IB Mathematics SL 2.4 Determine key features of graphs AI SL Paper 1- Exam Style Questions- New Syllabus
Question
(ii) In the context of this model, interpret what the value found in part (b)(i) represents.
Most-appropriate topic codes (IB Mathematics: Applications and Interpretation 2025):
• SL 2.4: Determine key features of graphs. — part (a)
• SL 2.5: Modelling with the following functions: Direct/inverse variation: \( f(x) = ax^n, n \in Z \) — parts (a), (b)
• SL 2.6: Modelling skills: Use the modelling process… reading, interpreting and making predictions based on the model. — part (b)(ii)
▶️ Answer/Explanation
(a)
Substitute \( t = 0.5 \) into \( h(t) \):
\( h(0.5) = \frac{20}{2(0.5) + 5} = \frac{20}{1 + 5} = \frac{20}{6} = \frac{10}{3} \approx 3.33 \)
\( \boxed{3.33} \) metres (or \( \frac{10}{3} \) m).
(b)(i)
We need \( h^{-1}(2.5) \), which is the time when the water level is 2.5 m.
Set \( h(t) = 2.5 \):
\( \frac{20}{2t + 5} = 2.5 \)
\( 20 = 2.5(2t + 5) \)
\( 20 = 5t + 12.5 \)
\( 5t = 7.5 \)
\( t = 1.5 \)
\( \boxed{1.5} \) hours.
(b)(ii)
Interpretation: It takes 1.5 hours for the water level to reach 2.5 metres.
Interpretation in context.
(c)
The range of \( h^{-1} \) corresponds to the domain of \( h \), which is given as \( t \geq 0 \).
\( \boxed{t \geq 0} \) or \( h^{-1} \geq 0 \).