Question

Average test scores this semester
Biology. Chemistry
Test 1. 85. 79
Test 2. 89. 77
Test 3. 82. 80
Test. 4. 78. 72
Average test scores last semester
80. 73
84. 74
76. 82
72. 69
Ms. Odonnell wants to compare how her students did on the science unit tests this semester with how they did last semester find the difference in the matrices which response is the difference in values in the second row, first column

Answer 1

To find the difference in the matrices for Ms. Odonnell's students' test scores, we need to set up the matrices for this semester and last semester.

**This semester's average test scores:**

| | Biology | Chemistry |
|---------|---------|-----------|
| Test 1 | 85 | 79 |
| Test 2 | 89 | 77 |
| Test 3 | 82 | 80 |
| Test 4 | 78 | 72 |

**Last semester's average test scores:**

| | Biology | Chemistry |
|---------|---------|-----------|
| Test 1 | 80 | 73 |
| Test 2 | 84 | 74 |
| Test 3 | 76 | 82 |
| Test 4 | 72 | 69 |

Now we will subtract the last semester's scores from this semester's scores for each corresponding test:

**Difference Matrix:**

| | Biology | Chemistry |
|---------|---------|-----------|
| Test 1 | 85 - 80 = 5 | 79 - 73 = 6 |
| Test 2 | 89 - 84 = 5 | 77 - 74 = 3 |
| Test 3 | 82 - 76 = 6 | 80 - 82 = -2 |
| Test 4 | 78 - 72 = 6 | 72 - 69 = 3 |

The difference for each value is as follows:

- For Biology:
- Test 1: 5
- Test 2: 5
- Test 3: 6
- Test 4: 6

- For Chemistry:
- Test 1: 6
- Test 2: 3
- Test 3: -2
- Test 4: 3

Specifically, you are asking for the difference in values in the second row, first column, which corresponds to **Test 2 for Biology**.

Calculating this:

\[
\text{Difference (Biology Test 2)} = 89 - 84 = 5
\]

Thus, the difference in values in the second row, first column is **5**.