A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Weight and Motion in a Straight Line Under Gravity — mark scheme explained
The short answer
In AQA A-Level Mathematics, understanding weight and motion in a straight line under gravity is crucial. This involves the concepts of gravitational acceleration ( g ) and its value in SI units to varying degrees of accuracy.
The question
A ball is dropped from a height of 45 meters. Calculate the time it takes to reach the ground.
[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 use of formulas, substitution of values, and final answers. For explanation questions, marks are given for clarity and completeness of reasoning.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Determine
- Find or establish something with certainty using given data.
- Explain
- Provide a clear and detailed account of how or why something happens.
- Show that
- Prove a statement or result by working through the steps.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 2-3 minutes per mark to ensure you have enough time to carefully read the question, perform calculations, and check your work.
- Use the equation s = ½gt 2 where s = 45 m and g = 9.81 m/s 2 .1 mark
- Rearrange to solve for time: t = √(2s/g) .1 mark
- Substitute the values: t = √(2 × 45 / 9.81) ≈ 3.03 s .1 mark
Final answer: 3.03 seconds
Work through every step correctly and you earn all 3 marks.
Another worked example
A stone is thrown vertically upwards with an initial velocity of 20 m/s. Calculate the maximum height it reaches.
- Use the equation v 2 = u 2 - 2gs where v = 0 m/s , u = 20 m/s , and g = 9.81 m/s 2 .1 mark
- Rearrange to solve for height: H = u 2 /2g .1 mark
- Substitute the values: H = (20) 2 / (2 × 9.81) ≈ 20.4 m .1 mark
Final answer: 20.4 meters
Work through every step correctly and you earn all 3 marks.
Common mistakes
Using the wrong value for gravitational acceleration g .
Why it happens: Students often memorize a specific value for g and use it in all problems without considering that it can vary depending on location.
Fix: Always check the problem statement to see if a specific value of g is given. If not, use 9.81 m/s 2 as a standard value.
Forgetting to consider the direction of motion when using kinematic equations.
Why it happens: Students may not account for the sign of velocity and displacement, leading to incorrect results in problems involving upward or downward motion.
Fix: Always define a positive direction (e.g., upwards) and use consistent signs for all variables. For example, if an object is thrown upwards, the initial velocity u is positive, and the acceleration due to gravity g is negative.
Confusing weight with mass.
Why it happens: Students sometimes use mass in place of weight or vice versa, leading to incorrect calculations.
Fix: Remember that weight W is the force due to gravity and is calculated as W = mg . Mass m is a scalar quantity measured in kilograms (kg).
Using incorrect units for weight, mass, or gravitational acceleration.
Why it happens: Students may mix up the units, leading to dimensional inconsistencies in their calculations.
Fix: Always use consistent units. Weight is measured in newtons (N), mass in kilograms (kg), and gravitational acceleration in meters per second squared (m/s 2 ).
Failing to consider the initial conditions when solving kinematic problems.
Why it happens: Students may overlook the importance of initial velocity and displacement, leading to incorrect solutions.
Fix: Always identify and use the given initial conditions (e.g., initial velocity u , initial displacement s 0 ) in your calculations. For example, if an object is dropped from rest, the initial velocity u is zero.
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 Time Of Fall | Use a kinematic equation to find the time for a dropped ball to hit the ground. | 3 |
| Calculate Maximum Height | Use kinematics equations to find the maximum height reached by a projectile. | 3 |
| Calculate Time Of Flight | Use kinematics equations to find the time for a projectile to reach maximum height. | 2 |
| Kinematics Meeting Point | Find when two stones with different initial motions meet using equations of uniformly accelerated motion. | 4 |
| Total across these question types | 12 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.