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 · Geometry · 6 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Coordinates

Coordinates

Midpoint coordinates in the plane

\[x_0=\frac{x_1+x_2}{2}\]
\[y_0=\frac{y_1+y_2}{2}\]
9–11 grade

Distance between two points in the plane

\[AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]
9–11 grade

Equation of a circle

NMT
\[(x-x_0)^2+(y-y_0)^2=R^2\]
9–11 grade

Equation of a line

\[Ax+By+C=0\]
Condition \(A^2+B^2\ne0\)
9–11 grade

Midpoint coordinates in space

NMT
\[x_0=\frac{x_1+x_2}{2}\]
\[y_0=\frac{y_1+y_2}{2}\]
\[z_0=\frac{z_1+z_2}{2}\]
10–11 grade

Distance between two points in space

NMT
\[AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]
10–11 grade