations, sequences, algebra, coordinate geometry, trigonometry, mensuration, statistics, probability, and exam revision.
Updated 9 May 20264 min read
How to Revise Formulae
Do not only read formulae. Cover the page, write them from memory, and solve one sum for each formula. Keep a separate list for formulae you forget often.
Relations and Functions
Concept
Reminder
Ordered pair
(x, y) where order matters.
Cartesian product
A x B = {(a, b): a in A, b in B}
Domain
Set of first elements or input values.
Range
Set of second elements or output values.
Function test
Every input must have exactly one output.
Numbers and Sequences
Concept
Formula or Rule
Euclid division lemma
a = bq + r, 0 <= r < b
HCF and LCM relation
HCF x LCM = product of two numbers
nth term of AP
a_n = a + (n - 1)d
Sum of first n terms
S_n = n/2 [2a + (n - 1)d]
Sum using first and last term
S_n = n/2 (a + l)
Algebra
Concept
Formula
(a + b)^2
a^2 + 2ab + b^2
(a - b)^2
a^2 - 2ab + b^2
a^2 - b^2
(a + b)(a - b)
Quadratic equation
ax^2 + bx + c = 0
Quadratic formula
x = [-b +- sqrt(b^2 - 4ac)] / 2a
Discriminant
D = b^2 - 4ac
Coordinate Geometry
Concept
Formula
Distance
sqrt((x2 - x1)^2 + (y2 - y1)^2)
Midpoint
((x1 + x2)/2, (y1 + y2)/2)
Slope
(y2 - y1) / (x2 - x1)
Area of triangle
`1/2
x1(y2-y3) + x2(y3-y1) + x3(y1-y2)
`
Trigonometry
Ratio
Meaning
sin theta
Opposite side / Hypotenuse
cos theta
Adjacent side / Hypotenuse
tan theta
Opposite side / Adjacent side
cosec theta
1 / sin theta
sec theta
1 / cos theta
cot theta
1 / tan theta
Trigonometric Identities
sin^2 theta + cos^2 theta = 1
1 + tan^2 theta = sec^2 theta
1 + cot^2 theta = cosec^2 theta
tan theta = sin theta / cos theta
cot theta = cos theta / sin theta
Mensuration
Shape
Formula
Cylinder curved surface area
2 pi rh
Cylinder total surface area
2 pi r(h + r)
Cylinder volume
pi r^2 h
Cone curved surface area
pi rl
Cone total surface area
pi r(l + r)
Cone volume
1/3 pi r^2 h
Sphere surface area
4 pi r^2
Sphere volume
4/3 pi r^3
Hemisphere curved surface area
2 pi r^2
Hemisphere total surface area
3 pi r^2
Statistics and Probability
Concept
Formula
Mean
sum of observations / number of observations
Mean from frequency table
sum fx / sum f
Probability
number of favourable outcomes / total number of outcomes
Last Week Formula Routine
1. Write all formulae from memory. 2. Mark the forgotten formulae in red. 3. Solve two textbook sums from each weak formula. 4. Reattempt one model paper formula question set. 5. Revise theorem statements with formulae.
Revision Checklist
AP formulae memorised
Algebra identities written correctly
Coordinate formulae practised
Trigonometric identities revised
Mensuration units checked
Statistics and probability formulae ready
Frequently Asked Questions
Write the formula sheet from memory every three days, then solve one example for each formula.
