Challenge: multi-step percentage reasoning

2026-12-20Exam & Challenge Ms Chu

Reverse percentages chained with successive changes.

Key formulas

\text{Divide by overall multiplier}

What this lesson covers

This lesson builds Secondary 2–3 skill in challenge percentage. 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 percentage) 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 percentage

Problem. Apply the method for challenge percentage with the numbers 4 and 3.

Solution. Identify the rule for challenge percentage. Substitute 4 and 3 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 percentage: what is 9+5?

Practice questions

Practice 1 on challenge percentage: compute with the value 18.
Practice 2 on challenge percentage: change the numbers and repeat the same method.
Practice 3 on challenge percentage: write one sentence explaining the key rule.
Practice 4 on challenge percentage: invent a similar exam-style question and solve it.

Study notes

What is the main idea of challenge percentage?

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.