Unit 1 · Physical Quantities and Units
The Complete Cambridge International AS & A Level Physics (9702) Guide · Cambridge International AS & A Level Physics (9702)Unit 1 · Physical Quantities and Units
- The Complete Cambridge International AS & A Level Physics (9702) Guide
- Cambridge International AS & A Level Physics (9702)
- 12 sections
Cambridge International does not publish a per-unit weighting for this exam. Exam structure (official): AS Level: Multiple Choice (75 min, 40 questions, 31%) · AS Level Structured Questions (75 min, 46%) · Advanced Practical Skills (120 min, 2 questions, 23%); A Level: Multiple Choice (75 min, 40 questions, 15.5%) · AS Level Structured Questions (75 min, 23%) · Advanced Practical Skills (120 min, 2 questions, 11.5%) · A Level Structured Questions (120 min, 38.5%) · Planning, Analysis And Evaluation (75 min, 2 questions, 11.5%). Be ready to carry the same unit skills and representations into a complete answer on every paper. A diameter and length must reach compatible SI units before the cylinder volume can be evaluated. The squared diameter makes its prefix conversion especially important, while the final uncertainty must match the precision of the volume.
- How Cambridge International AS & A Level Physics (9702) assesses this Cambridge International publishes no per-unit percentage for Cambridge International A Level Physics; Paper 1 accounts for 31% of the AS Level total and 15.5% of the A Level total. · AS Level: Multiple Choice (75 min, 40 questions, 31%) · AS Level Structured Questions (75 min, 46%) · Advanced Practical Skills (120 min, 2 questions, 23%) | A Level: Multiple Choice (75 min, 40 questions, 15.5%) · AS Level Structured Questions (75 min, 23%) · Advanced Practical Skills (120 min, 2 questions, 11.5%) · A Level Structured Questions (120 min, 38.5%) · Planning, Analysis And Evaluation (75 min, 2 questions, 11.5%) · show the model with A graph of volume (mm³) against d (mm)., A formula card that explains the cylinder relation identifies why diameter contributes two powers to the derived volume., A table linking key concept, why it matters, visible method.
- Key skills Physical Quantities, SI Units, Prefixes, Estimates and Homogeneity of Equations, Errors and Uncertainties: Systematic and Random Errors, Precision, Accuracy and Combining Uncertainties, Scalars and Vectors: Adding, Subtracting and Resolving Coplanar Vectors
- How to study for Unit 1 This page turns A graph of volume (mm³) against d (mm)., A formula card that explains the cylinder relation identifies why diameter contributes two powers to the derived volume., A table linking key concept, why it matters, visible method. into one route: Convert d and L before evaluating πd²L/4.
- The organizing decision Explain why changing millimetres to meters before squaring prevents a six-power prefix error in the cylinder volume.
What Cambridge International AS & A Level Physics (9702) Unit 1 covers
Use this map to connect each assessed skill to the relationship or representation that makes it visible.
Physical Quantities, SI Units, Prefixes, Estimates and Homogeneity of Equations
dimensional homogeneity; percentage uncertainty; coplanar vector02Errors and Uncertainties: Systematic and Random Errors, Precision, Accuracy and Combining Uncertainties
dimensional homogeneity; percentage uncertainty; coplanar vector03Scalars and Vectors: Adding, Subtracting and Resolving Coplanar Vectors
dimensional homogeneity; percentage uncertainty; coplanar vectorCambridge International does not publish a per-unit weighting for this exam.
Official unit name and weighting: Cambridge International syllabus.
Physical Quantities and Units
Connect the published share to the unit model
A diameter and length must reach compatible SI units before the cylinder volume can be evaluated. The squared diameter makes its prefix conversion especially important, while the final uncertainty must match the precision of the volume.
The worked calculation begins with d = 0.01240 m and L = 0.0480 m, then uses V = πd²L/4. Comparing the dimensions on both sides checks that the result is a volume rather than an area or length.
Keep the 1.01% uncertainty calculation beside the central value. Writing (5.80 ± 0.06) × 10⁻⁶ m³ makes both the magnitude and its justified precision visible.
A reliable measurement route starts by expressing each quantity in SI base dimensions and simplifying both sides of the proposed relation independently. Prefixes are converted before substitution, not after it. For a derived uncertainty, move between absolute and percentage forms as the expression requires, keep guard digits through the central calculation, and finish with the value, uncertainty and unit stated at compatible precision.
The decision that organizes this unit
Define the system and choose the route before calculating
Explain why changing millimetres to meters before squaring prevents a six-power prefix error in the cylinder volume.
Convert d and L before evaluating πd²L/4
Mechanism route and repair branches
Relationships to preserve
- Diameter and length: The millimetre prefix on d is squared in V.
- Uncertainty: The diameter contribution appears twice.
- Reported volume: Value and uncertainty need matching precision.
Representations to read
- A graph of volume (mm³) against d (mm).
- A formula card that explains the cylinder relation identifies why diameter contributes two powers to the derived volume.
- A table linking key concept, why it matters, visible method.
Branches to reject
- Squaring 12.40 mm and then labeling the result m³
- Treating diameter as the vertical quantity
- Combining mm³ with m³
| Key concept | Why it matters | Visible method |
|---|---|---|
| Diameter and length | The millimetre prefix on d is squared in V | Convert d and L before evaluating πd²L/4 |
| Uncertainty | The diameter contribution appears twice | Add 2(0.05/12.40) to 0.1/48.0 in percentage form |
| Reported volume | Value and uncertainty need matching precision | State (5.80 ± 0.06) × 10⁻⁶ m³ |
| Base-dimension comparison | It tests homogeneity before arithmetic can hide a bad relation. | Simplify both sides independently, then compare powers. |
| Compatible precision | The uncertainty and measured value describe one result. | Round only after the central value and uncertainty are known. |
How Cambridge International AS & A Level Physics (9702) assesses Physical Quantities and Units
What a complete response must make visible
Match the task to evidence that a reader can audit, then check the most likely reasoning failure before finalizing the response.
| Task | Evidence to show | Hurdle |
|---|---|---|
| Physical Quantities, SI Units, Prefixes, Estimates and Homogeneity of Equations | dimensional homogeneity; percentage uncertainty; coplanar vector | Squaring 12.40 mm and then labeling the result m³ |
| Errors and Uncertainties: Systematic and Random Errors, Precision, Accuracy and Combining Uncertainties | dimensional homogeneity; percentage uncertainty; coplanar vector | Treating diameter as the vertical quantity |
| Scalars and Vectors: Adding, Subtracting and Resolving Coplanar Vectors | dimensional homogeneity; percentage uncertainty; coplanar vector | Combining mm³ with m³ |
Worked example: dimensions, prefixes and uncertainty
Read each question as it appears on the exam paper, choose your answer, then tap it to see the feedback.
Practice 1: Cylinder measurement uncertainty
A digital calliper is used to measure a cylinder.
A cylinder has diameter 12.40 ± 0.05 mm and length 48.0 ± 0.1 mm. Calculate its volume and percentage uncertainty.
[4]Show all necessary working.
A. V = 5.80 × 10⁻⁶ m³ with 0.61% uncertainty.
❌ Not quite 😭 The volume is correct, but the uncertainty includes the diameter only once. Its fractional uncertainty must be counted twice because d is squared.
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B. V = (5.80 ± 0.06) × 10⁻⁶ m³ with 1.01% uncertainty.
✅ Correct! 😊 Correct. Both lengths are converted before substitution, and the two diameter contributions give the stated uncertainty.
C. V = 5.80 m³ with 1.01% uncertainty.
❌ Not quite 😭 The percentage treatment is right, but the millimetre measurements were not converted to meters before evaluating the cubic quantity.
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D. V = (5.80 ± 1.01) × 10⁻⁶ m³.
❌ Not quite 😭 This treats a percentage as an absolute uncertainty. The 1.01% must be applied to the calculated volume before reporting.
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Full explanation
- Step 1Convert first: d = 0.01240 m and L = 0.0480 m.
- Step 2V = πd²L/4 = 5.80 × 10⁻⁶ m³.
- Step 3Percentage uncertainty = 2(0.05/12.40 × 100%) + 0.1/48.0 × 100% = 1.01%.
- Step 4The absolute uncertainty is 0.06 × 10⁻⁶ m³, matched to the value's precision.
Practice 2: Testing dimensional consistency
A proposed relationship gives the distance traveled from rest.
Which expression is dimensionally consistent for distance s when acceleration a acts for time t?
[1]Choose the best answer.
A. s = at
❌ Not quite 😭 Acceleration multiplied by time has dimensions LT⁻¹, which are the dimensions of velocity rather than distance.
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B. s = at²
✅ Correct! 😊 Correct. LT⁻² multiplied by T² reduces to L, so a numerical constant could complete the physical relation.
C. s = a/t
❌ Not quite 😭 Dividing acceleration by time gives LT⁻³, which cannot represent a displacement.
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D. s = a²t
❌ Not quite 😭 This has dimensions L²T⁻³. Squaring acceleration introduces an extra length factor and the wrong time power.
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Full explanation
- Step 1Write the dimensions of acceleration as LT⁻² and of time as T.
- Step 2Test at: LT⁻² × T = LT⁻¹, so it is not a length.
- Step 3Test at²: LT⁻² × T² = L.
- Step 4Therefore at² is the only dimensionally consistent expression listed.
Key terms for Unit 1: Physical Quantities and Units
Models, uses, and boundaries
- Physical Quantities and Units
- The cylinder relation identifies why diameter contributes two powers to the derived volume. Use this relationship when the cylinder relation identifies why diameter contributes two powers to the derived volume..
- Worked example: dimensions, prefixes and uncertainty
- Substitute meters into πd²L/4 before attaching the cubic-meter unit. Use this relationship when substitute meters into πd²L/4 before attaching the cubic-meter unit..
- Physical Quantities and Units: change one condition
- With length fixed, the volume ratio follows the square of the diameter ratio. Use this relationship when with length fixed, the volume ratio follows the square of the diameter ratio..
- Physical Quantities and Units: test proposed results
- A proposed volume must survive the cubic-unit and power-of-ten checks. Use this relationship when a proposed volume must survive the cubic-unit and power-of-ten checks..
Cambridge International AS & A Level Physics (9702) Unit 1 FAQ
How much of Cambridge International AS & A Level Physics (9702) does Unit 1 carry?
Cambridge International does not publish a per-unit weighting for this exam.
What is the first move on a Physical Quantities and Units problem?
Convert d and L before evaluating πd²L/4
Which relationships should I preserve?
Diameter and length: The millimetre prefix on d is squared in V. Uncertainty: The diameter contribution appears twice. Reported volume: Value and uncertainty need matching precision.
Which representations should I practice?
Practice moving among A graph of volume (mm³) against d (mm)., A formula card that explains the cylinder relation identifies why diameter contributes two powers to the derived volume., A table linking key concept, why it matters, visible method..
What error should I check before submitting an answer?
Check for Squaring 12.40 mm and then labeling the result m³; Treating diameter as the vertical quantity; Combining mm³ with m³.
Evidence workshop
Continue from the free model into complete practice
The full unit guide continues with the chapter’s worked examples, figures, scoring tables, and answer checks.
- Worked example: dimensions, prefixes and uncertainty
- Physical Quantities and Units: change one condition
- Physical Quantities and Units: test proposed results
- Check the worked-example evidence for Physical Quantities and Units
Full unit practice. Open the complete guide for the full evidence workshop and synthesis.
Related Cambridge International AS & A Level Physics (9702) unit guides
Cambridge International AS & A Level Physics (9702) Exam Guide & Review
The whole exam and its official unit sequence.02Kinematics and Dynamics
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Cambridge International does not publish a per-unit weighting for this exam.How to study Cambridge International AS & A Level Physics (9702) Unit 1
Start with the organizing decision
Before solving, restate the decision in operational terms: Explain why changing millimetres to meters before squaring prevents a six-power prefix error in the cylinder volume.. Your first written move should be to Convert d and L before evaluating πd²L/4.
Practice the same idea in several representations
Rotate through A graph of volume (mm³) against d (mm)., A formula card that explains the cylinder relation identifies why diameter contributes two powers to the derived volume., A table linking key concept, why it matters, visible method.. Use each representation to practice Physical Quantities, SI Units, Prefixes, Estimates and Homogeneity of Equations, Errors and Uncertainties: Systematic and Random Errors, Precision, Accuracy and Combining Uncertainties, Scalars and Vectors: Adding, Subtracting and Resolving Coplanar Vectors, and explain what stays invariant when the surface form changes.
Turn each error into a repair check
After every attempt, audit the response for Squaring 12.40 mm and then labeling the result m³; Treating diameter as the vertical quantity; Combining mm³ with m³. Then redo only the first step that made the reasoning diverge, keeping units, direction, and model conditions visible.
Confirm current course details in the official Cambridge International syllabus for the 2025-2027 administration.
Where to go next
Return to the Cambridge International AS & A Level Physics (9702) to see every unit and plan your revision.