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3.1 Staff at public schools are required to adhere to stipulated percentages or fractions relating to the total number of weekly periods based on their post level - NSC Mathematical Literacy - Question 3 - 2024 - Paper 1
Question 3
3.1 Staff at public schools are required to adhere to stipulated percentages or fractions relating to the total number of weekly periods based on their post level. ... show full transcript
Worked Solution & Example Answer:3.1 Staff at public schools are required to adhere to stipulated percentages or fractions relating to the total number of weekly periods based on their post level - NSC Mathematical Literacy - Question 3 - 2024 - Paper 1
Step 1
3.1.1 Determine the number of staff members at Woodsill SS.
Answer
To determine the number of staff members at Woodsill SS, we count the number of entries in the provided table for Woodhill SS. Since there are 40 periods in total, and given the data provided, we can identify the staff allocation and total it.
The total number of staff members equals 10.
Step 2
3.1.2 Write down the modal number of periods per week for Moloto PS.
Answer
To find the modal number of periods per week for Moloto PS, we look for the value that appears most frequently in the dataset provided for the periods assigned to primary school staff.
The modal number is 32 periods, as it occurs most frequently.
Step 3
3.1.3 Calculate missing value D.
Answer
To calculate the missing value D for the deputy principal at Woodsill SS, we set up the equation based on the total number of periods:
egin{align*}
D + 26 + 30 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 40 &= 40
D + 5 imes 40 &= 33
D &= 33 imes 40 - 957
D &= 24
\end{align*}
Thus, the missing value D is 24 periods.
Step 4
3.1.4 Ina stated that since the calculated mean for Woodsill SS is 33, the median would be a better reflection of the average number of periods taught per staff member.
Answer
To examine Ina's statement, we first calculate the mean and median:
- The mean is already given as 33.
- To calculate the median, we first arrange the frequencies in increasing order: 26, 30, 32, 33, 34, 35, 36, 37, 38, 40.
- The median is calculated as:
35 = rac{10 ext{ terms}}{2}
Hence, the median is 35.
Since 35 is higher than the mean of 33, the median provides a better representation when there are outliers which could skew the mean.
Step 5
3.1.5 Determine, as a fraction, the probability of randomly selecting a staff member at Moloto PS who teaches 29 or more periods per week.
Answer
To determine this probability, we note that there are 6 staff members teaching 29 or more periods based on the totals in the table:
egin{align*}
ext{Total staff at Moloto PS} &= 12
ext{Probability} &= rac{6}{12} = rac{1}{2}.
\end{align*}
Thus, the probability is \ rac{1}{2}.
Step 6
Step 7
3.2.1 (b) Calculate the range of the percentages achieved for Task 2.
Answer
To find the range for Task 2, we first identify the highest and lowest percentages from the provided data:
- Highest percentage for Task 2: 81
- Lowest percentage for Task 2: 47
Thus, the range is calculated as:
egin{align*}
ext{Range} &= ext{Highest} - ext{Lowest}
ext{Range} &= 81 - 47 = 34.
\end{align*}
Step 8
3.2.1 (c) Identify the learner whose marks for both tasks can be classified as an outlier. Give a reason for your answer.
Answer
The learner identified as an outlier is learner H. This is because their marks of 82 for Task 1 and 40 for Task 2 deviate significantly from the pattern exhibited by other learners, particularly as the marks for Task 2 appear lower compared to Task 1.
Step 9
3.2.2 Verify, showing all calculations, whether the teacher's claim is VALID.
Answer
The teacher's claim states that the mean mark for both tasks falls within the school's subject policy. First, we calculate mean percentages for both tasks:
- Mean for Task 1 = rac{71 + 79 + 50 + 53 + 66 + 60 + 49 + 63 + 45 + 56}{10} = 66.7
- Mean for Task 2 = rac{53 + 69 + 53 + 49 + 50 + 47 + 61 + 65 + 47 + 81}{10} = 54.6
Now we find the difference:
egin{align*} ext{Difference} &= 66.7 - 54.6 = 12.1. \end{align*}
As 12.1 < 15, the teacher's claim is indeed VALID.
Step 10
3.2.3 Plotting the results of Learner K and L for both tasks on a graph.
Answer
The results for Learner K and L show the following percentages which should be plotted on the same graph previously used for other learners:
- Learner K (Task 1 = 82, Task 2 = 36)
- Learner L (Task 1 = 71, Task 2 = 40)
This creates a clearer representation to evaluate their performances relative to others.