Full mock exams and the final two weeks

Fourteen days before her exam date, Maya cleared her calendar of everything except work, sleep and the plan Luis had helped her write. She had studied for eleven weeks. Her error log had more than two hundred rows. Her last three practice scores were 81, 84 and 83 per cent. "The last two weeks are not for learning the trade," Luis told her. "You already know it. They're for making sure that what you know shows up on the day."

This lesson covers full-length mock exams, how to judge readiness from practice scores, a day-by-day plan for the final two weeks, the last forty-eight hours, the exam day itself, and what comes after. It ends with Maya's exam.

Full-length mock exams

A full mock is the closest rehearsal there is: 125 questions, four hours, the same rules as the real exam, in one sitting, ideally at the same time of day as the booking. It tests stamina, pacing and reading under fatigue as much as knowledge. Maya took two full mocks in the final two weeks, one on day 13 and one on day 6, with enough time after each to analyse it and act on the results.

A mock exam needs good questions. Maya built hers from three sources: question banks from her in-school or related instruction materials, questions her study group had written, and questions she had written herself from the blueprint and then set aside for a month so that she had forgotten the answers. She mixed topics in the proportions of the blueprint, so that a mock was a fair sample of the real thing.

• Take it at a table, not on a couch, with a timer visible and the phone in another room.
• Follow the two-pass plan and the checkpoints exactly as you will on the day.
• Mark only after the end, and record the time each section took.
• Log every wrong answer and every lucky guess by cause within twenty-four hours.
• Look at the score last. The error causes matter more than the number.

Reading a practice score

A single practice score is noisy. On any exam, a candidate's score varies from sitting to sitting because the questions vary and because the candidate does. Thinking about the score as a sample helps decide how much margin is enough.

This model is simple, because real questions are not all equally hard, but it gives the right intuition: a margin of ten percentage points above the pass mark is comfortable, and a margin of two or three is a coin toss on a bad day. The program below estimates the chance of passing for a range of true accuracies, using the exact binomial distribution rather than the approximation.

# Chance of passing for a given true accuracy (binomial model)
from math import comb, ceil

n, pass_mark = 125, 0.70
need = ceil(pass_mark * n)

def p_pass(p):
    return sum(comb(n, k) * p ** k * (1 - p) ** (n - k) for k in range(need, n + 1))

def pct(x):
    return f"{x:6.1%}" if x < 0.9995 else " >99.9%"

print(f"{n} questions, {need} needed to pass")
for acc in (0.68, 0.70, 0.72, 0.75, 0.78, 0.80, 0.85):
    print(f"  true accuracy {acc:.0%}: expected {acc * n:5.1f} correct, chance of passing {pct(p_pass(acc))}")

scores = [0.64, 0.71, 0.74, 0.78, 0.79, 0.81, 0.84, 0.83]       # Maya's practice scores
recent = sum(scores[-3:]) / 3
print(f"Average of the last three practice scores: {recent:.1%} -> chance of passing about {pct(p_pass(recent)).strip()}")

125 questions, 88 needed to pass
  true accuracy 68%: expected  85.0 correct, chance of passing  31.9%
  true accuracy 70%: expected  87.5 correct, chance of passing  50.5%
  true accuracy 72%: expected  90.0 correct, chance of passing  69.5%
  true accuracy 75%: expected  93.8 correct, chance of passing  90.0%
  true accuracy 78%: expected  97.5 correct, chance of passing  98.2%
  true accuracy 80%: expected 100.0 correct, chance of passing  99.6%
  true accuracy 85%: expected 106.2 correct, chance of passing  >99.9%
Average of the last three practice scores: 82.7% -> chance of passing about >99.9%

Two things stand out in the output. A candidate whose true accuracy is exactly the pass mark passes only about half the time. And the chance of passing rises steeply over a few percentage points, which is why the last few points of improvement in the final weeks are worth so much.

The final two weeks

Maya's plan for the last fourteen days balanced three kinds of work: full mocks to rehearse, targeted review driven by the error log, and light mixed practice to keep everything warm. New topics were off the list. The plan also tapered: the hardest work was in the first week, and the last two days were light.

The rule against new topics in the last week surprises some candidates. The reason is that a new topic studied in the final days is poorly learned and crowds out review of topics that are almost secure. The marks are in turning 70 per cent topics into 90 per cent topics, not in turning 0 per cent topics into 40 per cent ones.

The last forty-eight hours

Two days before the exam, Maya did a logistics check. She confirmed the location and the start time, looked up the route and parking, and planned to arrive thirty minutes early. She put her identification, the confirmation letter and a bottle of water by the door. The exam provides the calculator and the reference information, so she brought nothing else, and she knew where she would leave her phone.

The evening before, she read her formula sheet once, ate a normal dinner, and went to bed at her usual time. Luis had told her that one more evening of cramming would cost more in sleep than it gained in knowledge, and her mock exams had shown it: her worst score had come after a late night.

On the day

Maya's exam day routine was the one she had rehearsed twice. A normal breakfast. Arrive early, find the washroom, settle in. Read the instructions fully, including how to flag and how to move between questions. Then start the clock on her pacing plan.

• First pass, about 1 minute 45 seconds per question, best answer and flag on anything uncertain.
• Checkpoint at each quarter: on pace or ahead, ten seconds of rest, a sip of water.
• Review pass on flagged questions, closest first; change answers only for a reason.
• Final check: every question has an answer.

Two things happen to almost everyone during a long exam. A run of hard questions comes along and shakes confidence. And a question appears on a topic that seems never to have been studied. Maya had a response ready for both. For the run of hard questions, she reminded herself that the exam is a mix, and that hard questions are hard for everyone. For the unknown topic, she used elimination, chose the best remaining answer, flagged it and moved on. One question is a small share of the marks, and the next one is a fresh start.

Maya's exam

The exam was on a Tuesday morning at a testing centre on the east side of Hamilton. Maya finished the first pass with forty minutes to spare and twenty-two questions flagged. She changed three answers on review, each for a reason she could name: a NOT she had missed, a gauge pressure that should have been absolute, and a vent table column she had read one step too early. She handed in with ten minutes left. Five weeks later, a letter from Skilled Trades Ontario arrived. She had passed, with a score comfortably above the mark, and her Certificate of Qualification carried the Red Seal.

Luis took the crew for lunch. Grace sent a photo of the old galvanised pipe they had cut out together in Mrs. Patel's basement, with the caption "you've come a long way". Raj, now in his third year, asked whether he could borrow her error log. She said yes, but told him the log was not the useful part. The useful part was writing it.

After the exam

A Certificate of Qualification is not the end of learning. In Ontario, the certificate is renewed each year to stay in good standing. Codes change on a regular cycle, and a journeyperson is expected to keep up with each new edition. New materials, methods and equipment arrive every year, from press fittings to smart leak detection, and manufacturers' training is how most plumbers learn them. Many journeypersons go on to add certificates, such as a gas technician certificate, backflow prevention testing or medical gas installation, or to move into supervision, estimating, inspection, teaching or their own business.

Maya also took on a new role. Northbridge Mechanical assigned her an apprentice of her own, and the first thing she did was hand over a copy of the pacing plan and the six error causes. The habits that got her through the exam were the same ones that make a good plumber: read the whole question, check the definition, find the exception, carry the units, and test before you trust.

Managing nerves

Some anxiety before an exam is normal and even useful: it sharpens attention. Too much narrows attention and makes reading careless, which is exactly the error the log is designed to prevent. Maya used three techniques that are simple enough to work under pressure. Before the exam, she wrote down for two minutes what she was worried about, which research on test anxiety suggests can free up attention for the task. During the exam, she used slow breathing at each checkpoint, breathing out for longer than she breathed in. And when a hard question rattled her, she named the feeling to herself, "this is just a hard one", and returned to the five-step method, because a routine gives the mind something to do other than worry.

Preparation is the strongest defence against nerves. A candidate who has rehearsed the full exam twice, knows her pacing plan, and has a reason behind every answer she changes has very little left to be surprised by. Maya walked in nervous, but she was not afraid, because nothing about the morning was new.