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-4
(x−3)²−4 has minimum −4.
Engineering admission · Other / specialist pathway · Mathematics
Algebra, trigonometry, coordinate geometry and calculus
Connect algebra, trigonometry, coordinates and calculus in a worked solution.
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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
Keep domain restrictions and select a method from the structure. Factorisation solves some polynomials; differentiation identifies stationary values; integration computes a signed accumulation. A geometry step must use stated coordinates or conditions rather than an unlabelled sketch.
Worked example
For f(x)=x²−4x+1, complete the square: (x−2)²−3. Thus the minimum is −3 at x=2. The derivative 2x−4 gives the same stationary input.
- State the domain and plan.
- Show algebra and geometric meaning.
- Check with a second method when possible.
Your written practice
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2
(8−2)/(4−1)=2.
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1
The identity is 1 for every real angle.
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[x³] from 0 to 2 = 8.
Show antiderivative and both bounds.
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Show model answer and explanation
(x−2)(x−3)=0, so x=2 or 3; both give zero on substitution.
Show both roots and a check.
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Mathematics model test
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- Respect domains.
- Use labelled diagrams where useful.
- Keep symbolic and numerical steps consistent.
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