• Home
  • MDM 4U
    • MDM Spring eLO Calendar
    • Take me to the MDM4U Solutions Page!
    • Part 1: Median Analysis >
      • Mode, Median, and Quartiles
      • Typical and Outlier Values (Median)
      • Median Analysis Practice Test
    • Part 2: Mean Value Analysis >
      • Mean, Skew and Standard Deviation
      • Sigma Standard Deviation
      • Typical and Outlier Values (StDev)
      • Typical Values
      • Outliers
      • Mean Value Analysis Practice Test
      • Single Variable Analysis Practice Test
    • Part 3: The Normal Distribution >
      • The Normal Distribution
      • Z-Scores
      • Normal Distribution Practice Test
    • Part 4: Sorting and Dependence >
      • Intro to Set Notation
      • Intro to Probability
      • Sorting and Independence
      • Sorting and Independence Practice Test
    • Part 5: Correlation and Fit >
      • Correlation Cofficient
      • Scatterplots and Line of Best Fit
      • Line of Best Fit Practice Test
    • Part 6: Two Variable Analysis >
      • Extrapolation and Interpolation
      • A Full Two Variable Analysis
      • Two Variable Analysis Practice Test
    • Part 7: Probability Distributions >
      • Geometric Distribution
      • Binomial Distributions
      • Probability Distributions Practice Test
    • Part 8: Games of Chance >
      • Stochastic Processes
      • Games of Chance
      • Games of Chance Practice Test
    • Part 9: Counting Theory >
      • Permutations
      • Combinations
      • Cases
      • So you Think you've Learned to Count...
      • Counting Theory Practice Test
  • MHF 4U
    • MHF 4U Fall Calendar
    • Take me to the MHF4U Solutions Page!
    • Part 1: Limits and Logarithms >
      • What is Log?
      • Using Log to Solve Exponentials
      • Laws of Logarithms
      • Taking a Limit
      • Limits & Logarithms Practice Test
    • Part 2: Working with Functions >
      • BFDMAS
      • The Linear Algebra Method
      • Sometimes there is More than One Answer
      • Sometimes it Doesn't Work
      • Finding Intercepts
      • Working with Functions Practice Test
    • Part 3: Translations, Transformations, & Rates of Change >
      • Translations
      • Transformations
      • Welcome to the Sketch-o-thon
      • Domain and Range
      • Translations, Transformations & Rates Practice Test
    • Part 4: Rates of Change >
      • Average Rate of Change & Secants
      • Rates of Change & Tangents
      • Rates of Change Practice Test
    • Part 5: Analyzing Rational Expressions >
      • Polynomial Long Division
      • Sketching Polynomials
      • Analyzing Rational Functions
      • Sketching Rational Functions
      • Rational Analysis Practice Test
    • Part 6: Analyzing Composite Functions >
      • Multiplication Type Composites
      • Analyzing Composites Practice Test
  • MCV 4U
    • Take me to the MCV4U Solutions Page!
    • Part 0: Vectors >
      • MCV ISU 1 >
        • Vector Notation and Operations
        • Getting from Here to There
        • Equations of Lines in 3 Space
        • Analysis of Lines in 3 Space
        • MCV ISU 1 Practice Test
      • MCV ISU 2 >
        • The Inner Product & Projections
        • The Distance from a Point to a Line
        • The Cross Product
        • The Distance between Skew Lines
        • MCV ISU 2 Practice Test
      • MCV ISU 3 >
        • Equations for Planes
        • Linear Dependence & a Plane from 3 Points
        • Gauss Jordan Elimination
        • The Intersection of Two Planes
        • The Intersection of Three Planes
        • MCV ISU 3 Practice Test
    • Part 1: Taking the Derivative >
      • The Differential Operator
      • The Power, and Product Rules
      • Derivatives of Sine and Cosine
      • Euler's Number (Exponentials & Logarithms)
      • The Chain Rule
      • Managing Product & Chain Rule
      • Product, Chain, or Both?
      • Derivatives Practice Test
    • Part 2: Curve Sketching >
      • Determining the Vertical Asymptotes and Max / Min
      • Determining the Points of Inflection
      • Determining the Intercepts of Composite Functions
      • Beware the Domain Error
      • Determining the End Behaviour
      • Curve Sketching
      • Curve Sketching Practice Test
    • Part 3: Rates and Optimization >
      • Equations of Tangents
      • Newton's Method
      • Implicit Differentiation
      • Related Rates
      • Optimization
      • Applications of Derivatives Practice Test
    • Part 4: Integration >
      • Intro to Integration
      • Substitution for Integration
      • Integration by Parts
      • The Area under Curves
      • Integration Practice Test
    • Part 5: Techniques for Difficult Limits >
      • Fundamental Limits
      • The Replacement Technique
  • SPH 3U/4C
    • Take me to the SPH3U/4C Solutions Page!
    • Part 1: Energy and Power >
      • The Energy Equations
      • Power & Force
      • Energy Conversions
      • Power & Energy Practice Test
    • Part 2: Kinematics >
      • The Kinematics Equations (3U/4C)
      • Sometimes things are Negative...
      • Multiphase Motion
      • Sketching Motion
      • Kinematics Practice Test
    • Part 3: Forces & Mechanical Systems >
      • Masses over Pulleys
      • Strings & Levers
      • Energy of Balanced Levers
      • Things on Springs
      • Components
      • MultiComponent Machines
      • Mechanical Systems Practice Test
    • Part 4: Electricity & Magnetism >
      • Ohm's Law
      • Resistance in Series and Parallel
      • Solving Circuits
      • Drawing Field Lines
      • Electricity and Magnetism Practice Test
    • Part 5: Wave Behaviour (3U) >
      • Properties of Waves
      • MultiComponent Machines
    • Part 5: Fluid Behaviour (4C)
  • Home
  • MDM 4U
    • MDM Spring eLO Calendar
    • Take me to the MDM4U Solutions Page!
    • Part 1: Median Analysis >
      • Mode, Median, and Quartiles
      • Typical and Outlier Values (Median)
      • Median Analysis Practice Test
    • Part 2: Mean Value Analysis >
      • Mean, Skew and Standard Deviation
      • Sigma Standard Deviation
      • Typical and Outlier Values (StDev)
      • Typical Values
      • Outliers
      • Mean Value Analysis Practice Test
      • Single Variable Analysis Practice Test
    • Part 3: The Normal Distribution >
      • The Normal Distribution
      • Z-Scores
      • Normal Distribution Practice Test
    • Part 4: Sorting and Dependence >
      • Intro to Set Notation
      • Intro to Probability
      • Sorting and Independence
      • Sorting and Independence Practice Test
    • Part 5: Correlation and Fit >
      • Correlation Cofficient
      • Scatterplots and Line of Best Fit
      • Line of Best Fit Practice Test
    • Part 6: Two Variable Analysis >
      • Extrapolation and Interpolation
      • A Full Two Variable Analysis
      • Two Variable Analysis Practice Test
    • Part 7: Probability Distributions >
      • Geometric Distribution
      • Binomial Distributions
      • Probability Distributions Practice Test
    • Part 8: Games of Chance >
      • Stochastic Processes
      • Games of Chance
      • Games of Chance Practice Test
    • Part 9: Counting Theory >
      • Permutations
      • Combinations
      • Cases
      • So you Think you've Learned to Count...
      • Counting Theory Practice Test
  • MHF 4U
    • MHF 4U Fall Calendar
    • Take me to the MHF4U Solutions Page!
    • Part 1: Limits and Logarithms >
      • What is Log?
      • Using Log to Solve Exponentials
      • Laws of Logarithms
      • Taking a Limit
      • Limits & Logarithms Practice Test
    • Part 2: Working with Functions >
      • BFDMAS
      • The Linear Algebra Method
      • Sometimes there is More than One Answer
      • Sometimes it Doesn't Work
      • Finding Intercepts
      • Working with Functions Practice Test
    • Part 3: Translations, Transformations, & Rates of Change >
      • Translations
      • Transformations
      • Welcome to the Sketch-o-thon
      • Domain and Range
      • Translations, Transformations & Rates Practice Test
    • Part 4: Rates of Change >
      • Average Rate of Change & Secants
      • Rates of Change & Tangents
      • Rates of Change Practice Test
    • Part 5: Analyzing Rational Expressions >
      • Polynomial Long Division
      • Sketching Polynomials
      • Analyzing Rational Functions
      • Sketching Rational Functions
      • Rational Analysis Practice Test
    • Part 6: Analyzing Composite Functions >
      • Multiplication Type Composites
      • Analyzing Composites Practice Test
  • MCV 4U
    • Take me to the MCV4U Solutions Page!
    • Part 0: Vectors >
      • MCV ISU 1 >
        • Vector Notation and Operations
        • Getting from Here to There
        • Equations of Lines in 3 Space
        • Analysis of Lines in 3 Space
        • MCV ISU 1 Practice Test
      • MCV ISU 2 >
        • The Inner Product & Projections
        • The Distance from a Point to a Line
        • The Cross Product
        • The Distance between Skew Lines
        • MCV ISU 2 Practice Test
      • MCV ISU 3 >
        • Equations for Planes
        • Linear Dependence & a Plane from 3 Points
        • Gauss Jordan Elimination
        • The Intersection of Two Planes
        • The Intersection of Three Planes
        • MCV ISU 3 Practice Test
    • Part 1: Taking the Derivative >
      • The Differential Operator
      • The Power, and Product Rules
      • Derivatives of Sine and Cosine
      • Euler's Number (Exponentials & Logarithms)
      • The Chain Rule
      • Managing Product & Chain Rule
      • Product, Chain, or Both?
      • Derivatives Practice Test
    • Part 2: Curve Sketching >
      • Determining the Vertical Asymptotes and Max / Min
      • Determining the Points of Inflection
      • Determining the Intercepts of Composite Functions
      • Beware the Domain Error
      • Determining the End Behaviour
      • Curve Sketching
      • Curve Sketching Practice Test
    • Part 3: Rates and Optimization >
      • Equations of Tangents
      • Newton's Method
      • Implicit Differentiation
      • Related Rates
      • Optimization
      • Applications of Derivatives Practice Test
    • Part 4: Integration >
      • Intro to Integration
      • Substitution for Integration
      • Integration by Parts
      • The Area under Curves
      • Integration Practice Test
    • Part 5: Techniques for Difficult Limits >
      • Fundamental Limits
      • The Replacement Technique
  • SPH 3U/4C
    • Take me to the SPH3U/4C Solutions Page!
    • Part 1: Energy and Power >
      • The Energy Equations
      • Power & Force
      • Energy Conversions
      • Power & Energy Practice Test
    • Part 2: Kinematics >
      • The Kinematics Equations (3U/4C)
      • Sometimes things are Negative...
      • Multiphase Motion
      • Sketching Motion
      • Kinematics Practice Test
    • Part 3: Forces & Mechanical Systems >
      • Masses over Pulleys
      • Strings & Levers
      • Energy of Balanced Levers
      • Things on Springs
      • Components
      • MultiComponent Machines
      • Mechanical Systems Practice Test
    • Part 4: Electricity & Magnetism >
      • Ohm's Law
      • Resistance in Series and Parallel
      • Solving Circuits
      • Drawing Field Lines
      • Electricity and Magnetism Practice Test
    • Part 5: Wave Behaviour (3U) >
      • Properties of Waves
      • MultiComponent Machines
    • Part 5: Fluid Behaviour (4C)

SPH 4U: Grade Twelve Physics
(University Preparation, Spring 2016/17)

Part 1: Kinematics in 2D
February 6th to 24th

Test Date for Part 1:
Friday, February 24th
The Kinematics Equations
File Size: 2224 kb
File Type: pdf
Download File

Projectile Motion
File Size: 2977 kb
File Type: pdf
Download File

Targeting with Speed
File Size: 1749 kb
File Type: pdf
Download File

Targeting with Angles
File Size: 2299 kb
File Type: pdf
Download File

An Object on an Inclined Plane
File Size: 2457 kb
File Type: pdf
Download File

Double the Planes, Double the Fun
File Size: 2027 kb
File Type: pdf
Download File

Centripetal Force
File Size: 1082 kb
File Type: pdf
Download File

Part 2: Fun with Planets
March 7th to March 10th

Test Date for Part 2:
March 10th (?)
Universal Gravitation and Escape Velocity
File Size: 284 kb
File Type: pdf
Download File

Kepler's Law
File Size: 2783 kb
File Type: pdf
Download File

Conics
File Size: 2681 kb
File Type: pdf
Download File

Elliptical Orbits and the Hill Radius
File Size: 4539 kb
File Type: pdf
Download File

Part 3: Math with Planets
March 20th to 31st

Test Date for Part 3:
April 21st (?)
Finding the Barycentre
File Size: 2786 kb
File Type: pdf
Download File

Thinking about Tidal Bulges
File Size: 3117 kb
File Type: pdf
Download File

Life on Enceladus
File Size: 1727 kb
File Type: pdf
Download File

Net Gravitational Field
File Size: 3113 kb
File Type: pdf
Download File

Part 4: Relativity...
April 3rd to 21st

Test Date for Part 3:
April 21st
sph4u_notebook_speed_of_light_and_special_relativity.pdf
File Size: 6080 kb
File Type: pdf
Download File

sph4u_mass_energy_equivalence.pdf
File Size: 461 kb
File Type: pdf
Download File

sph4u_fission_and_fusion.pdf
File Size: 3286 kb
File Type: pdf
Download File

sph4u_nuclear_decay_series.pdf
File Size: 2939 kb
File Type: pdf
Download File

Part 5: Light & Warticles
May 1st to 19th

Test Date for Part 4:
May 19th
Part 6: Electromagnetism
May 23rd to June 16th

Test Date for Part 5:
June 16th
J. McDonald 2025
Mathemanomicon.ca
  • Home
  • MDM 4U
    • MDM Spring eLO Calendar
    • Take me to the MDM4U Solutions Page!
    • Part 1: Median Analysis >
      • Mode, Median, and Quartiles
      • Typical and Outlier Values (Median)
      • Median Analysis Practice Test
    • Part 2: Mean Value Analysis >
      • Mean, Skew and Standard Deviation
      • Sigma Standard Deviation
      • Typical and Outlier Values (StDev)
      • Typical Values
      • Outliers
      • Mean Value Analysis Practice Test
      • Single Variable Analysis Practice Test
    • Part 3: The Normal Distribution >
      • The Normal Distribution
      • Z-Scores
      • Normal Distribution Practice Test
    • Part 4: Sorting and Dependence >
      • Intro to Set Notation
      • Intro to Probability
      • Sorting and Independence
      • Sorting and Independence Practice Test
    • Part 5: Correlation and Fit >
      • Correlation Cofficient
      • Scatterplots and Line of Best Fit
      • Line of Best Fit Practice Test
    • Part 6: Two Variable Analysis >
      • Extrapolation and Interpolation
      • A Full Two Variable Analysis
      • Two Variable Analysis Practice Test
    • Part 7: Probability Distributions >
      • Geometric Distribution
      • Binomial Distributions
      • Probability Distributions Practice Test
    • Part 8: Games of Chance >
      • Stochastic Processes
      • Games of Chance
      • Games of Chance Practice Test
    • Part 9: Counting Theory >
      • Permutations
      • Combinations
      • Cases
      • So you Think you've Learned to Count...
      • Counting Theory Practice Test
  • MHF 4U
    • MHF 4U Fall Calendar
    • Take me to the MHF4U Solutions Page!
    • Part 1: Limits and Logarithms >
      • What is Log?
      • Using Log to Solve Exponentials
      • Laws of Logarithms
      • Taking a Limit
      • Limits & Logarithms Practice Test
    • Part 2: Working with Functions >
      • BFDMAS
      • The Linear Algebra Method
      • Sometimes there is More than One Answer
      • Sometimes it Doesn't Work
      • Finding Intercepts
      • Working with Functions Practice Test
    • Part 3: Translations, Transformations, & Rates of Change >
      • Translations
      • Transformations
      • Welcome to the Sketch-o-thon
      • Domain and Range
      • Translations, Transformations & Rates Practice Test
    • Part 4: Rates of Change >
      • Average Rate of Change & Secants
      • Rates of Change & Tangents
      • Rates of Change Practice Test
    • Part 5: Analyzing Rational Expressions >
      • Polynomial Long Division
      • Sketching Polynomials
      • Analyzing Rational Functions
      • Sketching Rational Functions
      • Rational Analysis Practice Test
    • Part 6: Analyzing Composite Functions >
      • Multiplication Type Composites
      • Analyzing Composites Practice Test
  • MCV 4U
    • Take me to the MCV4U Solutions Page!
    • Part 0: Vectors >
      • MCV ISU 1 >
        • Vector Notation and Operations
        • Getting from Here to There
        • Equations of Lines in 3 Space
        • Analysis of Lines in 3 Space
        • MCV ISU 1 Practice Test
      • MCV ISU 2 >
        • The Inner Product & Projections
        • The Distance from a Point to a Line
        • The Cross Product
        • The Distance between Skew Lines
        • MCV ISU 2 Practice Test
      • MCV ISU 3 >
        • Equations for Planes
        • Linear Dependence & a Plane from 3 Points
        • Gauss Jordan Elimination
        • The Intersection of Two Planes
        • The Intersection of Three Planes
        • MCV ISU 3 Practice Test
    • Part 1: Taking the Derivative >
      • The Differential Operator
      • The Power, and Product Rules
      • Derivatives of Sine and Cosine
      • Euler's Number (Exponentials & Logarithms)
      • The Chain Rule
      • Managing Product & Chain Rule
      • Product, Chain, or Both?
      • Derivatives Practice Test
    • Part 2: Curve Sketching >
      • Determining the Vertical Asymptotes and Max / Min
      • Determining the Points of Inflection
      • Determining the Intercepts of Composite Functions
      • Beware the Domain Error
      • Determining the End Behaviour
      • Curve Sketching
      • Curve Sketching Practice Test
    • Part 3: Rates and Optimization >
      • Equations of Tangents
      • Newton's Method
      • Implicit Differentiation
      • Related Rates
      • Optimization
      • Applications of Derivatives Practice Test
    • Part 4: Integration >
      • Intro to Integration
      • Substitution for Integration
      • Integration by Parts
      • The Area under Curves
      • Integration Practice Test
    • Part 5: Techniques for Difficult Limits >
      • Fundamental Limits
      • The Replacement Technique
  • SPH 3U/4C
    • Take me to the SPH3U/4C Solutions Page!
    • Part 1: Energy and Power >
      • The Energy Equations
      • Power & Force
      • Energy Conversions
      • Power & Energy Practice Test
    • Part 2: Kinematics >
      • The Kinematics Equations (3U/4C)
      • Sometimes things are Negative...
      • Multiphase Motion
      • Sketching Motion
      • Kinematics Practice Test
    • Part 3: Forces & Mechanical Systems >
      • Masses over Pulleys
      • Strings & Levers
      • Energy of Balanced Levers
      • Things on Springs
      • Components
      • MultiComponent Machines
      • Mechanical Systems Practice Test
    • Part 4: Electricity & Magnetism >
      • Ohm's Law
      • Resistance in Series and Parallel
      • Solving Circuits
      • Drawing Field Lines
      • Electricity and Magnetism Practice Test
    • Part 5: Wave Behaviour (3U) >
      • Properties of Waves
      • MultiComponent Machines
    • Part 5: Fluid Behaviour (4C)
  • Home
  • MDM 4U
    • MDM Spring eLO Calendar
    • Take me to the MDM4U Solutions Page!
    • Part 1: Median Analysis >
      • Mode, Median, and Quartiles
      • Typical and Outlier Values (Median)
      • Median Analysis Practice Test
    • Part 2: Mean Value Analysis >
      • Mean, Skew and Standard Deviation
      • Sigma Standard Deviation
      • Typical and Outlier Values (StDev)
      • Typical Values
      • Outliers
      • Mean Value Analysis Practice Test
      • Single Variable Analysis Practice Test
    • Part 3: The Normal Distribution >
      • The Normal Distribution
      • Z-Scores
      • Normal Distribution Practice Test
    • Part 4: Sorting and Dependence >
      • Intro to Set Notation
      • Intro to Probability
      • Sorting and Independence
      • Sorting and Independence Practice Test
    • Part 5: Correlation and Fit >
      • Correlation Cofficient
      • Scatterplots and Line of Best Fit
      • Line of Best Fit Practice Test
    • Part 6: Two Variable Analysis >
      • Extrapolation and Interpolation
      • A Full Two Variable Analysis
      • Two Variable Analysis Practice Test
    • Part 7: Probability Distributions >
      • Geometric Distribution
      • Binomial Distributions
      • Probability Distributions Practice Test
    • Part 8: Games of Chance >
      • Stochastic Processes
      • Games of Chance
      • Games of Chance Practice Test
    • Part 9: Counting Theory >
      • Permutations
      • Combinations
      • Cases
      • So you Think you've Learned to Count...
      • Counting Theory Practice Test
  • MHF 4U
    • MHF 4U Fall Calendar
    • Take me to the MHF4U Solutions Page!
    • Part 1: Limits and Logarithms >
      • What is Log?
      • Using Log to Solve Exponentials
      • Laws of Logarithms
      • Taking a Limit
      • Limits & Logarithms Practice Test
    • Part 2: Working with Functions >
      • BFDMAS
      • The Linear Algebra Method
      • Sometimes there is More than One Answer
      • Sometimes it Doesn't Work
      • Finding Intercepts
      • Working with Functions Practice Test
    • Part 3: Translations, Transformations, & Rates of Change >
      • Translations
      • Transformations
      • Welcome to the Sketch-o-thon
      • Domain and Range
      • Translations, Transformations & Rates Practice Test
    • Part 4: Rates of Change >
      • Average Rate of Change & Secants
      • Rates of Change & Tangents
      • Rates of Change Practice Test
    • Part 5: Analyzing Rational Expressions >
      • Polynomial Long Division
      • Sketching Polynomials
      • Analyzing Rational Functions
      • Sketching Rational Functions
      • Rational Analysis Practice Test
    • Part 6: Analyzing Composite Functions >
      • Multiplication Type Composites
      • Analyzing Composites Practice Test
  • MCV 4U
    • Take me to the MCV4U Solutions Page!
    • Part 0: Vectors >
      • MCV ISU 1 >
        • Vector Notation and Operations
        • Getting from Here to There
        • Equations of Lines in 3 Space
        • Analysis of Lines in 3 Space
        • MCV ISU 1 Practice Test
      • MCV ISU 2 >
        • The Inner Product & Projections
        • The Distance from a Point to a Line
        • The Cross Product
        • The Distance between Skew Lines
        • MCV ISU 2 Practice Test
      • MCV ISU 3 >
        • Equations for Planes
        • Linear Dependence & a Plane from 3 Points
        • Gauss Jordan Elimination
        • The Intersection of Two Planes
        • The Intersection of Three Planes
        • MCV ISU 3 Practice Test
    • Part 1: Taking the Derivative >
      • The Differential Operator
      • The Power, and Product Rules
      • Derivatives of Sine and Cosine
      • Euler's Number (Exponentials & Logarithms)
      • The Chain Rule
      • Managing Product & Chain Rule
      • Product, Chain, or Both?
      • Derivatives Practice Test
    • Part 2: Curve Sketching >
      • Determining the Vertical Asymptotes and Max / Min
      • Determining the Points of Inflection
      • Determining the Intercepts of Composite Functions
      • Beware the Domain Error
      • Determining the End Behaviour
      • Curve Sketching
      • Curve Sketching Practice Test
    • Part 3: Rates and Optimization >
      • Equations of Tangents
      • Newton's Method
      • Implicit Differentiation
      • Related Rates
      • Optimization
      • Applications of Derivatives Practice Test
    • Part 4: Integration >
      • Intro to Integration
      • Substitution for Integration
      • Integration by Parts
      • The Area under Curves
      • Integration Practice Test
    • Part 5: Techniques for Difficult Limits >
      • Fundamental Limits
      • The Replacement Technique
  • SPH 3U/4C
    • Take me to the SPH3U/4C Solutions Page!
    • Part 1: Energy and Power >
      • The Energy Equations
      • Power & Force
      • Energy Conversions
      • Power & Energy Practice Test
    • Part 2: Kinematics >
      • The Kinematics Equations (3U/4C)
      • Sometimes things are Negative...
      • Multiphase Motion
      • Sketching Motion
      • Kinematics Practice Test
    • Part 3: Forces & Mechanical Systems >
      • Masses over Pulleys
      • Strings & Levers
      • Energy of Balanced Levers
      • Things on Springs
      • Components
      • MultiComponent Machines
      • Mechanical Systems Practice Test
    • Part 4: Electricity & Magnetism >
      • Ohm's Law
      • Resistance in Series and Parallel
      • Solving Circuits
      • Drawing Field Lines
      • Electricity and Magnetism Practice Test
    • Part 5: Wave Behaviour (3U) >
      • Properties of Waves
      • MultiComponent Machines
    • Part 5: Fluid Behaviour (4C)