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 · 13 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Functions and graphs

Quadratic function

x-coordinate of the parabola vertex

\[x_0=-\frac b{2a}\]
Condition \(a\ne0\)
8–11 grade

Vertex form of a quadratic function

\[y=a(x-x_0)^2+y_0\]
Condition \(a\ne0\)
8–11 grade
Functions and graphs

Functions

Linear function

\[y=kx+b\]
7–11 grade

Quadratic function

\[y=ax^2+bx+c\]
Condition \(a\ne0\)
8–11 grade

Power function

\[y=x^\alpha\]
9–11 grade

Exponential function

\[y=a^x\]
Condition \(a\gt 0,\ a\ne1\)
10–11 grade

Logarithmic function

\[y=\log_a x\]
Condition \(a\gt 0,\ a\ne1,\ x\gt 0\)
10–11 grade
Functions and graphs

Graph transformations

Vertical graph translation

\[y=f(x)+b\]
8–11 grade

Horizontal graph translation

\[y=f(x-a)\]
8–11 grade

Stretch/compression along the x-axis

\[y=f(kx)\]
Condition \(k\ne0\)
8–11 grade

Stretch/compression along the y-axis

\[y=kf(x)\]
Condition \(k\ne0\)
8–11 grade

Reflection across the x-axis

\[y=-f(x)\]
8–11 grade

Reflection across the y-axis

\[y=f(-x)\]
8–11 grade