Class 11 Applied Mathematics Chapter 2 Handwritten Notes

The handwritten notes on Class 11 Applied Mathematics Chapter 2 Numerical Applications have been carefully prepared for one-shot revision, according to the latest 2026-27 CBSE syllabus. The PDF covers average, clocks, calendar odd days, time and work, speed, mensuration and seating arrangement in short student-friendly pages.

• Best for rapid revision: one PDF covers every major Numerical Applications block.
• Aligned to 2026-27: follows the current Class 11 Applied Mathematics Chapter 2 scope.
• Practice ready: formulas sit close to worked checks and common mistake notes.

Numerical Applications Handwritten Notes: What the PDF Covers

Numerical Applications joins practical arithmetic with short reasoning. Students meet averages, weighted mean, clock angles, calendar odd days, work-rate questions, speed-time problems, mensuration and seating arrangement. The safest first step is to identify the final quantity asked.

Numerical Applications Quick Video Recap

Source: Commerce Wallah by PW on YouTube

Average and Weighted Mean Formulas in Numerical Applications

Average questions are built around totals. The main formula is mean = sum of observations / number of observations. If one value is removed, compare old total and new total. If every value rises by the same number, the mean also rises by that number.

Weighted mean is used when some values count more than others. For example, marks with different weightage cannot be averaged directly. Multiply each value by its weight, add the products, and divide by the total weight.

• Use weighted mean for marks, months, wages and credits.
• Use simple mean only when every value has equal weight.
• For changed average questions, write total = average x count first.

Clock Angle Formula for Numerical Applications

Clock questions use relative angular speed. The minute hand moves 6 degrees per minute, while the hour hand moves 0.5 degree per minute. The minute hand gains 5.5 degrees per minute on the hour hand.

For a time written as H hours and m minutes, use angle = |30H - 5.5m|. If the result is more than 180 degrees, subtract it from 360 degrees. This gives the smaller angle.

• Right angle questions set the angle as 90 degrees.
• Straight angle questions set the angle as 180 degrees.
• Coincidence questions use the 5.5 degrees per minute relative speed.

Calendar Odd Day Method for Numerical Applications

Odd days are the extra days left after complete weeks are removed. An ordinary year has 1 odd day. A leap year has 2 odd days. A 400-year block has 0 odd days, so century checks need care.

For a date question, count complete years first. Then add completed months and the date number. Divide the total by 7 and use the remainder to shift the weekday. Century years are leap years only when divisible by 400.

Time, Work, Speed and Distance Revision Notes

Time and work questions become simple when the whole task is treated as 1. If A finishes a job in a days, A's one-day work is 1/a. Add daily rates when people work together. Subtract rates when one process undoes another.

Speed questions need unit discipline. Use distance = speed x time, and convert units before substitution. In train questions, distance is the train length for crossing a pole. It is train length plus platform length for crossing a platform.

• More workers usually reduce time when total work is fixed.
• Same distance average speed uses 2ab / (a + b).
• Same time average speed uses (a + b) / 2.

Mensuration and Seating Arrangement in Numerical Applications

Mensuration questions ask for perimeter, area, surface area or volume. Draw the shape before using formulas. For combined solids, split the figure and add only the needed visible surfaces.

Seating arrangement questions need a clear sketch. In a row, mark whether people face north or south. In a circular arrangement, fix one person first and move in one direction. This removes repeated arrangements.

How to Use Numerical Applications Handwritten Notes Before Tests

Use the PDF in two passes. First, read the formula boxes and copy the quick revision sheet. Second, cover the worked checks and solve them again. This helps students see which formula belongs to which story.

• Revise clock and calendar formulas first because they are memory-heavy.
• Then solve work-rate and speed questions with unit checks.
• Finish with mensuration diagrams and seating sketches.

Related Resources for Numerical Applications

Applied Mathematics Handwritten Notes for All Chapters