A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Quantities and Units in Mechanics — mark scheme explained
The short answer
In mechanics, understanding the fundamental quantities and units is crucial for solving problems accurately. The International System of Units (SI) provides a standardized framework for these measurements. This section covers both fundamental and derived quantities and their respective units. Fundamental Quantities and Units Length: Measured in meters (m).
The question
A car travels a distance of 150 meters in 10 seconds. Calculate its velocity.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculation questions, marks are typically awarded for correct substitution of values into the formula, showing intermediate steps, and providing the final answer with the correct unit. For conceptual questions, marks are often given for clear and concise explanations that demonstrate understanding.
What the command words demand
- Calculate
- Perform a numerical calculation using given data and appropriate formulas.
- Determine
- Find or establish by calculation, measurement, or research.
- Explain
- Provide reasons for something, often including the underlying principles or concepts.
- Identify
- Recognize and name specific quantities, units, or relationships.
- Show that
- Prove a given statement using logical steps and appropriate formulas.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 1-2 minutes per mark. For a 3-mark question, spend about 3-6 minutes.
- Identify the given values: Distance (d) = 150 m, Time (t) = 10 s0 marks
- Use the formula for velocity: v = d / t1 mark
- Substitute the values: v = 150 m / 10 s1 mark
- Calculate the result: v = 15 m/s1 mark
Final answer: 15 m/s
Work through every step correctly and you earn all 3 marks.
Another worked example
A ball is thrown vertically upwards with an initial velocity of 19.62 m/s. Using g = 9.81 m/s² (acting downwards), find its velocity after 2 seconds.
- Identify the given values: Initial velocity (u) = 19.62 m/s (upwards), Time (t) = 2 s0 marks
- Use the formula for final velocity under constant acceleration: v = u + at, taking g = 9.81 m/s² downwards so a = -9.81 m/s²1 mark
- Substitute the values: v = 19.62 m/s + (-9.81 m/s²) × 2 s2 marks
- Calculate the result: v = 19.62 - 19.62 = 0 m/s1 mark
Final answer: 0 m/s
Work through every step correctly and you earn all 4 marks.
Common mistakes
Confusing velocity with speed.
Why it happens: Velocity is a vector quantity, meaning it has both magnitude and direction, while speed is a scalar quantity (only magnitude).
Fix: Always specify the direction when dealing with velocity.
Using incorrect units for acceleration.
Why it happens: Acceleration is measured in meters per second squared (m/s 2 ), not just meters per second (m/s).
Fix: Ensure you use the correct unit for acceleration: m/s 2 .
Forgetting to convert units before calculations.
Why it happens: Inconsistent units can lead to incorrect results. For example, mixing meters and centimeters in the same calculation.
Fix: Always check and convert all measurements to consistent units before performing calculations.
Using mass instead of weight in force calculations.
Why it happens: Mass is a measure of the amount of matter, while weight is the gravitational force acting on that mass. They are not interchangeable.
Fix: Use the formula W = m × g to convert mass to weight when necessary.
Incorrectly calculating moment by using the wrong distance.
Why it happens: The distance used in the moment calculation must be the perpendicular distance from the point of rotation to the line of action of the force.
Fix: Ensure you use the correct perpendicular distance when calculating moment.
Forgetting that acceleration due to gravity is negative for downward motion.
Why it happens: In many problems, especially those involving vertical motion, the direction of acceleration due to gravity is downwards, which is typically represented as a negative value.
Fix: Always consider the direction of acceleration when solving problems involving gravity.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Velocity | Use the velocity formula to find speed from a distance and time. | 3 |
| Calculate Final Velocity | Use v = u + at to find the ball's velocity after a given time under gravity. | 4 |
| Calculate Acceleration | Rearrange Newton's second law to find acceleration from a given force and mass. | 3 |
| Calculate Moment | Calculate the moment of a force using its magnitude and perpendicular distance from the pivot. | 3 |
| Calculate Weight | Use the equation W = mg to find the weight of a known mass. | 3 |
| Total across these question types | 16 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.