ETA/NJATC-style · Original math and reading questions
IBEW aptitude practice
Prepare for algebra, functions and reading comprehension. Work through a full two-section sitting, or build confidence with an untimed drill.
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Try two examples before you start
These original worked examples are free, untimed and unscored. Choose an answer in your head, then reveal the method and why each option does or does not fit. Opening these examples does not start a sitting.
Example 1 · Algebra and functions
If F = 3(a − 2b) + 4, what is F when a = 5 and b = −1?
- A.
13
- B.
19
- C.
25
- D.
31
Reveal the answer and method
Answer C: 25
Subtracting 2b means subtracting −2, which adds 2 inside the parentheses. Evaluate that group before multiplying by 3 and adding 4.
Work through the steps
- Substitute the given values: F = 3(5 − 2 × (−1)) + 4.
- Calculate the parentheses: 5 − (−2) = 7.
- Multiply, then add: 3 × 7 + 4 = 25.
Why each option does or doesn’t fit
A.13
This comes from treating b as positive: 3(5 − 2) + 4 = 13. The stated value of b is −1.
B.19
This is 3 × 5 + 4; it omits the −2b term inside the parentheses.
C.25
The grouped value is 5 − 2(−1) = 7, so F = 3 × 7 + 4 = 25.
Correct answer
D.31
Adding another 2 before multiplying gives 31, but the expression contains only the one term −2b.
Example 2 · Reading comprehension
Reading passage
What a stock record can tell you
A maintenance depot once kept a single list of the parts in its storeroom. Staff updated quantities when they had time, but the list did not show when a bin had last been checked. A neat column of figures could therefore create more confidence than the information justified. Workers sometimes promised parts to another team before discovering that a listed quantity was several days old.
The supervisor introduced a small change. Every quantity would now appear beside the date of a physical check. A zero would mean that someone had checked the bin and found it empty. A blank would mean that no quantity had yet been recorded, rather than that the bin contained nothing. These distinctions made gaps in the information visible.
The procedure did not require staff to count the whole storeroom before answering every request. Frequently used bins would be checked each morning; slower-moving items would follow a weekly schedule. For an urgent request, a worker would verify the relevant bin before promising a quantity. Parts could still be removed between scheduled checks, so a recent entry was useful evidence rather than a guarantee of present availability.
At first, some staff preferred the old list because it looked more complete. The supervisor explained that a blank space could be more helpful than an undated number: it told the next person where another check was needed. The purpose was not to make the record look certain, but to show what had actually been established and when.
What is the difference between a zero and a blank under the new procedure?
- A.
A zero records a checked empty bin; a blank means no quantity has yet been recorded.
- B.
A zero identifies a slow-moving item; a blank identifies an item used every morning.
- C.
A zero means replacement parts have been ordered; a blank means an order is still needed.
- D.
A zero marks an old entry; a blank shows that a physical check occurred that day.
Reveal the answer and method
Answer A: A zero records a checked empty bin; a blank means no quantity has yet been recorded.
The passage assigns distinct meanings to the two entries. Zero is evidence of a completed check that found nothing; a blank identifies missing recorded information.
Evidence in the passage
“A zero would mean that someone had checked the bin and found it empty.”
“A blank would mean that no quantity had yet been recorded, rather than that the bin contained nothing.”
Why each option does or doesn’t fit
A.A zero records a checked empty bin; a blank means no quantity has yet been recorded.
This accurately states the two definitions given in the second paragraph.
Correct answer
B.A zero identifies a slow-moving item; a blank identifies an item used every morning.
Checking frequency depends on how often items are used, but zero and blank do not label those categories.
C.A zero means replacement parts have been ordered; a blank means an order is still needed.
The passage does not use either entry to record whether a replacement order has been placed.
D.A zero marks an old entry; a blank shows that a physical check occurred that day.
Dates identify when checks occurred. A blank is not evidence that a check happened that day.
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