Andrew and Duncan went fishing for carp on a friend's farm - NSC Mathematical Literacy - Question 3 - 2023 - Paper 2

The total mass of the carp is calculated as follows:

• Mass of Andrew's carp: 2,375 kg
• Mass of Duncan's carp:
  • First carp: 1.2 kg
  • Second carp: 0.750 kg or 0.75 kg

Total mass = 2.375 kg + 1.2 kg + 0.75 kg = 4.325 kg

Thus, the total mass of the carp they caught is 4.325 kg.

The volume of one hole is calculated using the formula:

Volume = length × width × depth = 0.3 m × 0.3 m × 0.6 m = 0.054 m³

For 12 holes: Total volume = 12 × 0.054 m³ = 0.648 m³

The reason Andrew had some concrete left over could be due to the fact that when mixing concrete, there is always some excess material that does not get used completely when pouring into the holes. Additionally, some volume may have been lost in spillage or during the mixing process. Therefore, even though he calculated the exact volume required, practical losses in concrete mixing and pouring would result in some leftover concrete.

To determine the mass of river sand needed for 1 m³ of concrete:

The ratio of cement to river sand to stone is given. Since we're told 0.75 m³ of concrete requires 5.5 bags of cement, we need to find the equivalent mass of river sand for 1 m³.

Mass of river sand needed for 1 m³ can be calculated:

• Since 0.75 m³ uses 5.5 bags of cement, 1 m³ uses (5.5 / 0.75) × 1 = 7.33 bags of cement.
• Each bag of cement weighs 50 kg, therefore: Mass of cement = 7.33 bags × 50 kg/bag = 366.5 kg.
• The remaining portion (river sand and stone) needs to be calculated based on proportions according to the initial statement.

Each concrete post has two sides to paint: Area = 2 × (length × width) = 2 × (1.6 m × 0.125 m) = 0.4 m² or 4,000 cm²

For 12 posts: Total area for posts = 12 × 4,000 cm² = 48,000 cm².

To verify Duncan's statement:

1. Calculate the total area of the posts combined and the caps.
2. The total area of the posts and caps is calculated by adding Their areas:
   • Use the earlier calculated area of the posts and post caps respectively.
   • Total should match or differ from 52,704 cm² to validate.

To calculate the litres of paint needed: Given spread rate = 12.46 litre/m², Total area = 52,704 cm² is equivalent to 5.2704 m².

Litres of paint needed: = Total area / spread rate = 5.2704 m² × 12.46 litre/m² = 65.70 litres.