Problem 50 - College Algebra and Calculus: An Applied Approach

Question

Course Grade To get an \(\mathrm{A}\) in a course, you need an average of \(90 \%\) or better on four tests. The first three tests are worth 100 points each and the fourth is worth 200 points. Your scores on the first three tests are 87,92, and 84\. What must you score on the fourth test to get an A for the course?

Step-by-Step Solution

Answer

You must score 187 out of 200 on the fourth test to get an A for the course.

Step 1: Understand the scoring system

Firstly, it is important to know how the scoring system works. To get an A in the course, an average of 90% or higher is needed on four tests. The total possible points from these tests are \(100 * 3\) for the first three tests and 200 for the fourth test making a total of \(300 + 200 = 500\) points.

Step 2: Calculate total points needed for an A grade

To get an A in this course, an average score of at least 90% is required. For the total points across all four tests, this means \(.9 * 500 = 450\) points are required to get an A.

Step 3: Account for the points already earned

The scores for the first three tests are provided as 87, 92, and 84. These add up to \(87 + 92 + 84 = 263\) points. These are points that have been already secured towards the total needed for an A grade.

Step 4: Calculate points required for fourth test

Subtract the total points already earned from the total required to calculate the points required on the fourth test. In this case, the calculation will be \(450 - 263 = 187\). This means to get an A in the course, a score of 187 out of 200 is required on the fourth test.

Key Concepts

Average Percentage Calculation

When calculating an average percentage, it is important to understand the simple principle of finding the mean value within a set of numbers. In the context of course grading, this procedure is essential to determine if a desired grade will be achieved. For example, if a course requires an average of 90% or above across four tests for an A grade, you need to add up the scores of these tests and then divide by the total possible points to find the average percentage.
Using the given exercise, the total points for a course are calculated, and then the student's scores across these assessments are summed up. By dividing the student's total by the course total and multiplying by 100, you determine if the percentage meets or exceeds the requirement for an A.
Keep in mind:

• Adding individual scores gives the numerator for the percentage calculation.
• The total potential score serves as the denominator.
• Multiplying by 100 converts the fraction into a percentage.

Weighted Scoring System

A weighted scoring system is a method used to reflect the importance of different assignments or tests within a course. Instead of treating all tests equally, different weights are assigned based on their significance to the final grade. For instance, in this scenario, the fourth test carries more weight because it is worth 200 points, compared to the 100 points per each of the first three tests.
This approach adjusts the impact individual exams have on the overall course grade. Understanding this can help students prioritize their efforts on assessments that have greater weight. Here's how you can view this:

• Calculating weighted scores involves determining the points contribution each test makes towards the final grade.
• Tests with higher point values have a larger impact on the final score calculation.

Weighted scores are essential in many educational settings, ensuring grades reflect a balanced view of a student's ability according to the instructor's standards.

Test Score Requirements

Understanding what you need to score on remaining tests is crucial for strategic study planning. Knowing the score requirements after calculating totals, helps students focus on areas needing more improvement. In problems like the given exercise, it's essential to work backwards from a goal, like achieving an A in the course, by identifying the score needed on future assessments.
Here's the step-by-step process:

• First, calculate the total required points for the desired grade.
• Subtract the points already earned to determine the deficit.
• This deficit is the minimum score needed on the upcoming test to reach the course grade objective.

Incorporating this knowledge into study habits allows students to efficiently allocate time and resources for preparations, particularly when certain tests weigh more heavily than others.