Mambo SSS, is a small private school in the Lady Frere area of the Eastern Cape - NSC Mathematical Literacy - Question 1 - 2016 - Paper 1

Given the ratio of boys to girls exempted is 1:3, let the number of boys exempted be A and the number of girls exempted be 3A. Since a total of 8 learners were exempted:

$A + 3A = 8$ This gives us: $4A = 8$ $A = 2$.

Therefore, the number of girls exempted = 3A = 3(2) = 6.

Each girl would have paid R450 for the month. Thus, the total fees for the exempted girls are: $6 imes 450 = R2700$.

After the SGB meeting:

For Grade 8 and 9: The increased fee is: $300 + 0.05 imes 300 = 315$

For Grades 10-12 (after a 2.5% reduction): The reduced fee is: $450 - 0.025 imes 450 = 438.75$

Thus, the new monthly school fees are:

• Grade 8 & 9: R315
• Grade 10-12: R438.75.

To find the total fees collected in 2015, we calculate the fees for each grade:

For Grades 8 & 9 (39 learners): $39 imes 315 imes 11 = R13485$

For Grades 10-12 (total 85 learners): $85 imes 438.75 imes 11 = R428226.25$

Adding these totals: $13485 + 428226.25 = R441711.25$.

Thus, the total school fees collected in 2015 would be R441711.25.

The total amount invested is R150,000 at an interest rate of 9.5% for 12 months:

The interest earned would be: 150000 imes rac{9.5}{100} = 14250

Thus, the total amount earned from the investment is R14250.

From the total learners in Grade 11 (42 total), using the earlier ratio of boys to girls in exemptions: Let boys in Grade 11 = A, then girls = 3A

Thus, $A + 3A = 42$ $4A = 42$ This results in: $A = 10.5$

Thus, the number of boys in Grade 11 is rounded down to 10.

To find the probability of selecting a Grade 11 learner, The total number of learners is 167. The number of learners in Grade 11 is 42. Thus, the probability is given by: P( ext{Grade 11}) = rac{ ext{Number in Grade 11}}{ ext{Total Number of Learners}} = rac{42}{167} o 0.2515.

Thus, the probability of randomly selecting a Grade 11 learner from the school is approximately 0.2515.