Show model answer and explanation
9
Half-perimeter is 14; 14−5=9.
Engineering admission · Other / specialist pathway · Mathematics
Multi-step numerical reasoning and checking solutions
Solve a multi-step numerical problem and test whether the result is feasible.
About this lesson and its coverage
Original Model Test for Exam unit. These questions and suggested practice times are independent Kidemy material, not an official or past paper. Choose modules for the target programme; all listed subjects are not required for every applicant.
Learn the idea
Translate a constraint into equations before calculating. A numerical solution may be algebraically valid but physically impossible. Check units, signs, domains and bounds. When an optimisation gives several candidates, compare feasible stationary points and boundaries.
Worked example
A rectangle with perimeter 20 has sides x and 10−x. Its area A=x(10−x)=25−(x−5)², with 0<x<10. Maximum area is 25 at a square 5 by 5.
- Write constraints and domain.
- Solve and compare candidates.
- Substitute back and interpret feasibility.
Your written practice
Show your working on paper. Check your answer, then choose Next.
Show model answer and explanation
49
The 7×7 square gives 49.
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5
18/3.6=5.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
A=10x−x²=25−(x−5)²≤25, with equality at x=5.
Use the domain and equality condition.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
It violates the original physical domain.
Check original constraints rather than the transformed equation alone.
Progress and browser storage
Notebook challenge, sources and further study
Reasoning model test
Create a constrained geometry problem and compare two solution methods.
Review with a guardian or teacher
- State feasibility limits.
- Check boundary behaviour.
- Explain the final quantity with units.
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