IB Mathematics Applications & Interpretation (AI) HL Internal Assessment Example

The research question is present but phrased loosely; consider rewording to a specific, testable inquiry (e.g., “How can a vector equation determine the interception point in 2D missile defense?”).

The aim statement is cut off mid-sentence (“I have a passion for the theme of”); complete and clarify it to establish precise objectives.

This personal narrative is engaging but overly long and distracts from the mathematical focus; tighten the rationale to emphasize key motivations.

Historical context appears here within technical exposition and interrupts logical flow; reserve background history for a distinct section or condense.

The historical origin of vectors is interesting but peripheral; focus discussion on how vector equations model missile paths for conciseness.

Figure 1 appears disconnected from surrounding text; place the graph adjacent to its discussion for clearer integration.

References to Leibniz and Newton add little to the projectile model; reduce historical detail and allocate more space to explaining calculus in context.

Inconsistent axis assignment: you locate Seoul at (0,197) but later use x-distance; clarify whether horizontal or vertical axis represents ground distance.

Diagram lacks axis labels and units; adding these will make the vector-time illustration more precise.

The term “power of the missile” is non-standard; define horizontal component as $v_0\cos \theta$ and introduce variables formally.

Units switch between meters and kilometers; maintain consistent units throughout and annotate conversions explicitly.

The derivation of $t=x/(v_0\cos \theta )$ is correct; consider showing the intermediate algebraic steps for fuller clarity.

Expressing the position vector in bracket notation (e.g. ⟨x,y⟩) would improve mathematical presentation consistency.

State explicitly the conversion factor (1000 m/km) when converting 197 km to 197 000 m to reinforce clarity.

When computing $t$, specify whether your calculator is in degree or radian mode to avoid ambiguity.

The final intersection equation is cluttered and contains typos; derive each term systematically and use consistent notation to clarify.

Well done linking family military experiences to the exploration context; this demonstrates genuine personal engagement.

The placement of THAAD at 30 km from Seoul is a personal choice; explain how this assumption influences the intersection solution.

Screenshot is clear; consider supplementing with an analytic method to reinforce understanding and avoid reliance on technology alone.

Conclusion mentions 3D vector equations, which the exploration never covers; align your conclusion strictly with the 2D analysis performed.

Evaluation lists limitations but remains superficial; include quantitative error analysis and assess the impact of rounding on interception accuracy.

You correctly note simplifying by ignoring air resistance and environment; explicitly listing and justifying these assumptions will strengthen your model.

Time parameter $t$ is introduced abruptly; specify its start point and units to improve the reader’s understanding.

Using a calculator to solve for $\theta$ is fine, but note the possibility of two valid launch angles; discuss why you select 14.43°.

Deriving the quadratic form for $y(x)$ and solving $y=0$ shows strong competence in simultaneous equations.

Identifying the intercept condition and solving for range demonstrates good understanding of projectile motion fundamentals.

Calculating the vertex’s y-coordinate correctly shows you understand how to apply the quadratic function to find maximum height.