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percent of test - weighted course test scores

The final course average is computed using five tests.

The tests are not counted equally. They are weighted as follows:

counts 20% of final grade - 1st test
counts 20% of final grade - 2nd test
counts 10% of final grade - 3rd test
counts 25% of final grade - 4th test
counts 25% of final grade - 5th test

The results of the first three tests are shown below:

counts 20% of final grade - 1st test = 69.57 test score

counts 20% of final grade - 2nd test = 58.54 test score

counts 10% of final grade - 3rd test = 9.5 test score

What score would I have to make on the next 2 tests to make 80% in the course?

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Dec 25, 2013

weighted test scores
by: Staff

Answer

Part I

Final Grade is based on a weighted average of five test scores.

This is a widely used method of determining a course grade.

As you will see, it is impossible to achieve an 80% grade for the course because of the low scores received on the first three tests.

Even if you received 100% on each of the remaining two tests, the course grade would only be 76.6%

$Determining the Course Grade is based on a weighted average of individual test results$

Course Grade = (20% of 1st test score) + (20% of 2nd test score) + (10% of 3rd test score) + (25% of 4th test score) + (25% of 5th test score)

Course Grade = (20% * 1st test score) + (20% * 2nd test score) + (10% * 3rd test score) + (25% * 4th test score) + (25% * 5th test score)

Course Grade = (0.2 * 1st test score) + (0.2 * 2nd test score) + (0.1 * 3rd test score) + (0.25 * 4th test score) + (0.25 * 5th test score)

Course Grade = (0.2 * 69.57) + (0.2 * 58.54) + (0.1 * 9.5 ) + (0.25 * 4th test score) + (0.25 * 5th test score)

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Dec 25, 2013

weighted test scores
by: Staff

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Part II

$Formula for Determining the Course Grade is based on a weighted average$

$Converting a % Weighted Average to a decimal weighted average$

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Dec 25, 2013

weighted test scores
by: Staff

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Part III

$Computing the course grade based on: 3 known test scores and 2 unknown test scores$

Course Grade = 13.914 + 11.708 + 0.95 + (0.25 * 4th test score) + (0.25 * 5th test score)

Course Grade = 26.572 + (0.25 * 4th test score) + (0.25 * 5th test score)

Course Grade = 26.572 + 0.25 * (4th test score + 5th test score)

$Computing the course grade with two unknown test scores$

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Dec 25, 2013

weighted test scores
by: Staff

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Part IV

80 = 26.572 + 0.25 * (4th test score + 5th test score)

80 - 26.572 = 26.572 + 0.25 * (4th test score + 5th test score) - 26.572

53.428 = 26.572 + 0.25 * (4th test score + 5th test score) - 26.572

53.428 = 26.572 - 26.572 + 0.25 * (4th test score + 5th test score)

53.428 = 0 + 0.25 * (4th test score + 5th test score)

53.428 = 0.25 * (4th test score + 5th test score)

53.428 / 0.25 = 0.25 * (4th test score + 5th test score) / 0.25

213.712 = 0.25 * (4th test score + 5th test score) / 0.25

213.712 = (0.25 / 0.25) * (4th test score + 5th test score)

213.712 = (1) * (4th test score + 5th test score)

213.712 = (4th test score + 5th test score)

(4th test score + 5th test score) = 213.712

The scores on both the 4th and 5th tests must each be 106.856 (which is 213.712 / 2) to achieve an 80% for the course. This means that you must receive a score of greater than 100% on each test.

Who knows . . . perhaps the teacher will give extra credit.

$Substitute 80% in the equation for the course grade$

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Dec 25, 2013

weighted test scores
by: Staff

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Part V

$Solve the equation for unknown test scores - step 1$

$Solve the equation for unknown test scores - step 2$

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Dec 25, 2013

weighted test scores
by: Staff

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Part VI

$Necessary test scores for the 4th and 5th tests to achieve 80% average for the course$

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What is the highest possible course grade you could achieve if you scored 100% on the remaining two tests?

Course Grade = (0.2 * 69.57) + (0.2 * 58.54) + (0.1 * 9.5 ) + (0.25 * 4th test score) + (0.25 * 5th test score)

Highest Possible Course Grade = (0.2 * 69.57) + (0.2 * 58.54) + (0.1 * 9.5 ) + (0.25 * 100) + (0.25 * 100)

Highest Possible Course Grade = 13.914 + 11.708 + 0.95 + 25+ 25

Highest Possible Course Grade = 76.572 ≈ 76.6%

Thanks for writing.

Staff
www.solving-math-problems.com

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percent of test - weighted course test scores

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