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4
36−32.
O Level · English Medium · Cambridge · Mathematics
Equations, patterns and functions
Use quadratics and functions in graphical and algebraic forms.
About this lesson and its coverage
Original Kidemy O Level progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
Roots, intercepts and turning points answer different questions. A discriminant b²−4ac describes the count of real roots for a real quadratic with a≠0. Inverses need a one-to-one domain.
Worked example
For x²−4x+4=0, the discriminant is 0 and the repeated root is 2. For f(x)=5x−3, f⁻¹(x)=(x+3)/5.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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5
(x−5)²=0.
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17
20−3.
Write in your own words. A guardian or teacher should review this response.
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(2x−1)(x−3)=0, so x=1/2 or 3.
Give both roots.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
The quadratic has no real root because the quadratic formula requires a square root of a negative value.
State the domain.
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Notebook challenge, sources and further study
Apply the idea
Sketch a quadratic and verify roots and turning point algebraically.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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