Free worksheet and solutions · AQA A Level · 7408
Simultaneous Equations Quadratics and Physical Roots Worksheet
A-level physics simultaneous and quadratic equations worksheet with worked answers. Model trolley motion, handle delayed starts and select physically valid roots.
What is covered
Questions and skills covered
The worksheet contains 6 pages of printable questions. A separate 6-page solutions PDF makes it easy to mark, review or share answers after the activity.
- Common position origins and clock times
- Alignment condition versus equal velocities or equal travel distances
- Simultaneous linear position models and elimination
- Constructing a quadratic from constant-acceleration motion
- Signed numerical quadratic coefficients and both formula branches
- Substitution into both original models
- Negative roots before the trial
- Delayed launch and elapsed time t minus launch time
- Positive roots outside a piecewise model domain
- Two positive encounters and relative velocity
- Limits after a controller changes motion
- Negative discriminant and no intersection
- Adjusting a starting position to achieve alignment
- Repeated root, equal velocities and tangency without overtaking
About this activity
An automated inspection rig uses an autonomous trolley and loading carriage on separate parallel lanes. Independent trials test when their longitudinal registration points align; they can pass without collision.
Before you start
Equation rearrangement and expansion; Constant-velocity and constant-acceleration motion; Substitution and the quadratic formula
Specification fit
This shared PDF includes the applicable boards’ references and a board-neutral footer. Choose an eligible course below and check the scope before assigning it.
- AQA A Level 7408 · Mathematical skills · 3.4.1.3
- OCR A A Level H556 · Mathematical skills · 3.1.1(a), 3.1.1(b), 3.1.1(c), 3.1.2(a)(i)
AQA A Level Physics Worksheets
7408 · 3.4.1.3
Choose the correct pathway: A guided mathematical-skills worksheet using separate alignment trials on two parallel inspection-rig lanes. Construct simultaneous position equations, eliminate an unknown, form quadratics and interpret one, two or no real encounters. Delayed clocks and finite operating intervals determine which roots describe events. A final changed starting gap produces tangency without overtaking. Selected straight-line motion applications, not complete linear-motion topic coverage. Shared A-level pair only: no automatic AS/GCSE route or required-practical tag.
Classroom use
Use the worksheet for class practice, homework, intervention, cover work or revision. Keep the PhysicsUK attribution intact when sharing copies with pupils.
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