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A student takes two tests - OCR - GCSE Maths - Question 7 - 2023 - Paper 3

Question 7

A student takes two tests. In Test 1, the student scores 45 out of 60. Test 2 is also out of 60. Work out how many marks the student needs in Test 2 to have a mean... show full transcript

Worked Solution & Example Answer:A student takes two tests - OCR - GCSE Maths - Question 7 - 2023 - Paper 3

Step 1

Calculate the total marks needed for a mean of 70%

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Answer

To find out how many marks are needed for a mean of 70% over the two tests, we first need to calculate the total marks the student needs to achieve.

The total maximum marks for both tests combined is:

$60 + 60 = 120$

To find the total marks required for a mean of 70%, we calculate:

$ext{Mean} = rac{ ext{Total Marks}}{ ext{Number of Tests}}$

Thus,

$70 = rac{ ext{Total Marks}}{2}$

From this, we find:

$ext{Total Marks} = 70 imes 2 = 140$

Step 2

Determine the marks needed in Test 2

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Answer

The student scored 45 marks in Test 1. Therefore, to calculate the marks needed in Test 2, we set up the equation:

$ext{Marks in Test 1} + ext{Marks in Test 2} = ext{Total Marks Needed}$

Substituting the known values gives:

$45 + ext{Marks in Test 2} = 140$

Now, solving for Marks in Test 2 yields:

$ext{Marks in Test 2} = 140 - 45 = 95$

Thus, the student needs 95 marks in Test 2 to achieve a mean of 70%.

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