CBSE · Class 6-12

Class 9 · Ganita Manjari

Unit 5 · Class 9Ganita Manjari

I'm Up and Down, and Round and Round

Cyclic and repeating patterns; periodic behaviour.

Lessons

4 concepts

1
Periodicity
If $f(x + T) = f(x)$ for all $x$ , we say $f$ has period $T$ . Smallest such $T$ is the fundamental period.
2
Modular Arithmetic
'Clock arithmetic'. $17 \mod 12 = 5$ (17:00 hours = 5 PM). Applications: calendars, cryptography, error detection.
3
Cyclic Decimals
$1/7 = 0.\overline{142857}$ — 6-digit cycle. Cycle length divides $q-1$ for prime $q$ .
4
Applications
Predict day of week 100 days later using $\mod 7$ . Predict AM/PM 15 hours later using $\mod 12$ .

Skills to practise

Skill · medium

I'm Up and Down, and Round and Round — Practice