HAST Spatial Reasoning 2

Question 1

A shape cast a square shadow when viewed from the front and a circular shadow from above. What 3D shape is it?

Accepted Answer

Cylinder

Answer

A cylinder viewed from the front shows a rectangular/square shadow and from above shows a circular shadow.

Question 2

Five unit cubes are arranged in a plus (+) shape (one center, four arms). How many faces of the unit cubes are visible from outside?

Accepted Answer

20

Answer

Each unit cube has 6 faces; 5 cubes = 30 faces total; where cubes touch, 2 faces are hidden per join; 4 joins → 8 hidden faces; 30 − 8 = 22 — recalculating for a flat plus shape: 4 touching pairs × 2 hidden faces = 8 hidden; 30 − 8 = 22.

Question 3

An isometric drawing shows a shape with 3 visible faces: a top, a front, and a right side. Each face is a 2×2 square grid. What is the shape?

Accepted Answer

A 2×2×2 cube

Answer

Three square faces visible from top, front, and right, each 2×2, is characteristic of a 2×2×2 cube.

Question 4

A rectangular piece of paper is folded in half twice (each fold halves the paper). How many layers of paper are there?

Accepted Answer

4

Answer

Each fold doubles the number of layers: 1 → 2 → 4 layers after two folds.

Question 5

On a coordinate grid, point A is at (2, 3). It is reflected across the y-axis. What are its new coordinates?

Accepted Answer

(−2, 3)

Answer

Reflecting across the y-axis negates the x-coordinate while leaving the y-coordinate unchanged: (2, 3) → (−2, 3).

HAST - Higher Ability Selection Test Practice Test

HAST - Higher Ability Selection Test Practice Test

HAST Spatial Reasoning 2