Quadratic Equations

Summary and Exam Tips for Quadratic Equations

Quadratic Equations is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. In this section, students will learn to solve quadratic equations using various methods such as factorisation, completing the square, and the quadratic formula. Quadratic equations typically have two solutions, which may be distinct or equal.

To solve quadratic equations by factorisation, rearrange the equation to equal zero, factorise, and set each factor to zero to find the solutions. For example, solving $x^2 - x - 6 = 0$ involves factorising to $(x-3)(x+2) = 0$, yielding solutions $x = 3$ or $x = -2$. When factorisation is not possible, the quadratic formula $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ is used, as demonstrated in solving $24x^2 - 22x - 35 = 0$.

Understanding these methods is crucial for solving quadratic inequalities and applying these concepts in various mathematical problems. Practice questions and past paper questions are essential for mastering these techniques.

Exam Tips

• Understand the Basics: Ensure you are comfortable with rearranging equations and basic algebraic manipulations, as these are foundational skills for solving quadratic equations.
• Factorisation First: Always check if the quadratic can be factorised easily before moving on to more complex methods like the quadratic formula.
• Quadratic Formula: Memorise the quadratic formula and practice using it, especially for equations that do not factorise neatly.
• Check Your Solutions: Always substitute your solutions back into the original equation to verify their correctness.
• Practice Regularly: Work through past paper questions and practice problems to build confidence and improve your problem-solving speed.