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.
Ratios and percentages

Proportions

Fundamental property of a proportion

\[\frac ab=\frac cd\Longleftrightarrow ad=bc\]
Condition \(b\ne0,\ d\ne0\)
6–8 grade
Ratios and percentages

Percentages

p percent of a number

\[B=A\cdot\frac{p}{100}\]
5–9 grade

What percent B is of A

\[p=\frac BA\cdot100\%\]
Condition \(A\ne0\)
5–9 grade

Changing a number by p percent

\[A_{\uparrow}=A\left(1+\frac p{100}\right)\]
\[A_{\downarrow}=A\left(1-\frac p{100}\right)\]
6–9 grade
Ratios and percentages

Proportionality

Direct proportion

\[y=kx\]
Condition \(k\ne0\)
6–9 grade

Inverse proportion

\[y=\frac{k}{x}\]
Condition \(k\ne0,\ x\ne0\)
6–9 grade