Math Problem Statement

solve

A student is taking an advanced anatomy class in which the midterm and final exams are both worth 40% each, and homework is worth 20% of the final grade. The midterm exam score is 88, the homework average score is 84, and the final exam score is 83. What is the student's overall average, and what score would the student have needed on the final exam to achieve a 4.0 (92% overall)?

Solution

The problem describes an advanced anatomy class where the grading breakdown is:

  • Midterm exam: 40% (with a score of 88)
  • Homework: 20% (with an average score of 84)
  • Final exam: 40% (with a score of 83)

1. Calculate the overall average:

We can find the overall average by using the weighted sum of the scores based on the percentage contribution of each component.

Overall average=0.40×Midterm score+0.20×Homework score+0.40×Final exam score\text{Overall average} = 0.40 \times \text{Midterm score} + 0.20 \times \text{Homework score} + 0.40 \times \text{Final exam score}

2. To determine the score needed for a 4.0 GPA (which requires a 92% overall score):

Let the needed final exam score be xx. The equation would be:

0.40×88+0.20×84+0.40×x=920.40 \times 88 + 0.20 \times 84 + 0.40 \times x = 92

Now, let's solve both parts.1. The student's overall average score for the class is 85.2%.

  1. To achieve a 4.0 GPA (which requires an overall score of 92%), the student would have needed a perfect score of 100% on the final exam.

Feel free to ask for further details or clarifications. Here are some related questions:

  1. How do weighted averages work in different grading systems?
  2. What if the final exam had a different weight?
  3. How can a student improve performance in courses with heavy exam weighting?
  4. How does a 4.0 GPA compare to other grading scales?
  5. What strategies are effective for preparing for high-stakes exams like finals?

Tip: Always ensure to understand the weight of each component in your grading system to better strategize your study plan.

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Math Problem Analysis

Mathematical Concepts

Weighted Average
Algebra

Formulas

Overall Average = (0.40 * Midterm Score) + (0.20 * Homework Score) + (0.40 * Final Exam Score)
0.40 * Midterm Score + 0.20 * Homework Score + 0.40 * x = 92

Theorems

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Suitable Grade Level

Grades 9-12