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In South Africa there are ordinary schools and special schools - NSC Mathematical Literacy - Question 4 - 2016 - Paper 2
Question 4
In South Africa there are ordinary schools and special schools. Special schools are for learners with special needs. Ordinary schools are divided into public schools... show full transcript
Worked Solution & Example Answer:In South Africa there are ordinary schools and special schools - NSC Mathematical Literacy - Question 4 - 2016 - Paper 2
Step 1
4.1.1 Showing ALL calculations, identify the province in which approximately 46% of the total number of learners attended independent schools.
Answer
To find the province with approximately 46% of the total learners in independent schools, first calculate 46% of the total learners. Using the provided data:
Total learners = 538,421
Calculate 46%:
Now, check each province's independent school enrolment. The closest province is Gauteng with 246,989 learners, which is around 45.87% of the total. Thus, Gauteng is the province where approximately 46% of learners attended independent schools.
Step 2
4.1.2 A teacher from an ordinary public school is randomly selected to attend a national conference in 2014. Determine the probability that this teacher will be a teacher from the Eastern Cape.
Answer
The total number of teachers in South Africa is given in TABLE 4, and the number of teachers from the Eastern Cape is specifically noted there. The probability is calculated as follows:
P( ext{Eastern Cape}) = rac{ ext{Number of teachers from Eastern Cape}}{ ext{Total number of teachers}}Substituting the numbers from the table gives:
For example, if there are 61,260 teachers from the Eastern Cape and a total of 390,608 teachers:
P( ext{Eastern Cape}) ext{ } rac{61260}{390608} ext{ } ext{ or } ext{ } rac{61,260}{390,608} ext{ } ext{ approximately } 0.1568 ext{ or } 15.68 ext{%.}Step 3
4.1.3 Calculate the missing value A if the mean number of learners per province in public schools is 1 346 335.
Answer
Given the mean number of learners in public schools as 1,346,335, to find A, we can use the total number of learners formula from the table:
Calculating the totals gives:
Therefore, the missing value A is 665,516.
Step 4
4.1.4 After reading the data in TABLE 4, a teacher stated: 'In South Africa, the teacher-to-learner ratio of independent schools is better than that of public schools.' Verify, showing ALL calculations, whether this teacher's statement is valid.
Answer
To verify the teacher's statement, calculate the teacher-to-learner ratio for both independent and public schools:
- From TABLE 4, get the number of teachers and learners for each type of school.
- The formula for teacher-to-learner ratio is:
For public schools, if there are 390,608 learners and 12,117,015 teachers:
ext{Ratio}_{public} = rac{390608}{122117015} ext{ } ext{ ( calculate ratio)}For independent schools, if there are 34,482 learners and 538,421 teachers:
ext{Ratio}_{independent} = rac{34482}{538421} ext{ } ext{ ( calculate ratio)}Compare both ratios. If the ratio of independent schools is less than that of public schools, then the teacher's statement is valid.
Step 5
4.1.5 The number of learners in ordinary schools increased from 2012 to 2014. Give ONE possible reason for this annual increase.
Answer
One possible reason for the increase in the number of learners in ordinary schools could be the annual growth of the population in South Africa, leading to an increase in the number of school-age children. Additionally, learners transferring from special schools to ordinary schools could also contribute to this increase. This demographic change impacts the enrolment numbers in ordinary schools positively.