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5.1 A survey published by the Department of Education reported on the number of schools, learners and teachers in ordinary public schools and independent schools during 2013 - NSC Mathematical Literacy - Question 5 - 2017 - Paper 1

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5.1 A survey published by the Department of Education reported on the number of schools, learners and teachers in ordinary public schools and independent schools dur... show full transcript

Worked Solution & Example Answer:5.1 A survey published by the Department of Education reported on the number of schools, learners and teachers in ordinary public schools and independent schools during 2013 - NSC Mathematical Literacy - Question 5 - 2017 - Paper 1

Step 1

Which province had the second lowest number of learners?

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Answer

According to the data in TABLE 3, the province with the second lowest number of learners is the Free State.

Step 2

Determine the total number of teachers in South Africa for 2013.

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Answer

To find the total number of teachers, sum the number of teachers across all provinces.

The total number of teachers is:

66007+24475+74823+96057+57108+34936+8972+26194+36451=42502366 007 + 24 475 + 74 823 + 96 057 + 57 108 + 34 936 + 8 972 + 26 194 + 36 451 = 425 023

Step 3

Calculate the percentage of schools found in KwaZulu-Natal.

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Answer

The percentage of schools in KwaZulu-Natal can be calculated using:

ext{Percentage of schools} = rac{ ext{Number of schools in KZN}}{ ext{Total number of schools}} imes 100

Using the values from the TABLE, substitute the correct numbers to find the percentage.

Step 4

Use the formula below and determine the LSR for Gauteng.

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Answer

To calculate the Learner-School Ratio (LSR) for Gauteng, use the formula:

ext{LSR} = rac{ ext{Total number of learners in Gauteng}}{ ext{Total number of schools in Gauteng}}

After substituting the values from the TABLE, the LSR can be computed.

Step 5

Write down the modal ratio.

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Answer

The modal ratio is the most frequently occurring Learner-Teacher ratio among the provinces, which can be identified from the calculated ratios.

Step 6

Arrange the ratios in descending order.

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Answer

List all the Learner-Teacher Ratios calculated and arrange them from highest to lowest value.

Step 7

Determine the median ratio.

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Answer

To find the median, first arrange the learner-teacher ratios in ascending order. The median will be the middle value in this ordered list.

Step 8

Write down the percentage of learners who arrive late if it does not rain.

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Answer

From the tree diagram, when it does not rain, 10% of learners arrive late.

Step 9

Write down the missing outcomes (a) and (b).

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Answer

(a) The probability of a learner being late (L) given it does not rain (N) is 0.1.

(b) The probability of a learner not being late (D) given it does not rain is 0.9.

Step 10

Write down the probability (as a simplified common fraction) of randomly selecting a learner who arrived late for school on a rainy day.

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Answer

The probability of selecting a learner who is late on a rainy day can be derived using the values from the tree diagram and simplifying it.

Step 11

If the school has 1 562 learners, determine how many learners will not be late if the chance for rain is 25%.

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Answer

To find the number of learners who will not be late, calculate:

extNumbernotlate=extTotallearnersimesP(extnotlateextonarainyday) ext{Number not late} = ext{Total learners} imes P( ext{not late} ext{ on a rainy day})

Use the data from the problem to find this number.

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