Here you can find a summary of the main formulas you need to know. This list was not organized by years of schooling but thematically. Just choose one of the topics and you will be able to view the formulas related to this subject. This is not an exhaustive list, ie it’s not here all math formulas that are used in mathematics class, only those that were considered most important.

Area

area
Square		A=l2A=l2	ll : length of side
Rectangle		A=w×hA=w×h	ww : width hh : height
Triangle		A=b×h2A=b×h2	bb : base hh : height
Rhombus		A=D×d2A=D×d2	DD : large diagonal dd : small diagonal
Trapezoid		A=B+b2×hA=B+b2×h	BB : large side bb : small side hh: height
Regular polygon		A=P2×aA=P2×a	PP : perimeter aa : apothem
Circle		A=πr2A=πr2 P=2πrP=2πr	rr : radius PP : perimeter
Cone (lateral surface)		A=πr×sA=πr×s	rr : radius ss : slant height
Sphere (surface area)		A=4πr2A=4πr2

Volumes

 Volumes

Cube		V=s3V=s3	ss: side
Parallelepiped		V=l×w×hV=l×w×h	ll: length ww: width hh: height
Regular prism		V=b×hV=b×h	bb: base hh: height
Cylinder		V=πr2×hV=πr2×h	rr: radius hh: height
Cone (or pyramid)		V=13b×hV=13b×h	bb: base hh: height
Sphere		V=43πr3

Functions and equations

Directly Proportional	y=kxy=kx                k=yxk=yx	kk: Constant of Proportionality
Inversely Proportional	y=kxy=kx                k=yxk=yx
ax2+bx+c=0ax2+bx+c=0	Quadratic formula	x=−b±b2−4ac−−−−−−−√2ax=-b±b2-4ac2a
Concavity	Concave up: a>0a>0
Concave down: a<0a<0
Discriminant	Δ=b2−4acΔ=b2-4ac
Vertex of the parabola	V(−b2a,−Δ4a)V(-b2a,-Δ4a)
y=a(x−h)2+ky=a(x-h)2+k	Concavity	Concave up: a>0a>0
Concave down: a<0a<0
Vertex of the parabola	V(h,k)V(h,k)
Zero-product property	A×B=0⇔A=0∨B=0A×B=0⇔A=0∨B=0	ex : (x+2)×(x−1)=0⇔(x+2)×(x-1)=0⇔ x+2=0∨x−1=0⇔x=−2∨x=1x+2=0∨x-1=0⇔x=-2∨x=1
Difference of two squares	(a−b)(a+b)=a2−b2(a-b)(a+b)=a2-b2	ex : (x−2)(x+2)=x2−22=x2−4(x-2)(x+2)=x2-22=x2-4
Perfect square trinomial	(a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2	ex : (2x+3)2=(2x)2+2⋅2x⋅3+32=(2x+3)2=(2x)2+2⋅2x⋅3+32= 4×2+12x+94×2+12x+9
Binomial theorem (x+y)n=∑k=0n nCk xn−k yk

exponents

Product	am×an=am+nam×an=am+n	ex : 35×32=35+2=3735×32=35+2=37
am×bm=(a×b)mam×bm=(a×b)m	ex : 35×25=(3×2)5=6535×25=(3×2)5=65
Quotient	am÷an=am−nam÷an=am-n	ex : 37÷32=37−2=3537÷32=37-2=35
am÷bm=(a÷b)mam÷bm=(a÷b)m	ex : 65÷25=(6÷2)5=3565÷25=(6÷2)5=35 ex : 53÷23=(52)353÷23=(52)3
Power of Power	(am)p=am×p(am)p=am×p	ex : (52)3=52×3=56(52)3=52×3=56
Zero Exponents	a0=1a0=1	ex : 80=180=1
Negative Exponents	a−n=(1a)na-n=(1a)n	ex : 3−2=(13)23-2=(13)2 ex : (23)−4=(32)4(23)-4=(32)4
Fractional Exponents	apq=ap−−√qapq=apq	ex : 243=24−−√3243=243