PHYS 165 MODULE 2 EXAM — PHYSICS
(PORTAGE LEARNING) —
MEASUREMENTS, SI UNITS,
DIMENSIONAL ANALYSIS & VECTOR
MATHEMATICS
OFFICIAL PRACTICE EXAM 2026/2027
══════════════════════════════════════
SECTION 1: MEASUREMENTS & UNCERTAINTY Q1 – Q10
══════════════════════════════════════
Question 1 of 50
A student uses a micrometer caliper to measure the diameter of a steel ball bearing in five
repeated trials, obtaining 12.34 mm, 12.36 mm, 12.35 mm, 12.35 mm, and 12.37 mm. The
manufacturer specifies the true diameter as 12.30 mm. Which statement best characterizes
this data set?
A. The measurements are accurate but not precise.
B. The measurements are both accurate and precise.
C. The measurements are precise but not accurate. ✓ CORRECT
D. The measurements are neither accurate nor precise.
Correct Answer: C
Rationale: The five readings vary by only 0.03 mm, demonstrating high precision, yet the mean
of 12.35 mm deviates systematically from the true value of 12.30 mm, indicating poor
accuracy. Choice A incorrectly assumes that consistency near a wrong value constitutes
accuracy, when in fact accuracy requires proximity to the accepted standard. When evaluating
measurement data, always check repeatability first for precision, then compare the mean to
the known true value for accuracy.
Question 2 of 50
In an optics laboratory, a researcher calibrates a photodetector against a NIST-traceable
standard and discovers that the instrument consistently reports intensity values that are 5%
higher than the certified reference across the entire measurement range. Which type of error
does this behavior represent?
A. Random error
,B. Systematic error ✓ CORRECT
C. Instrumental precision error
D. Human parallax error
Correct Answer: B
Rationale: A consistent, repeatable 5% offset in a single direction indicates systematic error,
which arises from calibration bias or an inherent instrumental offset rather than
unpredictable scatter. Choice A describes random error, which would manifest as
unpredictable fluctuations above and below the true value without a constant directional bias.
On exam day, look for keywords like "consistently" or "always reads high" as hallmarks of
systematic error.
Question 3 of 50
Two introductory physics students independently measure the local acceleration due to
gravity using identical pendulum apparatus. Student A obtains 9.72 m/s², 9.74 m/s², and 9.73
m/s², while Student B obtains 9.78 m/s², 9.82 m/s², and 9.80 m/s². The accepted value for the
location is 9.80 m/s². Which statement best describes Student A's data?
A. Student A's measurements are accurate but not precise.
B. Student A's measurements are both accurate and precise.
C. Student A's measurements are precise but not accurate. ✓ CORRECT
D. Student A's measurements are neither accurate nor precise.
Correct Answer: C
Rationale: Student A's three trials span only 0.02 m/s², demonstrating excellent precision, but
the mean of 9.73 m/s² misses the accepted 9.80 m/s² by a clear systematic margin. Choice
B misidentifies the data as accurate because the values cluster tightly, confusing internal
consistency with proximity to the true value. Remember that precision is a property of the
data set itself, while accuracy requires an external reference standard.
Question 4 of 50
A metrology laboratory reports the length of a standard gauge block as 25.000 mm ± 0.002
mm. What is the percent relative uncertainty of this measurement?
A. 0.008% ✓ CORRECT
B. 0.08%
C. 0.80%
D. 0.0008%
Correct Answer: A
Rationale: Relative uncertainty equals the absolute uncertainty divided by the measured value,
so 0.002 mm divided by 25.000 mm yields 0.00008, which converts to 0.008%. Choice B
, incorrectly shifts the decimal by one place, a common error when converting between
decimal and percentage form. Always verify your power of ten when moving from fractional
to percent uncertainty.
Question 5 of 50
An engineer measures the voltage across a resistor with a digital multimeter and records
four readings: 12.45 V, 12.48 V, 12.44 V, and 12.46 V. If the absolute uncertainty is taken as
one-half of the range, what is the percent relative uncertainty of the mean voltage?
A. 0.08%
B. 0.16% ✓ CORRECT
C. 0.32%
D. 0.64%
Correct Answer: B
Rationale: The half-range of the four readings is 0.02 V, and dividing this by the mean of
approximately 12.46 V yields a relative uncertainty of 0.16%. Choice D mistakenly uses the
full range of 0.04 V instead of the half-range, which doubles the calculated percentage. For
symmetric scatter, use half the range or the standard deviation to represent the absolute
uncertainty.
Question 6 of 50
A ballistic pendulum experiment yields a calculated muzzle velocity of 312 m/s for a
projectile, while the manufacturer's specified velocity for the same charge is 325 m/s. What is
the percent error of the experimental result?
A. 4.3%
B. 3.8%
C. 5.0%
D. 4.0% ✓ CORRECT
Correct Answer: D
Rationale: Percent error is calculated as the absolute difference between the experimental
and accepted values divided by the accepted value, so |312 − 325| / 325 × 100% = 4.0%.
Choice A incorrectly uses the experimental value of 312 m/s in the denominator, which
violates the convention that the accepted value always serves as the reference. Always
anchor percent error to the known standard, not to your own measurement.
Question 7 of 50
(PORTAGE LEARNING) —
MEASUREMENTS, SI UNITS,
DIMENSIONAL ANALYSIS & VECTOR
MATHEMATICS
OFFICIAL PRACTICE EXAM 2026/2027
══════════════════════════════════════
SECTION 1: MEASUREMENTS & UNCERTAINTY Q1 – Q10
══════════════════════════════════════
Question 1 of 50
A student uses a micrometer caliper to measure the diameter of a steel ball bearing in five
repeated trials, obtaining 12.34 mm, 12.36 mm, 12.35 mm, 12.35 mm, and 12.37 mm. The
manufacturer specifies the true diameter as 12.30 mm. Which statement best characterizes
this data set?
A. The measurements are accurate but not precise.
B. The measurements are both accurate and precise.
C. The measurements are precise but not accurate. ✓ CORRECT
D. The measurements are neither accurate nor precise.
Correct Answer: C
Rationale: The five readings vary by only 0.03 mm, demonstrating high precision, yet the mean
of 12.35 mm deviates systematically from the true value of 12.30 mm, indicating poor
accuracy. Choice A incorrectly assumes that consistency near a wrong value constitutes
accuracy, when in fact accuracy requires proximity to the accepted standard. When evaluating
measurement data, always check repeatability first for precision, then compare the mean to
the known true value for accuracy.
Question 2 of 50
In an optics laboratory, a researcher calibrates a photodetector against a NIST-traceable
standard and discovers that the instrument consistently reports intensity values that are 5%
higher than the certified reference across the entire measurement range. Which type of error
does this behavior represent?
A. Random error
,B. Systematic error ✓ CORRECT
C. Instrumental precision error
D. Human parallax error
Correct Answer: B
Rationale: A consistent, repeatable 5% offset in a single direction indicates systematic error,
which arises from calibration bias or an inherent instrumental offset rather than
unpredictable scatter. Choice A describes random error, which would manifest as
unpredictable fluctuations above and below the true value without a constant directional bias.
On exam day, look for keywords like "consistently" or "always reads high" as hallmarks of
systematic error.
Question 3 of 50
Two introductory physics students independently measure the local acceleration due to
gravity using identical pendulum apparatus. Student A obtains 9.72 m/s², 9.74 m/s², and 9.73
m/s², while Student B obtains 9.78 m/s², 9.82 m/s², and 9.80 m/s². The accepted value for the
location is 9.80 m/s². Which statement best describes Student A's data?
A. Student A's measurements are accurate but not precise.
B. Student A's measurements are both accurate and precise.
C. Student A's measurements are precise but not accurate. ✓ CORRECT
D. Student A's measurements are neither accurate nor precise.
Correct Answer: C
Rationale: Student A's three trials span only 0.02 m/s², demonstrating excellent precision, but
the mean of 9.73 m/s² misses the accepted 9.80 m/s² by a clear systematic margin. Choice
B misidentifies the data as accurate because the values cluster tightly, confusing internal
consistency with proximity to the true value. Remember that precision is a property of the
data set itself, while accuracy requires an external reference standard.
Question 4 of 50
A metrology laboratory reports the length of a standard gauge block as 25.000 mm ± 0.002
mm. What is the percent relative uncertainty of this measurement?
A. 0.008% ✓ CORRECT
B. 0.08%
C. 0.80%
D. 0.0008%
Correct Answer: A
Rationale: Relative uncertainty equals the absolute uncertainty divided by the measured value,
so 0.002 mm divided by 25.000 mm yields 0.00008, which converts to 0.008%. Choice B
, incorrectly shifts the decimal by one place, a common error when converting between
decimal and percentage form. Always verify your power of ten when moving from fractional
to percent uncertainty.
Question 5 of 50
An engineer measures the voltage across a resistor with a digital multimeter and records
four readings: 12.45 V, 12.48 V, 12.44 V, and 12.46 V. If the absolute uncertainty is taken as
one-half of the range, what is the percent relative uncertainty of the mean voltage?
A. 0.08%
B. 0.16% ✓ CORRECT
C. 0.32%
D. 0.64%
Correct Answer: B
Rationale: The half-range of the four readings is 0.02 V, and dividing this by the mean of
approximately 12.46 V yields a relative uncertainty of 0.16%. Choice D mistakenly uses the
full range of 0.04 V instead of the half-range, which doubles the calculated percentage. For
symmetric scatter, use half the range or the standard deviation to represent the absolute
uncertainty.
Question 6 of 50
A ballistic pendulum experiment yields a calculated muzzle velocity of 312 m/s for a
projectile, while the manufacturer's specified velocity for the same charge is 325 m/s. What is
the percent error of the experimental result?
A. 4.3%
B. 3.8%
C. 5.0%
D. 4.0% ✓ CORRECT
Correct Answer: D
Rationale: Percent error is calculated as the absolute difference between the experimental
and accepted values divided by the accepted value, so |312 − 325| / 325 × 100% = 4.0%.
Choice A incorrectly uses the experimental value of 312 m/s in the denominator, which
violates the convention that the accepted value always serves as the reference. Always
anchor percent error to the known standard, not to your own measurement.
Question 7 of 50
