NMT / ZNO

Formulas and reference

A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.

ZNO — full reference · Algebra · 6 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Quadratic equation

Quadratic equation

Quadratic equation

NMT
\[ax^2+bx+c=0\]
Condition \(a\ne0\)
8–11 grade

Discriminant

NMT
\[D=b^2-4ac\]
8–11 grade

Roots for D>0

NMT
\[x_1=\frac{-b-\sqrt D}{2a}\]
\[x_2=\frac{-b+\sqrt D}{2a}\]
Condition \(D\gt 0\)
8–11 grade

Root for D=0

NMT
\[x_1=x_2=-\frac b{2a}\]
Condition \(D=0\)
8–11 grade

Factorization of a quadratic trinomial

NMT
\[ax^2+bx+c=a(x-x_1)(x-x_2)\]
8–11 grade

Vieta's theorem

\[x_1+x_2=-\frac ba\]
\[x_1x_2=\frac ca\]
Condition \(a\ne0\)
8–11 grade