FAST Future Aptitude Selection Tool Spatial Reasoning 5 — Questions and Answers
Question 1: A square piece of paper is folded in half diagonally, then the right corner of the folded triangle is folded to meet the top corner. What shape is the result?
- Smaller triangle (Correct answer)
- Rectangle
- Pentagon
- Parallelogram
Correct answer: Smaller triangle
Folding a triangle's corner to another corner always produces a smaller triangle.
Question 2: An arrow pointing north is rotated 135° counterclockwise. In which direction does it now point?
- Southeast (Correct answer)
- Southwest
- Northwest
- Northeast
Correct answer: Southeast
North rotated 135° counterclockwise passes through west (90°) and reaches southeast (180°+45° past north in reverse = SE).
Question 3: Which of the following transformations changes the size of a geometric figure?
- Rotation
- Reflection
- Translation
- Dilation (Correct answer)
Correct answer: Dilation
Dilation scales a figure, changing its size, while rotation, reflection, and translation preserve size.
Question 4: A rectangular room measures 10 ft × 12 ft. A scale drawing uses 1 inch = 4 ft. What are the dimensions of the room in the drawing?
- 2.5 in × 3 in (Correct answer)
- 4 in × 6 in
- 5 in × 6 in
- 2 in × 3 in
Correct answer: 2.5 in × 3 in
10 ÷ 4 = 2.5 inches and 12 ÷ 4 = 3 inches, giving 2.5 × 3 in.
Question 5: Looking at a cube from the corner so that three faces are visible, how many faces are hidden from view?
- 2
- 3 (Correct answer)
- 4
- 1
Correct answer: 3
A cube has 6 faces; viewing from a corner exposes 3 faces, so 3 are hidden.
Question 6: A piece is moved 4 units right and 3 units down on a grid. Which transformation describes this movement?
- Rotation
- Reflection
- Translation (Correct answer)
- Dilation
Correct answer: Translation
Moving a figure a fixed distance in a fixed direction without turning or flipping is a translation.
Question 7: Which cross-section is produced when a cone is cut parallel to its base?
- Ellipse
- Triangle
- Circle (Correct answer)
- Parabola
Correct answer: Circle
A cut parallel to the base of a cone produces a circular cross-section.
FAST Future Aptitude Selection Tool Spatial Reasoning 5
A square piece of paper is folded in half diagonally, then the right corner of the folded triangle is folded to meet the top corner.
What shape is the result?