3.1 Calculate, in rand per minute, the rate for solo flying - NSC Mathematical Literacy - Question 3 - 2019 - Paper 2

To determine the total approximate cost for obtaining a private pilot’s licence, we sum up all related expenses:

• 28 hours flying with instructor at R2,050 per hour:

$28 \times R2,050 = R57,400$

• Solo flying for 18 hours at total cost R31,050

• 15 hours ground lesson at R1,242.20 per hour:

$15 \times R1,242.20 = R18,633$

• 2-hour ground lesson costs R700
• Flying kit including notes costs R6,544
• 7 examinations at R190 per examination:

$7 \times R190 = R1,330$

Now, summing all costs:

$ext{Total} = R57,400 + R31,050 + R18,633 + R700 + R6,544 + R1,330 = R116,657$

To calculate the total invested amount after two years at an interest rate of 8.5% compounded annually:

Using the formula for compound interest:

$A = P(1 + r)^n$

Where:

• A = total amount after n years
• P = initial principal (R90,000)
• r = annual interest rate (0.085)
• n = number of years (2)

Calculating:

$A = 90000(1 + 0.085)^2 = 90000(1.085)^2 \approx 90000(1.171225) \approx R105,690.25$

To verify if this is sufficient, we compare it with the total cost of R116,657. Since R105,690.25 < R116,657, Franco does not have enough funds.

A possible reason for the increased probability of passing after the second attempt could be that:

• Students had more time to prepare and practice for their retest, allowing them to improve their understanding and skills.

Let:

• A = number of students who passed in the first attempt = 24
• Total students in first attempt = 120 (given pass rate of 20%)

Thus:

$A = 120 - 24 = 96$

Next, for the second attempt:

• Total students = 67
• Pass rate = 30%:

To find B for the second attempt, we calculate:

$B = 67(0.30) = 20.1 \approx 20 \ (as \ an \ integer)$

Using the failure rates:

• C (students who passed after 2nd attempt) = 30% of 67 = 20
• D (total who passed overall):

$D = 24 + 20 = 44 \text{ (total passed) }$

To verify the conversion of 26,000 hours into weeks, we first convert hours:

$\text{Total hours per week} = \frac{26,000}{168} \approx 154.76 \text{ weeks}$

To further break this down:

• Days per week is calculated as:

$\text{days} = 26,000 \div 24 = 1,083.33 \text{ days}$

This breaks down to: $1,083.33 \div 7 \approx 154 \text{ weeks} + 5 \text{ days}$

And the remainder 8 hours confirms that the instructor's statement is valid.

The total number of loose parts in a box can be counted directly from the assembly instructions provided in the annexure. Ensure to count every individual component listed, including legs, panels, and screws.

1. Place the bench face down on a flat surface. Ensure stability during assembly.

2. Align the bench legs with the pre-drilled holes on the bench seat.

The long panel serves as a main support structure connecting the legs, providing stability and strength to the assembled bench. It plays a key role in keeping the assembly rigid and durable.