PHYS 165 Module 2 Exam: Physics
Portage Learning | 2026/2027 Academic Year | 25 Questions
Measurements, SI Units, Dimensional Analysis, and Vector Mathematics
Abstract
This document constitutes the official PHYS 165 Module 2 Examination for the 2026/2027 academic
year, administered through Portage Learning. The examination encompasses 25 questions distributed
across four foundational domains of measurement science and vector mathematics. The first domain
addresses the International System of Units (SI), significant figures, and dimensional analysis,
evaluating the student's capacity to identify base and derived quantities, apply rules for significant
figures in computations, and use dimensional analysis to verify the consistency of physical equations
and convert between unit systems. The second domain examines the distinction between scalar and
vector quantities, requiring the identification of physical quantities as scalars or vectors and an
understanding of the operational differences between them, including the role of direction in vector
addition versus simple arithmetic addition of scalars. The third domain focuses on vector addition,
subtraction, and graphical methods, testing the application of the triangle and parallelogram rules for
vector composition, the head-to-tail method for multiple vectors, and the geometric interpretation of
vector subtraction as the addition of a negated vector. The fourth domain covers vector components,
resolution, and unit vectors, emphasizing the decomposition of vectors into orthogonal components
using trigonometry, the reconstruction of vectors from their components, and the use of unit vector
notation (i-hat, j-hat, k-hat) to express vectors in two- and three-dimensional coordinate systems. Each
question is accompanied by a detailed rationale, an analysis of incorrect distractors, and a reference to
the relevant 2026 course material or standard physics textbook. This examination assesses the critical
application of mathematical principles and proven methodologies to understand the foundational tools
of physics measurement and vector analysis.
Content Area Overview
Content Area Questions Key Topics Weight
SI Units, Significant Figures 1-7 Base vs. derived SI units, metric prefixes, 28%
& Dimensional Analysis significant figure rules, propagation of
uncertainty, dimensional consistency checks,
unit conversion via dimensional analysis
Scalar vs. Vector Quantities 8-13 Identification of scalar and vector quantities, 24%
magnitude and direction, vector notation,
operational differences between scalar and
vector arithmetic, displacement vs. distance
Vector Addition, Subtraction 14-19 Triangle rule, parallelogram rule, head-to-tail 24%
& Graphical Methods method, vector subtraction as addition of a
negative vector, resultant vector magnitude
and direction, commutative and associative
properties
Vector Components, 20-25 Component decomposition using sine and 24%
Resolution & Unit Vectors cosine, reconstruction from components, unit
vector notation (i, j, k), vector magnitude from
components, direction angle calculation, two-
and three-dimensional vector operations
, Examination Questions
Domain: SI Units, Significant Figures & Dimensional Analysis
1. Which of the following is a base SI quantity?
A) Force
B) Velocity
C) Mass
D) Energy
Correct Answer: C - Mass
Rationale: The seven base SI quantities are length, mass, time, electric current, thermodynamic
temperature, amount of substance, and luminous intensity. Mass, with the SI unit kilogram (kg), is one
of these fundamental base quantities. Force, velocity, and energy are all derived quantities that can be
expressed in terms of base quantities through physical laws and definitions.
Why Wrong: Option A (force) is derived from mass times acceleration (kg*m/s^2 = newton). Option B
(velocity) is derived from length divided by time (m/s). Option D (energy) is derived from force times
distance (kg*m^2/s^2 = joule). None of these are base SI quantities.
Reference: Portage Learning PHYS 165 Module 2, Section 1: Base and Derived SI Units; Halliday &
Resnick, Fundamentals of Physics, Chapter 1.
2. The result of multiplying 3.2 cm by 4.15 cm should be reported as:
A) 13.28 cm^2
B) 13.3 cm^2
C) 13 cm^2
D) 13.280 cm^2
Correct Answer: C - 13 cm^2
Rationale: For multiplication and division, the result must have the same number of significant figures
as the factor with the fewest significant figures. The value 3.2 has two significant figures and 4.15 has
three, so the product must be reported with two significant figures. The raw product is 13.28, which
rounds to 13 cm^2 when expressed with two significant figures.
Why Wrong: Option A reports four significant figures, retaining all digits from the raw calculation.
Option B reports three significant figures, following the rule for the factor with more significant figures.
Option D adds a trailing zero to imply five significant figures, which is unjustified.
Reference: Portage Learning PHYS 165 Module 2, Section 2: Significant Figure Rules; Young &
Freedman, University Physics, Chapter 1.
3. The SI prefix 'micro' represents a factor of:
A) 10^(-3)
B) 10^(-6)
C) 10^(-9)
D) 10^(-12)
Correct Answer: B - 10^(-6)
Rationale: The prefix 'micro' (symbol: mu) corresponds to a factor of one millionth, or 10^(-6). This is
part of the standardized SI prefix system where each prefix represents a specific power of ten. For
example, 1 micrometer = 1 x 10^(-6) meters, and 1 microsecond = 1 x 10^(-6) seconds.
Why Wrong: Option A (10^(-3)) corresponds to the prefix 'milli' (m). Option C (10^(-9)) corresponds to
the prefix 'nano' (n). Option D (10^(-12)) corresponds to the prefix 'pico' (p). Each of these is a distinct SI
prefix with a different order of magnitude.
Reference: Portage Learning PHYS 165 Module 2, Section 1: Metric Prefixes; Halliday & Resnick,
Fundamentals of Physics, Chapter 1.
Portage Learning | 2026/2027 Academic Year | 25 Questions
Measurements, SI Units, Dimensional Analysis, and Vector Mathematics
Abstract
This document constitutes the official PHYS 165 Module 2 Examination for the 2026/2027 academic
year, administered through Portage Learning. The examination encompasses 25 questions distributed
across four foundational domains of measurement science and vector mathematics. The first domain
addresses the International System of Units (SI), significant figures, and dimensional analysis,
evaluating the student's capacity to identify base and derived quantities, apply rules for significant
figures in computations, and use dimensional analysis to verify the consistency of physical equations
and convert between unit systems. The second domain examines the distinction between scalar and
vector quantities, requiring the identification of physical quantities as scalars or vectors and an
understanding of the operational differences between them, including the role of direction in vector
addition versus simple arithmetic addition of scalars. The third domain focuses on vector addition,
subtraction, and graphical methods, testing the application of the triangle and parallelogram rules for
vector composition, the head-to-tail method for multiple vectors, and the geometric interpretation of
vector subtraction as the addition of a negated vector. The fourth domain covers vector components,
resolution, and unit vectors, emphasizing the decomposition of vectors into orthogonal components
using trigonometry, the reconstruction of vectors from their components, and the use of unit vector
notation (i-hat, j-hat, k-hat) to express vectors in two- and three-dimensional coordinate systems. Each
question is accompanied by a detailed rationale, an analysis of incorrect distractors, and a reference to
the relevant 2026 course material or standard physics textbook. This examination assesses the critical
application of mathematical principles and proven methodologies to understand the foundational tools
of physics measurement and vector analysis.
Content Area Overview
Content Area Questions Key Topics Weight
SI Units, Significant Figures 1-7 Base vs. derived SI units, metric prefixes, 28%
& Dimensional Analysis significant figure rules, propagation of
uncertainty, dimensional consistency checks,
unit conversion via dimensional analysis
Scalar vs. Vector Quantities 8-13 Identification of scalar and vector quantities, 24%
magnitude and direction, vector notation,
operational differences between scalar and
vector arithmetic, displacement vs. distance
Vector Addition, Subtraction 14-19 Triangle rule, parallelogram rule, head-to-tail 24%
& Graphical Methods method, vector subtraction as addition of a
negative vector, resultant vector magnitude
and direction, commutative and associative
properties
Vector Components, 20-25 Component decomposition using sine and 24%
Resolution & Unit Vectors cosine, reconstruction from components, unit
vector notation (i, j, k), vector magnitude from
components, direction angle calculation, two-
and three-dimensional vector operations
, Examination Questions
Domain: SI Units, Significant Figures & Dimensional Analysis
1. Which of the following is a base SI quantity?
A) Force
B) Velocity
C) Mass
D) Energy
Correct Answer: C - Mass
Rationale: The seven base SI quantities are length, mass, time, electric current, thermodynamic
temperature, amount of substance, and luminous intensity. Mass, with the SI unit kilogram (kg), is one
of these fundamental base quantities. Force, velocity, and energy are all derived quantities that can be
expressed in terms of base quantities through physical laws and definitions.
Why Wrong: Option A (force) is derived from mass times acceleration (kg*m/s^2 = newton). Option B
(velocity) is derived from length divided by time (m/s). Option D (energy) is derived from force times
distance (kg*m^2/s^2 = joule). None of these are base SI quantities.
Reference: Portage Learning PHYS 165 Module 2, Section 1: Base and Derived SI Units; Halliday &
Resnick, Fundamentals of Physics, Chapter 1.
2. The result of multiplying 3.2 cm by 4.15 cm should be reported as:
A) 13.28 cm^2
B) 13.3 cm^2
C) 13 cm^2
D) 13.280 cm^2
Correct Answer: C - 13 cm^2
Rationale: For multiplication and division, the result must have the same number of significant figures
as the factor with the fewest significant figures. The value 3.2 has two significant figures and 4.15 has
three, so the product must be reported with two significant figures. The raw product is 13.28, which
rounds to 13 cm^2 when expressed with two significant figures.
Why Wrong: Option A reports four significant figures, retaining all digits from the raw calculation.
Option B reports three significant figures, following the rule for the factor with more significant figures.
Option D adds a trailing zero to imply five significant figures, which is unjustified.
Reference: Portage Learning PHYS 165 Module 2, Section 2: Significant Figure Rules; Young &
Freedman, University Physics, Chapter 1.
3. The SI prefix 'micro' represents a factor of:
A) 10^(-3)
B) 10^(-6)
C) 10^(-9)
D) 10^(-12)
Correct Answer: B - 10^(-6)
Rationale: The prefix 'micro' (symbol: mu) corresponds to a factor of one millionth, or 10^(-6). This is
part of the standardized SI prefix system where each prefix represents a specific power of ten. For
example, 1 micrometer = 1 x 10^(-6) meters, and 1 microsecond = 1 x 10^(-6) seconds.
Why Wrong: Option A (10^(-3)) corresponds to the prefix 'milli' (m). Option C (10^(-9)) corresponds to
the prefix 'nano' (n). Option D (10^(-12)) corresponds to the prefix 'pico' (p). Each of these is a distinct SI
prefix with a different order of magnitude.
Reference: Portage Learning PHYS 165 Module 2, Section 1: Metric Prefixes; Halliday & Resnick,
Fundamentals of Physics, Chapter 1.
