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Question 2

From Math Analysis HL Paper 2 (May 2025, TZ2)

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  1. [Maximum mark: 6]

The following diagram shows a square-based right-pyramid with vertex V(1, 7, 0). Point X(-3, 4, 2) is the centre of the base ABCD.

A 3D diagram of a square-based right-pyramid. The vertex is labeled V, and the base corners are labeled A, B, C, D. The center of the base is labeled X. Dashed lines indicate hidden edges and the height from V to X.
A 3D diagram of a square-based right-pyramid. The vertex is labeled V, and the base corners are labeled A, B, C, D. The center of the base is labeled X. Dashed lines indicate hidden edges and the height from V to X.

(a) Find VX. [2]

The square base has side length 5 cm.

(b) Find AC. [2]

(c) Find the size of the angle between the edge [VC] and the base of the pyramid. [2]