Formula Sheet
Math Formulas Complete Cheatsheet
Essential formulas for arithmetic, geometry, algebra, trigonometry and statistics — your go-to formula sheet.
01Arithmetic▼
% change
(new-old)/old x 100
Increase or decrease.
Compound interest
A=P(1+r/n)^(nt)
P=principal,r=rate,n=freq/yr.
Simple interest
I=PRT/100
R=rate%, T=time in years.
LCM & GCD
LCM(a,b)=a*b/GCD(a,b)
Proportion
a/b=c/d -> ad=bc
Cross multiply.
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Order of operations (BODMAS): Brackets, Orders, Division, Multiplication, Addition, Subtraction.
022D Geometry▼
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | l x w | 2(l+w) |
| Square | s^2 | 4s |
| Triangle | 1/2 bh | a+b+c |
| Circle | pi*r^2 | 2*pi*r |
| Trapezium | 1/2(a+b)h | a+b+c+d |
| Sector | 1/2 r^2 theta (rad) | r*theta+2r |
FORMULACircle formulas
Arc length = r*theta (theta in radians) Sector area = (1/2)r^2*theta Segment area = (1/2)r^2(theta-sin theta)
033D Geometry▼
| Shape | Volume | Surface Area |
|---|---|---|
| Cube | s^3 | 6s^2 |
| Cuboid | lwh | 2(lw+lh+wh) |
| Sphere | (4/3)*pi*r^3 | 4*pi*r^2 |
| Cylinder | pi*r^2*h | 2*pi*r^2+2*pi*r*h |
| Cone | (1/3)*pi*r^2*h | pi*r^2+pi*r*l (l=slant) |
| Pyramid | (1/3)*base*h | base + lateral faces |
04Algebra▼
Difference of squares
a^2-b^2=(a+b)(a-b)
Perfect square
(a+b)^2=a^2+2ab+b^2
Sum of cubes
a^3+b^3=(a+b)(a^2-ab+b^2)
Quadratic formula
x=(-b+-sqrt(b^2-4ac))/2a
Binomial expansion
(a+b)^n = sum C(n,k) a^(n-k) b^k
Pascal's triangle gives C(n,k).
FORMULAKey expansions
(a+b)^2 = a^2+2ab+b^2 (a+b)^3 = a^3+3a^2*b+3a*b^2+b^3 (a-b)^2 = a^2-2ab+b^2 a^2-b^2 = (a+b)(a-b)
05Statistics▼
Mean
x-bar = sum(x)/n
Average.
Variance (pop)
sigma^2 = sum(x-mean)^2/n
Std deviation
sigma = sqrt(variance)
Same units as data.
z-score
z=(x-mu)/sigma
Std deviations from mean.
Combinations
C(n,r)=n!/(r!(n-r)!)
Permutations
P(n,r)=n!/(n-r)!
Ordered.
❓ Quiz
Compound interest formula?
A=P(1+r/n)^(nt): P=principal, r=annual rate, n=compounding frequency/year, t=years.
06Trigonometry▼
SOH CAH TOA
sin=Opp/Hyp, cos=Adj/Hyp, tan=Opp/Adj
Right triangle.
Sine rule
a/sinA=b/sinB=c/sinC
Any triangle.
Cosine rule
a^2=b^2+c^2-2bc*cosA
Any triangle.
Area triangle
1/2*ab*sinC
Two sides + included angle.
Double angle sin
sin2A=2sinA*cosA
Double angle cos
cos2A=cos^2A-sin^2A
Three forms exist.