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 · 7 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Probability and statistics

Probability

Classical probability

NMT
\[P(A)=\frac mn\]

m — number of favorable equally likely outcomes; n — total number of outcomes.

9–11 grade

Probability of the complementary event

\[P(\overline A)=1-P(A)\]
9–11 grade

Sum of probabilities of mutually exclusive events

\[P(A\cup B)=P(A)+P(B)\]
Condition \(A\cap B=\varnothing\)
10–11 grade

Product of probabilities of independent events

\[P(A\cap B)=P(A)P(B)\]
Condition \(A and B are independent\)
10–11 grade
Probability and statistics

Statistics

Arithmetic mean

\[\bar x=\frac{x_1+x_2+\cdots+x_n}{n}\]
6–11 grade

Mean with frequencies

\[\bar x=\frac{x_1n_1+\cdots+x_kn_k}{n_1+\cdots+n_k}\]
9–11 grade

Range of a data set

\[R=x_{\max}-x_{\min}\]
9–11 grade