A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Kinematics Language and Concepts — mark scheme explained
The short answer
Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. In AQA A-Level Mathematics, understanding and using the language of kinematics is crucial for solving problems related to motion.
The question
A car travels from point A to point B, which are 100 meters apart. It then returns to point A. Calculate the total distance travelled and the displacement of the car.
[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 kinematics questions, marks are typically awarded for correct use of formulas, accurate calculations, and clear presentation of answers. Ensure you show all steps in your working and include units where necessary.
What the command words demand
- Calculate
- Perform a mathematical operation to find a specific value.
- Determine
- Find or establish something with certainty, often through calculation or reasoning.
- Explain
- Provide reasons or details for a particular concept or phenomenon.
- Describe
- Give a detailed account of the characteristics or features of something.
- Sketch
- Draw a rough outline or graph to represent a relationship or motion.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes per question to ensure you have enough time to read the problem carefully, select the appropriate formula, perform calculations, and check your work.
- The car travels from point A to point B, a distance of 100 meters.0 marks
- It then returns to point A, another 100 meters.0 marks
- Total distance travelled = 100 meters + 100 meters = 200 meters.2 marks
- Displacement is the change in position from the initial to the final point. Since the car returns to its starting point, displacement = 0 meters.2 marks
Final answer: Distance travelled: 200 meters; Displacement: 0 meters
Work through every step correctly and you earn all 4 marks.
Another worked example
A particle moves along a straight line with an initial velocity of 5 m/s. It accelerates uniformly at 2 m/s 2 for 10 seconds. Calculate the final velocity and the displacement during this time.
- Initial velocity (u) = 5 m/s0 marks
- Acceleration (a) = 2 m/s 20 marks
- Time (t) = 10 s0 marks
- Final velocity (v) can be calculated using the formula: v = u + at1 mark
- v = 5 m/s + (2 m/s 2 × 10 s) = 5 m/s + 20 m/s = 25 m/s2 marks
- Displacement (s) can be calculated using the formula: s = ut + 1 ⁄ 2 at 21 mark
- s = (5 m/s × 10 s) + 1 ⁄ 2 (2 m/s 2 × 10 2 )1 mark
- s = 50 m + 100 m = 150 m1 mark
Final answer: Final velocity: 25 m/s; Displacement: 150 meters
Work through every step correctly and you earn all 6 marks.
Common mistakes
Confusing displacement with distance travelled.
Why it happens: Displacement is a vector quantity that considers direction, while distance travelled is a scalar quantity that does not. Students often mix these up when solving problems.
Fix: Always consider the direction of motion when calculating displacement and use the total path length for distance travelled.
Using speed instead of velocity in vector calculations.
Why it happens: Speed is a scalar quantity, while velocity is a vector quantity. Using speed in place of velocity can lead to incorrect results in problems involving direction.
Fix: Ensure you use the appropriate formula and consider the direction when dealing with velocity.
Forgetting to include units in answers.
Why it happens: Units are essential for clarity and correctness. Omitting them can lead to marks being deducted.
Fix: Always include the appropriate units (e.g., meters, seconds) in your final answers.
Incorrectly interpreting graphs.
Why it happens: Students often misinterpret the slope and area under kinematic graphs. For example, they might confuse the slope of a position-time graph with acceleration instead of velocity.
Fix: Practice identifying what different parts of the graph represent (slope for velocity, area for displacement).
Using incorrect formulas for kinematic equations.
Why it happens: There are several kinematic equations, and using the wrong one can lead to incorrect results. Students might mix up the equations for velocity, displacement, and acceleration.
Fix: Memorize the key kinematic equations and practice applying them in different scenarios.
Neglecting negative signs in vector quantities.
Why it happens: Negative signs indicate direction, which is crucial for vector quantities like displacement and velocity. Ignoring them can lead to incorrect answers.
Fix: Always pay attention to the sign of vector quantities and include them in your calculations.
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 |
|---|---|---|
| Distance And Displacement | Calculate total distance travelled and overall displacement for a return journey. | 4 |
| Kinematics Calculation | Use the SUVAT equations to find final velocity and displacement under uniform acceleration. | 6 |
| Vertical Projectile Motion | Use kinematics equations to find maximum height and time for an upwardly thrown ball. | 5 |
| Uniform Acceleration Kinematics | Use SUVAT equations to find a car's acceleration and distance travelled from given motion values. | 4 |
| Total across these question types | 19 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.