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PURE 1. QUADRATICS

A Level Mathematics 9709 Examinations 2023 – 2025 Pure 1

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WHY DO WE STUDY QUADRATICS?

  • At IGCSE: linear or straight-line graphs.�They arise in the world around you. E.g.: a cell phone contract:
    • y = the monthly cost
    • c = fixed monthly charge
    • m = cost per minute
    • x = number of minutes used.
  • Quadratic functions have interesting properties
    • a maximum or a minimum value
    • graph has interesting symmetry
    • 🡪 can think about more complicated functions
    • Shape: the path of a ball as it travels through the air (called its trajectory). Discovering that the trajectory is a quadratic was one of Galileo’s major successes in the early 17th century.

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1. Factorising quadratics

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2. Completing the Square

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algebraic method for completing the square

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3. Quadratic Formula

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4. Solving simultaneous equations (one linear and one quadratic)

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Practice questions

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Solving more complex quadratic equations

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5. Maximum and minimum values

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6. Solving quadratic inequalities

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7. Number of roots of a quadratic equation

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7. Number of roots of a quadratic equation

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8. Intersection of a line and a quadratic curve

How do you think this relates to the discriminant?

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