CAST Exam

1. Question 1 · Mechanical Concepts

   A surveyor walks the route shown: 50 m east, 30 m north, then 10 m west. How far is the surveyor from the starting point?
   • A.70 m
   • B.90 m
   • C.50 m
   Show answer and explanation

   Answer: C. 50 m

   Net east-west movement is 50 − 10 = 40 m east, and net north movement is 30 m. Displacement = √(40² + 30²) = √2,500 = 50 m. The figure 90 m is the total distance walked, not the straight-line change in position; 70 m simply adds the two net legs.

2. Question 2 · Mechanical Concepts

   Wide tank X and narrow tube Y are open at the top and joined by a pipe at the bottom. Water is poured into tank X. When the water stops moving, where is the water level?
   • A.Higher in tube Y
   • B.Higher in tank X
   • C.Level in both
   Show answer and explanation

   Answer: C. Level in both

   In connected open vessels, water settles where the pressure at the bottom is equal on both sides, which happens only when the surfaces are at the same height. The width of each container does not matter.

3. Question 3 · Reading Comprehension

   Which statement best expresses the central point of Passage 1?
   • A.Electrical current is the most dangerous form of energy found in an industrial plant
   • B.Personal locks are more reliable than tags for controlling hazardous energy
   • C.Operators must be told whenever a machine is shut down for any reason at all
   • D.Hazardous energy must be isolated, locked, released, and verified before work begins
   Show answer and explanation

   Answer: D. Hazardous energy must be isolated, locked, released, and verified before work begins

   The passage walks through the whole energy-control sequence (isolate, lock, relieve stored energy, verify zero energy) so that no one is hurt during service. The statement that hazardous energy must be isolated, locked, released, and verified covers every paragraph. The passage says electrical current is the most familiar hazard, not the most dangerous; notification is one step only; and locks and tags are never compared.

4. Question 4 · Reading Comprehension

   Based on the passage, which slab is at greatest risk of permanent damage if it freezes tonight?
   • A.One in a heated enclosure that has reached 700 psi
   • B.One placed this morning that has reached about 300 psi
   • C.One placed last week that has reached about 2,500 psi
   • D.One under insulated blankets that stays above 50°F
   Show answer and explanation

   Answer: B. One placed this morning that has reached about 300 psi

   The second paragraph says concrete that freezes before reaching roughly 500 psi can be permanently weakened. Only the slab at about 300 psi is below that point; the others are stronger or are kept from freezing.

5. Question 5 · Mathematics

   A 25-ft ladder leans against a wall with its foot 7 ft from the wall. The foot slides out until it is 15 ft from the wall. How far down the wall does the top of the ladder slide?
   • A.4 ft
   • B.8 ft
   • C.6 ft
   • D.20 ft
   • E.2 ft
   Show answer and explanation

   Answer: A. 4 ft

   First height: √(25² − 7²) = √576 = 24 ft. Second height: √(25² − 15²) = √400 = 20 ft. The top drops 24 − 20 = 4 ft. 8 ft is the change at the foot; 20 ft is the new height, not the drop.

6. Question 6 · Mechanical Concepts

   A survey crew walks the path shown: 300 m north, 400 m east, then 300 m south. What is the crew's displacement from the starting point S?
   • A.500 m northeast
   • B.400 m east
   • C.1,000 m east
   Show answer and explanation

   Answer: B. 400 m east

   Displacement depends only on the start and end points. The 300 m north and 300 m south cancel, leaving 400 m east. 1,000 m is the total distance walked, and 500 m northeast would be the displacement after only the first two legs.

7. Question 7 · Mechanical Concepts

   An open tank full of water has three equal-sized holes, A, B and C, in its side. From which hole does water leave at the highest speed?
   • A.Hole C
   • B.Hole B
   • C.Hole A
   Show answer and explanation

   Answer: A. Hole C

   Water pressure increases with depth (P = density × g × depth), so the deepest hole has the greatest pressure pushing water out and the fastest stream. Hole C is the deepest.

8. Question 8 · Reading Comprehension

   Which title best fits Passage 1?
   • A.The Physics of Lightning and Ground Current
   • B.How Utilities Insulate Overhead Conductors
   • C.Training Requirements for Crane Operators
   • D.Working Safely Near Overhead Power Lines
   Show answer and explanation

   Answer: D. Working Safely Near Overhead Power Lines

   The passage covers why contact happens, safe clearance distances, step potential, how to leave energized equipment, and prevention. "Working Safely Near Overhead Power Lines" covers all of it; the passage says overhead conductors are often not insulated, and lightning and operator training are not discussed.

9. Question 9 · Reading Comprehension

   The second paragraph mainly describes
   • A.what the entry permit contains and who signs it
   • B.the duties of the attendant during entry
   • C.how the atmosphere in the space is tested
   • D.which spaces are classified as permit spaces
   Show answer and explanation

   Answer: A. what the entry permit contains and who signs it

   The second paragraph lists what the written permit identifies, says the entry supervisor signs it after every condition is met, and notes that it is posted at the entrance. Testing, the attendant, and classification are in other paragraphs.

10. Question 10 · Mathematics

    Each of three gate frames is 5 ft wide and 12 ft long and needs one diagonal brace from corner to corner. What total length of brace lumber is needed?
    • A.45 ft
    • B.39 ft
    • C.36 ft
    • D.13 ft
    • E.51 ft
    Show answer and explanation

    Answer: B. 39 ft

    Each diagonal = √(5² + 12²) = √169 = 13 ft. Three braces = 39 ft. 51 ft adds the two sides of each frame (17 × 3); 13 ft is only one brace.

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