Time — Clock & Calendar • Topic 4 of 6

Calendar

A calendar lays out the days, weeks and months of a year as a grid, and reading it well means understanding two cycles. The week cycles through seven named days — Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday — and because it repeats every 7 days, the same date one week later always falls on the same weekday. That gives a quick trick: to find the day after, say, 10 days, divide 10 by 7 (1 week, remainder 3) and shift forward by the remainder of 3 days. The year cycles through 12 months whose day-counts you must know: 31 for January, March, May, July, August, October and December; 30 for April, June, September and November; and 28 for February, rising to 29 in a leap year. That leap year is the second cycle. The Earth takes roughly 365.25 days to orbit the Sun, so the quarter-day is banked up and repaid as one extra day every four years — February 29. The rule for CTET Paper I: a year is a leap year if it is divisible by 4, but a century year (ending in 00) qualifies only if it is divisible by 400. So 2000 was a leap year (2000 / 400 = 5) while 1900 was not (1900 / 400 is not whole). One more handy idea is 'odd days' — the days left over beyond whole weeks: a common year has 1 odd day, a leap year 2, which is why a fixed date drifts forward one weekday each ordinary year and two across a leap year.

✅ Solved examples

1. Was the year 2000 a leap year? Was 1900? Justify each.
Both are century years, so the divisible-by-400 test applies. 2000 / 400 = 5 (whole), so 2000 was a leap year. 1900 / 400 = 4.75 (not whole), so 1900 was NOT a leap year, even though it is divisible by 4.
2. If 5 October is a Monday, what day of the week is 26 October?
26 - 5 = 21 days later. Since 21 is a multiple of 7 (21 / 7 = 3 weeks), the weekday repeats. So 26 October is also a Monday.
3. How many days are there altogether in a leap year, and how many odd days does it have?
A leap year has 366 days. Dividing by 7: 366 / 7 = 52 weeks remainder 2. So it has 2 odd days (a common year has only 1).
4. Today is Wednesday. What day will it be after 10 days?
Divide 10 by 7: 1 week and remainder 3. The full week returns to Wednesday, then shift 3 more days: Thursday, Friday, Saturday. So it will be Saturday.

✏️ Practice — try these, take hints as needed

1. Is 2024 a leap year?
It is not a century year.
Check divisibility by 4: 2024 / 4.
Yes — 2024 / 4 = 506 exactly, and it is not a century year.
2. If 3 March is a Friday, what day is 17 March?
Find the gap: 17 - 3.
14 days is exactly 2 weeks.
Friday (14 days later is a whole number of weeks)
3. How many odd days does a common year have?
365 / 7 leaves a remainder.
Remainder is the odd days.
1 odd day
4. Which month gains an extra day in a leap year, and what does it become?
The shortest month.
28 becomes 29.
February, which has 29 days

📝 Topic test — 8 questions

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