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 · 5 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Equations

Equations

Linear equation

\[ax+b=0\Rightarrow x=-\frac ba\]
Condition \(a\ne0\)
7–9 grade
Equations

Absolute value

Equation with absolute value

\[|f(x)|=a\Longleftrightarrow f(x)=\pm a\]
Condition \(a\ge0\)
8–11 grade
Equations

Radical equations

Basic radical equation

\[\sqrt{f(x)}=g(x)\Longleftrightarrow\begin{cases}f(x)=g^2(x)\\g(x)\ge0\end{cases}\]
9–11 grade
Equations

Exponential equations

Exponential equation with equal bases

\[a^{f(x)}=a^{g(x)}\Longleftrightarrow f(x)=g(x)\]
Condition \(a\gt 0,\ a\ne1\)
10–11 grade
Equations

Logarithmic equations

Logarithmic equation with equal bases

\[\log_a f(x)=\log_a g(x)\Longleftrightarrow\begin{cases}f(x)=g(x)\\f(x)\gt 0\\g(x)\gt 0\end{cases}\]
Condition \(a\gt 0,\ a\ne1\)
10–11 grade