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 · 12 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Antiderivatives and integrals

Antiderivatives

Antiderivative of 1

NMT
\[\int 1\,dx=x+C\]
11–11 grade

Antiderivative of a power function

NMT
\[\int x^\alpha dx=\frac{x^{\alpha+1}}{\alpha+1}+C,\quad \alpha\ne-1\]
11–11 grade

Antiderivative of 1/x

NMT
\[\int\frac{dx}{x}=\ln|x|+C\]
11–11 grade

Antiderivative of e^x

NMT
\[\int e^x dx=e^x+C\]
11–11 grade

Antiderivative of a^x

\[\int a^x dx=\frac{a^x}{\ln a}+C\]
11–11 grade

Antiderivative of sin x

NMT
\[\int\sin x\,dx=-\cos x+C\]
11–11 grade

Antiderivative of cos x

NMT
\[\int\cos x\,dx=\sin x+C\]
11–11 grade

Antiderivative of 1/cos²x

NMT
\[\int\frac{dx}{\cos^2x}=\tg x+C\]
11–11 grade

Antiderivative of 1/sin²x

\[\int\frac{dx}{\sin^2x}=-\ctg x+C\]
11–11 grade
Antiderivatives and integrals

Definite integral

Newton–Leibniz formula

NMT
\[\int_a^b f(x)\,dx=F(b)-F(a)\]
11–11 grade

Area under a curve

\[S=\int_a^b f(x)\,dx\]
Condition \(f(x)\ge0\ \text{on}\ [a;b]\)
11–11 grade

Area between graphs

\[S=\int_a^b|f(x)-g(x)|\,dx\]
11–11 grade