Math Problem Statement

In your calculus class, your final grade is based on four categories. The categories are tests, labs, homework assignments, and a final exam. The final average for the course is the weighted average of scores earned in these categories with the following weights.

Assignments Tests Labs Homework Final Exam Weights 51% 11% 17% 21%

Suppose you earned the following grades on each of the categories; 86% on tests, 70% on labs, 80% on homework assignments, and 91% on the final exam. Determine your weighted average in the course. Record the average below as a percentage accurate to two decimal places.

Course Average: %

Solution

To calculate your weighted average in the course, we will use the following formula for the weighted average:

Weighted Average=(Test Grade×Test Weight)+(Lab Grade×Lab Weight)+(Homework Grade×Homework Weight)+(Final Exam Grade×Final Exam Weight)\text{Weighted Average} = (\text{Test Grade} \times \text{Test Weight}) + (\text{Lab Grade} \times \text{Lab Weight}) + (\text{Homework Grade} \times \text{Homework Weight}) + (\text{Final Exam Grade} \times \text{Final Exam Weight})

Here are the grades and their corresponding weights:

  • Test grade: 86%, Weight: 11% (0.11)
  • Lab grade: 70%, Weight: 17% (0.17)
  • Homework grade: 80%, Weight: 21% (0.21)
  • Final Exam grade: 91%, Weight: 51% (0.51)

Now, let’s calculate the weighted average:

Weighted Average=(86×0.11)+(70×0.17)+(80×0.21)+(91×0.51)\text{Weighted Average} = (86 \times 0.11) + (70 \times 0.17) + (80 \times 0.21) + (91 \times 0.51)

Let me compute that.The weighted average for your course is 84.57%, accurate to two decimal places.

Would you like any further details or have questions about this calculation?

Here are 5 follow-up questions you might consider:

  1. How do different weights affect your overall grade?
  2. What would happen if the weight of the final exam changed?
  3. How can you improve your weighted average in a specific category?
  4. How are weighted averages used in other fields besides education?
  5. How would missing an assignment impact your final grade?

Tip: Always double-check the weights and scores when calculating weighted averages to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Weighted Averages
Percentages

Formulas

Weighted Average = (Test Grade * Test Weight) + (Lab Grade * Lab Weight) + (Homework Grade * Homework Weight) + (Final Exam Grade * Final Exam Weight)

Theorems

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Suitable Grade Level

Grades 10-12