Question 4 of 4intermediate🔧 ApplyLong Answer5 marks

Based upon the data of the past five years, try and forecast the average percentage of marks in Mathematics that your school would obtain in the Class X board examination at the end of the year.

Correct Answer

To forecast the average percentage of marks in Mathematics for the Class X board examination, we follow the stages of mathematical modelling.

Step 1 (Understanding the problem): We need to predict the average percentage of marks in Mathematics based on past five years' data. We assume that the past performance is a good indicator of future results and that conditions remain similar.

Step 2 (Mathematical description): Collect the average Mathematics percentages for the past five years from school records. Represent this data mathematically, perhaps as a sequence of values. We can calculate the mean of these percentages to find the average. We may also identify any trend (increasing, decreasing, or stable) in the data.

Step 3 (Solving the mathematical problem): Calculate the arithmetic mean of the five years' percentages. If the data shows a consistent pattern, we can use it for prediction. For instance, if percentages are 75, 78, 76, 80, and 79, the mean is:

75+78+76+80+795=77.6%\frac{75+78+76+80+79}{5} = 77.6\%

Step 4 (Interpreting the solution): The calculated average gives us a forecast for the upcoming board examination. However, we must remember that this is an estimate. Like predicting election results through exit polls or estimating fish population, our forecast is based on assumptions. Factors like changed syllabus, new teaching methods, or student calibre may affect actual results.

Exercise: EXERCISE A2.3 | Q: 1 | (Page Page 11)
For More Understanding

Explanation

This question from Exercise A2.3 requires students to apply the mathematical modelling process learned in the chapter. The answer demonstrates all four steps: understanding the problem, mathematical description, solving, and interpretation.

The context emphasizes that mathematical modelling helps solve real-world problems through estimation and prediction, similar to examples like election forecasts and fish population estimation. Students should understand that forecasts are estimates based on assumptions.

Solution Steps

  1. Step 1: Identify the problem - forecasting marks based on past data

  2. Step 2: Collect and represent past five years' data mathematically

  3. Step 3: Calculate mean and identify trends

  4. Step 4: Interpret the result as a forecast while acknowledging limitations

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