Answer the questions below about the 2012 calendar. 1. Is 2012 a leap year? How do you know? 2. School started on 11 January. We break up on 23 March. How many days is the school term, excluding Saturdays and Sundays? 3. Calculate the number of days from 6 May to 19 August. 4. I am on holiday from 31 July to 23 November. How many days is that? 5. In which century are we living? 6. On which day of the week does your birthday fall this year?

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Let's address each question step by step.

### 1. Is 2012 a leap year? How do you know?
A year is a leap year if:
- It is divisible by 4.
- If it is divisible by 100, it must also be divisible by 400.

For 2012:
- $$ 2012 \div 4 = 503 $$ (divisible by 4)
- $$ 2012 \div 100 = 20.12 $$ (not divisible by 100)

Since 2012 is divisible by 4 and not a century year, it is a leap year.

### 2. School started on 11 January. We break up on 23 March. How many days is the school term, excluding Saturdays and Sundays?
To find the number of days between 11 January and 23 March, we will calculate the total days and then exclude weekends.

- **January**: 31 days - 11 days = 20 days (from 11 to 31)
- **February**: 29 days (leap year)
- **March**: 23 days (from 1 to 23)

Total days = $$ 20 + 29 + 23 = 72 $$ days.

Next, we need to count the weekends:
- From 11 January to 23 March, we can find the total number of Saturdays and Sundays.

Calculating the number of weekends:
- 11 January 2012 is a Wednesday.
- The first weekend is on 14-15 January.
- The last weekend before 23 March is on 17-18 March.

Counting the weekends:
- Total weeks = $$ \frac{72}{7} \approx 10.29 $$ weeks, which means there are 10 full weeks and 2 extra days.
- Each week has 1 Saturday and 1 Sunday, so there are $$ 10 	imes 2 = 20 $$ weekend days.
- The extra days (from 19 to 23 March) include 19 (Monday), 20 (Tuesday), 21 (Wednesday), 22 (Thursday), and 23 (Friday) - no additional weekends.

Total weekend days = 20.

Thus, the number of school days = $$ 72 - 20 = 52 $$ days.

### 3. Calculate the number of days from 6 May to 19 August.
To find the number of days from 6 May to 19 August:
- **May**: 31 - 6 = 25 days (from 6 to 31)
- **June**: 30 days
- **July**: 31 days
- **August**: 19 days (from 1 to 19)

Total days = $$ 25 + 30 + 31 + 19 = 105 $$ days.

### 4. I am on holiday from 31 July to 23 November. How many days is that?
To find the number of days from 31 July to 23 November:
- **July**: 31 - 31 = 0 days (only the 31st)
- **August**: 31 days
- **September**: 30 days
- **October**: 31 days
- **November**: 23 days (from 1 to 23)

Total days = $$ 0 + 31 + 30 + 31 + 23 = 115 $$ days.

### 5. In which century are we living?
We are currently in the 21st century. The 21st century includes the years 2001 to 2100.

### 6. On which day of the week does your birthday fall this year?
To determine the day of the week for a specific date, we can use the known day of the week for a reference date. For example, 1 January 2012 was a Sunday.

To find the day of the week for any date, we can calculate the total number of days from the reference date to the target date and then find the remainder when divided by 7.

If you provide your birthday date, I can calculate the exact day of the week for you.
1. **2012 is a leap year** because it is divisible by 4 and not by 100. 2. **The school term is 52 days** when excluding weekends. 3. **There are 105 days** from 6 May to 19 August. 4. **The holiday period is 115 days** from 31 July to 23 November. 5. **We are in the 21st century**. 6. **Your birthday falls on a specific day of the week**, which can be determined by calculating the number of days from a known reference date.

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