Challenge: full quadratic factorisation set

2026-12-21Exam & Challenge Mr Yip

Factorise several quadratics including a≠1 and perfect squares.

Key formulas

\text{ac method} / \text{cross method}

What this lesson covers

This lesson builds Secondary 2–3 skill in challenge quadratic. Read the key formulas, study the worked example, then attempt the written practice and the four-question MCQ review.

Method

Write every step. Name the rule you use (challenge quadratic) before substituting numbers. Keep units and signs visible until the final sentence.

Common mistakes

Students often rush the sign, use the wrong percentage base, or cancel terms instead of factors. Pause after each line and ask whether the step is reversible.

Exam habit

Underline the question verb (simplify, solve, factorise, find). Box the final answer and, where sensible, substitute back for a quick check.

Worked example

Worked example — challenge quadratic

Problem. Apply the method for challenge quadratic with the numbers 5 and 4.

Solution. Identify the rule for challenge quadratic. Substitute 5 and 4 carefully with signs in brackets if needed. Complete each operation on a new line. State the final answer clearly and check by reversing one step.

Review quiz

1 / 4

Warm-up on challenge quadratic: what is 3+6?

Practice questions

Practice 1 on challenge quadratic: compute with the value 19.
Practice 2 on challenge quadratic: change the numbers and repeat the same method.
Practice 3 on challenge quadratic: write one sentence explaining the key rule.
Practice 4 on challenge quadratic: invent a similar exam-style question and solve it.

Study notes

What is the main idea of challenge quadratic?

Apply the stated formula or rule with clear steps, then check by reversing or substituting.

How should I revise this topic?

Cover the worked example, redo the practice without notes, then complete the MCQ set and log any wrong options.