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Let's break down the problem step by step to solve it.

### Problem Recap:
Timothy's scores on the last five tests are: 9, 8, 10, 7, 8. He needs to find the score on his sixth test to achieve a mean (average) score of 8 across all six tests.

### Step-by-Step Solution:

1. **Mean Formula**:
   The mean of a set of numbers is the sum of the numbers divided by the total number of scores.

   \[
   \text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}
   \]

   We are given that the required mean is 8, and there will be 6 tests in total.

2. **Current Scores**:
   The sum of the scores from the five tests is:
   \[
   9 + 8 + 10 + 7 + 8 = 42
   \]

3. **Total Score Needed**:
   To find the total score Timothy must achieve for an average of 8 over 6 tests:
   \[
   8 = \frac{\text{Total score of all six tests}}{6}
   \]
   Multiplying both sides by 6 gives:
   \[
   8 \times 6 = \text{Total score of all six tests} = 48
   \]

4. **Score Needed on the Sixth Test**:
   Since the total score of the first five tests is 42, the score required on the sixth test is:
   \[
   48 - 42 = 6
   \]

### Answer:
Timothy must score **6** on his sixth test to achieve a mean of 8.

Would you like any further clarifications?

### Related Questions:
1. How would the required score change if the desired mean was 9 instead of 8?
2. If Timothy's lowest score had been 5 instead of 7, what score would he need on the sixth test for an average of 8?
3. How can you calculate the required score if the number of tests increases to 7?
4. What would Timothy's mean be if he scored 10 on his next test instead of the required 6?
5. If Timothy's score on the sixth test is less than 6, how would this affect the mean?

### Tip:
Always ensure you correctly sum up all scores before dividing when calculating an average.

Timothy achieved the following scores out of 10 on his last five Maths tests: 9, 8, 10, 7, 8. What score must he get on the sixth test to have a mean of 8?

Learn how to calculate the score needed on a sixth test to achieve a mean of 8, given five previous test scores. This problem involves calculating the arithmetic mean, summing test scores, and simple algebra. Suitable for students in Grades 6-8.

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