Quadratics

Summary and Exam Tips for Quadratics

Quadratics is a subtopic of Pure Mathematics 1, which falls under the subject Mathematics in the Cambridge International A Levels curriculum. Quadratic equations are expressed in the form $ax^2 + bx + c = 0$. Key methods for solving these equations include factorisation, completing the square, and using the quadratic formula. Factorisation involves expressing the quadratic as a product of two binomials. Completing the square rewrites the equation in the form $p(x+q)^2 + r = 0$, which helps in identifying the vertex of the parabola. The quadratic formula, derived from completing the square, provides a direct method to find the roots by substituting values of $a$, $b$, and $c$.

Quadratics also involve solving simultaneous equations where one is linear and the other quadratic, determining the maximum and minimum values of quadratic functions, and solving quadratic inequalities. The discriminant ($b^2 - 4ac$) is crucial in determining the nature and number of roots. Additionally, understanding the intersection of a line and a quadratic curve is essential, as it can result in two, one, or no intersection points.

Exam Tips

• Master the Basics: Ensure you are comfortable with the quadratic formula, factorisation, and completing the square. These are foundational skills for solving quadratic equations.

• Understand the Discriminant: The discriminant ($b^2 - 4ac$) is key to understanding the nature of roots. Remember, if it's positive, there are two distinct real roots; if zero, one real root; and if negative, no real roots.

• Graphical Interpretation: Practice sketching graphs of quadratic functions to visualize solutions, especially when dealing with inequalities and intersections with lines.

• Simultaneous Equations: When solving simultaneous equations involving a quadratic and a linear equation, substitution is often the most efficient method. Ensure you can rearrange and substitute effectively.

• Practice Problem-Solving: Work through past paper questions to familiarize yourself with different types of quadratic problems and their solutions. This will boost your confidence and problem-solving speed during exams.