IB Mathematics SL 2.2 Function and their domain range graph AA SL Paper 1- Exam Style Questions- New Syllabus

Question

Italia’s Pizza Company supplies and delivers large cheese pizzas. The total cost to the customer, \( C \), in GBP, is modelled by the function:

\[ C(n) = 34.50n + 8.50, \quad n \geq 2, \quad n \in \mathbb{Z} \]

where \( n \) is the number of large cheese pizzas ordered. This total cost includes a fixed cost for delivery.

Part (a):
State, in the context of the question,
(i) what the value of 34.50 represents;
(ii) what the value of 8.50 represents.

Part (b):
Write down the minimum number of pizzas that can be ordered.

Part (c):
Aayush has 450 GBP. Find the maximum number of large cheese pizzas that Aayush can order from Italia’s Pizza Company.

▶️ Answer/Explanation

Detailed Solutions

Part (a)

(i) The value 34.50 is the coefficient of \( n \) in \( C(n) = 34.50n + 8.50 \), representing the cost per large cheese pizza in GBP.

Answer: The cost of each large cheese pizza.

(ii) The value 8.50 is the constant term in \( C(n) \), representing the fixed delivery cost in GBP, independent of the number of pizzas ordered.

Answer: The fixed delivery cost.

Part (b)

The domain is given as \( n \geq 2 \), \( n \in \mathbb{Z} \). Thus, the minimum number of pizzas is the smallest integer satisfying this condition.

Answer: 2

Part (c)

Aayush has 450 GBP. Solve for the maximum \( n \) such that:

\[ 34.50n + 8.50 \leq 450 \]

\[ 34.50n \leq 441.50 \]

\[ n \leq \frac{441.50}{34.50} \approx 12.7971 \]

Since \( n \in \mathbb{Z} \), the maximum \( n \) is the greatest integer less than or equal to 12.7971, which is 12.

Verify: For \( n = 12 \), \( C(12) = 34.50 \cdot 12 + 8.50 = 414 + 8.50 = 422.50 \leq 450 \).

For \( n = 13 \), \( C(13) = 34.50 \cdot 13 + 8.50 = 448.50 + 8.50 = 457 > 450 \).

Answer: 12

IB Mathematics SL 2.2 Function and their domain range graph AA SL Paper 1- Exam Style Questions